My Goal in Blogging

I started this blog in May of 2008, shortly after my election to the School Committee, because I believed it was very important to both provide the community with an opportunity to share their thoughts with me about our schools and to provide me with an opportunity for me to ask questions and share my thoughts and reasoning. I have found the conversation generated on my blog to be extremely helpful to me in learning community views on many issues. I appreciate the many people who have taken the time to share their views. I believe it is critical to the quality of our public schools to have a public discussion of our community priorities, concerns and aspirations.

Wednesday, December 2, 2009

The Root of Many Problems: Elementary School Math

There has been considerable interest on my blog on issues of math/science education in the Amherst schools, and thus I am doing yet another post on this topic. And I'm going to start by saying that I believe a problem in our district for years has been the elementary school math curriculum we used, which is called Investigations. This post will describe why I think this curricula is a problem, and how I believe it has led to other problems, and what I think we should do.

The Problem With Investigations


The Investigations curriculum is on the very far end of the "reform math" end of the spectrum (read more about this controversy at: http://en.wikipedia.org/wiki/Math_wars). You can also google "investigations math" and read what others have said about this curriculum (including petitions in other districts to have it removed). Here is what else I think is relevant for parents/teachers/community members to know:

1. Investigations (first version) was chosen some time ago by teachers/
administrators in Amherst (about 20 years ago), and at that time, we knew less about different approaches to teaching math and there were few options.

2. The second version of Investigations was purchased in the summer of 2007 because there was extra money left over in the budget. At the time of this purchase, I was on a math curricula review committee (consisting of teachers, administrators, parents) in our district (appointed by Jere Hochman), and this committee wasn't consulted about this purchase, nor, to the best of my knowledge, were any elementary school math teachers. No other curricula were considered for adoption at that time, nor was the effectiveness of this curriculum in our district, or in any district, examined.

3. The first version of Investigations has been shown to have serious problems in terms of actually teaching math. A recent independent randomized study of 4 different curricula published by the Institute for Education Sciences (http://ies.ed.gov/ncee/pubs/20094052/pdf/20094052.pdf) revealed quite clearly that Investigations is an ineffective curriculum. In fact, using a superior curricula compared to Investigations was a better predictor of math achievement than was the effect of having bigger classes (22-25 kids) rather than smaller classes (13-17). In other words, it would be better for kids to have bigger classes with a GOOD curricula than a smaller class with the Investigations curricula. Importantly, the disadvantage created by Investigations wasn't influenced by student characteristics (such as family income or race), district characteristics, or by most teacher characteristics (such as education level or math competence). Now, this study used the Investigations - first version curricula, but there isn't any evidence suggesting that the new version is in fact better!

4. I have heard from elementary school teachers in our district that Investigations is a very difficult curricula for many children to master -- it is very wordy (with less focus on strictly numbers and calculations than more traditional curricula), and thus is particularly hard for ELL students and special ed students. The Amherst district requires a lot of supplementation of Investigations with material from other curricula to help children master math, and therefore each teacher independently is often required to develop such materials (thereby decreasing both horizontal and vertical alignment in our schools). We ask elementary school teachers to teach all subjects -- reading, writing, math, science, social studies -- and asking them to also develop/find math curricula to supplement an incomplete curricula that many students struggle with just isn't a good (or fair) use of their time. In fact, a 2007 survey of all teachers in the district regarding their experience with math revealed the following: "Several teachers express dissatisfaction with the Investigations curriculum, particularly for teaching ESL students, and a desire for clearer curriculum guidelines." Note: I was on this math review council prior to my election to the School Committee in 2008, and as part of my work on this council, I compiled these survey findings (you can read these results yourself, and Jere Hochman's conclusion at: http://www.arps.org/node/214).


Problems Caused By Having a Poor Elementary Math Curricula

1. Poor math MCAS scores. The most obvious problem with having a poor elementary school math curricula is that kids don't learn a lot of math! In turn, three of our four elementary schools (all except Marks Meadow) failed to make adequate yearly progress (AYP) on the math MCAS in 2009 in the aggregate (meaning for all students considered as a whole). In addition, in every single subgroup (meaning group of kids that is large enough to be considered as a subset at a given school), with the exception of white kids, at every schools failed to make AYP on the 2009 math MCAS -- low income kids, special ed kids, and Hispanic kids. In contrast, only Marks Meadow and Crocker Farm failed to make AYP in the aggregate in English Language Arts, and these schools both teach a high number of ELL students who are likely to struggle some with reading in English. So, to me these low MCAS math scores point to a failure of our curricula, and thus in some respects to a failure of district leadership, NOT a failure of our elementary school teachers.

2. The creation of "extensions" in 7th grade: Because we have a weak math curricula in elementary school, teachers are forced to supplement in various ways (probably easier for more experienced teachers to do than newer ones), and thus kids arrive at the middle school from 7 different elementary schools and having had probably 20ish different 6th grade teachers (and of course 20ish K to 5 grade teachers before that). In other words, children's math knowledge when they arrive at the middle school simply must vary tremendously, as each teacher has supplemented (or not) a math curricula that has been demonstrated in empirical research to be relatively ineffective. The 7th grade teachers are therefore stuck trying to teach children who have massive gaps in their preparation (not in their math ability or potential), and thus needed to work out some solution that felt fair to students (and didn't penalize students for their poor preparation). This led to the development of the "extensions" model in which all kids were kept together in one class throughout 7th grade (instead of grouping kids by math ability/preparation into different tracks), and kids who wanted to have the option of taking 8th grade honors algebra have to do extra homework assignments (called "extensions").

I believe the development of this model was created with the best of intentions ... to give all kids a chance at doing 8th grade algebra, and I believe this is a noble and laudable goal (and I commend the MS teachers/administration for attempting to solve the very difficult problem caused by uneven math preparation in our elementary schools in such a creative way). However, I think this extensions approach (again, it is a uniquely Amherst idea, not used in any other districts) has three fundamental problems.

First, it is very, very hard for teachers (particularly in increasingly larger classes due to budget cuts) to simultaneously teach kids at such different levels of math preparation -- we are setting out to make teachers' jobs harder, and that strikes me as unfair and unrealistic (maybe this type of differentiation is possible with class sizes of 15 -- but not with nearly twice that).

Second, parents who are informed about the benefits of algebra in 8th grade (and its importance for getting to calculus in 12th grade) are requiring their kids to do extensions (and, in some cases, are working with their kids themselves to teach this material and/or paying for tutors to help their kids master material that isn't fully taught in class); other parents don't know and thus aren't requiring it. Thus, this model simply leads to tracking by parent choice/education/ knowledge, which is in some ways even worse than the old system (in which math ability/preparation had at least some influence on the recommended track).

Third, this model can lead to kids being peer-pressured to NOT do the extra homework -- I've had parents of color tell me their kids are told by peers that doing this extra work is "acting white." I can certainly imagine that stereotypes about girls being bad at math lead some 7th grade girls to opt out of extra math homework. In turn, kids who are in friendship groups with high achieving peers may do the extensions, but those who are in friendship groups with lower achieving students may choose not to do them (even if a particular child is actually quite able/ready to do such extra work). Again, letting 12-year-olds choose whether to do extra homework as a way of determining who is able to have access to 8th grade algebra seems like a very problematic approach ... at least based on my 11 1/2 year-old son, many kids in this age group don't tend to make great decisions that focus on the long-term consequences of their choices.

I believe the problems with the extension model have led both students and parents to feel more negatively about middle school math than about math either in elementary or high school (and may have contributed to greater dissatisfaction with the middle school - and potentially led more families to opt for charter/private school in 7th grade, which of course costs the district in multiple ways). The survey conducted in 2007 that I described previously also asked students and parents to assess the math curriculum. Here is what they said:

  • Students in elementary and high school find math classes more challenging than those in middle school. Similarly, while students at all three types of schools are most likely to describe their math program as “good,” more students in elementary school and high school rate the math program as “excellent” than as “adequate”, whereas more students in middle school rate the math program as “adequate” than as “excellent.” Student comments, while relatively rare, focus most consistently on a perceived lack of challenge for high achieving students (for elementary and middle students), and on the extreme differences in terms of challenge of the college-prep and honors math tracks (for high school students).

  • Of the parents who chose to complete the survey, most (from all three types of schools) describe their child as often or always challenged in math class. While parents at all three types of schools are most likely to describe their math program as “good,” there are also differences in responses by type of school: more than twice as many parents of elementary school children rate the math program as “adequate” than as “excellent”, more parents of middle school children rate the math program as “adequate” or “poor” than as “excellent,” and more parents of high school students rate the math program as “excellent” than as “adequate.” In addition, many of the parents who choose to provide comments on the elementary and middle school surveys note a lack of challenge in the curriculum for their child, and virtually all negative comments from parents of high school students comment on poor math instruction in the middle school.

3. The need to eliminate the option to take 9th grade biology. As it seems like everyone in Amherst knows by now, I am opposed to requiring our 9th graders to take a science course that delays the initiation of core sciences until 10th grade when this approach isn't being used in any other districts (and thus it simply isn't clear whether this is a good approach to starting high school science). Although my concerns about this requirement have been described as "teacher bashing", my understanding (from talking to many people in the district) is that these teachers were reacting in the only way they felt they could to a very real problem -- that kids came into high school with very different levels of math preparation (some had had honors algebra and were ready for geometry, and some were just starting algebra), and these kids were tracked into different science classes (honors biology for the kids who were finished with algebra, earth science for the kids who were taking algebra). The teachers felt, and I agree with them on this, that having a cohesive science curriculum for ALL 9th graders was a good idea -- and I commend the high school teachers (who I understand are superb teachers) -- for having the desire to make sure that all kids had a rich and engaging (and consistent) 9th grade science class (instead of having some kids tracked one way and some kids tracked another way).

So, the high school science teachers had what I believe was/is an admirable goal, but they were stuck -- because the biology class (which I understand was excellent in 9th grade) required kids to have had algebra FIRST, yet only 1/3 of kids coming from the middle school had had algebra (and the earth science, which was generally less successful, was taken by those kids who had NOT had algebra in middle school -- and lets remember that this class was taught for a long time by a teacher who was later fired for having child porn in his possession, which probably didn't enhance the reputation of this class). They therefore created a new course that took a portion of biology (ecology), and another new course that was interdisciplinary to expose kids to how different science fields intersected (environmental science). But the need to create these two new courses (again, not seen as required or even offered courses at any other high school) was driven in part by the very different preparation kids had in terms of math coming to the high school from the middle school (and of course the very different preparation kids had in terms of math coming to the middle school from the elementary schools). So, in a very real sense, the core of the problems I see in terms of math/science in our district are rooted in our use (for many years now) of a relatively ineffective elementary school math curriculum.


My Suggestions for Improving Math/Science in the Amherst Public Schools

1. My first suggestion is really obvious -- let's review various elementary math curricula and choose a better one!

I don't know anything about math curricula for elementary school (or any age, for that matter), but I know a lot about research and comparisons. So, I started with gathering data on what other districts use (again, using the 11 comparison schools selected by the "how are we doing" subcommittee). This research revealed the following:

  • The most frequently used by these districts was Everyday Math (Evanston, Montclair, Newton, Oak Park, Princeton, Shaker Heights).

  • Investigations is used by three of the schools (Chapel Hill, Northampton, White Plains).

  • Think Math! (a relatively new math curriculum) is used in two of the comparison schools (Brookline and Framingham).

Then, I gathered data on whether there was objective evidence on the effectiveness of any of these curricula. I found two pieces of information:

  • The "What Works Clearinghouse" reports four studies showing Everyday Math is an effective curricula (http://ies.ed.gov/ncee/wwc/reports/elementary_math/eday_math/).

  • Framingham, MA, conducted a pilot test in 2008-2009 of Investigations (which they had been using) and ThinkMath!. They used each curriculum in four of their elementary schools, and had teachers rate the ease of use and quality of instruction and achievement of these curricula. According to their superintendent for curriculum and instruction, the teachers vastly preferred ThinkMath! which is now being used in all of their schools.

So, my suggestion is that the Amherst schools give considerable thought to adopting either Everyday Math or Think Math! starting in 2010. I am very glad that Dr. Rodriguez will be working, as one of his goals, on accomplishing a review of the elementary math curriculum this year, and I look forward (as a member of the School Committee and the mother of a five-year-old!) to hearing the results of that review later this year. I would be very interested in hearing from elementary school teachers who are familiar with either of these curriculum to learn their thoughts.

2. My second suggestion is to eliminate the extensions model and return to grouping students by ability/preparation in 7th grade (which virtually all other districts do), but to allow for flexible grouping (not fixed or tracked).

I believe we should offer two tracks of math (a higher track and a lower track) starting in 7th grade, and that decisions about placement should be based on a combination of recommendations from 6th grade teachers, a standardized placement test at the end of 6th grade, and MCAS scores (like virtually all other districts). Teachers could then be asked to make a particular effort to identify students of color and low income students who have the potential to succeed in a higher level math classes as a way to increase representation of students who are traditionally-underrepresented in such classes in high school. There could also be some flexibility in the groupings -- students who are showing high levels of mastery in the lower track could be recommended by their teacher to move into the higher track at some point during the 7th grade year, or could move to the higher track for the start of 8th grade.

3. My third suggestion is to offer two levels of algebra in 8th grade: regular algebra and honors algebra.

Right now, we have three levels of math in 8th grade: a VERY small number of kids take geometry (those who placed into honors algebra in 7th grade - about 10 to 15 kids each year), about 1/3 take honors algebra, and then about 2/3rd take "regular math." We do NOT offer "regular algebra." I see two problems with this approach. First, I don't see how we offer honors algebra and "regular math" but not regular (non-honors) algebra -- there are probably kids in the lower math group that could succeed quite well at algebra, but aren't ready for honors algebra. Thus, moving the "regular math" class to an algebra class seems like the right way to go (again, this hasn't been possible because of the weak math preparation students arrive having -- but with a new math curricula K to 5, this should be much more feasible). Second, this model is like a pyramid, with few kids on top, more kids in the middle, and most kids at the very bottom. That isn't have math ability/preparation is typically distributed in any district/group I've heard of -- ability/preparation typically is distributed like a bell curve -- there are few kids at the top and few kids at the bottom, and most kids in the middle (the middle, in this case, would be regular algebra). So, my suggestion is to have all kids complete algebra by the end of 8th grade (a goal that many districts across the country are taking on), which would involve making sure all kids were ready at the end of 7th grade to take a real algebra course (not just pre-algebra) -- which I believe would be possible through the combination of a more rigorous (and consistent) elementary school math curriculum and a 7th grade math class in which kids were grouped by ability/preparation so that teachers could focus on teaching what kids really needed to master in a particular class.

4. My final suggestion is to require either biology or physics of all kids in 9th grade.

So, let's say we had all kids finish algebra in 8th grade ... then we should be able to require all 9th grade kids to take one of the core sciences that relies on a strong algebra basis (which should be in line with the high school teachers' goal of having a consistent 9th grade science experience). Based on my review of other districts (see an earlier blog post -- November), virtually all districts that require a particular course in 9th grade (as opposed to giving some options for 9th grade courses) require either biology (Evanston, IL; Farmingham, MI; Madison, WI; South Orange, NJ; Northampton, MA; East Longmeadow, MA; Longmeadow, MA) or physics (Brookline, MA; Cambridge, MA; Columbia, MO; Newton, MA). Those both seem like good options to me -- they teach a core science right in 9th grade, which allows kids to take three years of core science (biology, chemistry, physics -- in some order) AND allow kids to take an AP science class in any discipline they want (biology, chemistry, physics, environmental studies) without making kids double-up on science in a subsequent year (and thus sacrifice something else to do so). I would be very interested in hearing from high school science teachers at ARHS whether they think one of these courses (biology or physics) would be a better fit for the interests of our students - as well as the resources (e.g., textbooks? lab space? training to teach physics first?) needed to enact such a change.

66 comments:

Anonymous said...

I'm overwhelmed at the amount of research you are doing. NO ONE has done this much work trying to improve the schools here. And it's so nice to have someone validate what a lot of us felt about the math curriculum here. Thank you so much. Ali

jennifer said...

Hi, Catherine,

I ran across your blog while google-searching on math/chemistry education issues. Fascinating and a bit appalling.
The elementary and MS math issues you are addressing are universal. The push for 8th grade algebra (see the Algebra Project, or the new requirements in Minn., for instance)is always met with the criticism that the kids aren't ready for algebra - as if this is a problem with algebra or kids instead of the K-7 curriculum.
The problem isn't the kids (even allowing for variable developmental rates). There's no real reason schools can't manage to teach the necessary math functions, symbols and fractions in K - 7 for developmentally typical students. Grade school teachers are generalists and shouldn't be expected to put together a math curriculum. They should get the guidance to work with a proven program, and adapt it to work in their classrooms. The other challenge is the chronic shortage of MS math teachers qualified to teach algebra. But nobody should get away with blaming the kids for "not being ready".
My three kids are in Northampton, and my two daughters did 8th grade algebra (that includes the "I hate math and science" younger one). They will also take four years of HS math and science - to keep their options open. Which will be easier for me to enforce because three years of each in a NHS graduation requirement (I can't believe the anemic math/science requirements at ARHS - a very large number of colleges and universities have application requirements of 3 years math/science). Hope you can make some changes,

Jennifer Innes

Joel said...

Fantastic information, thanks Catherine.

Also, thanks to Jennifer for the information on Northampton HS. It's an increasingly appealing option.

Finally, let me add that as problematic as all of this information on Math and Science is, it isn't an outlier. I was on the now defunct Social Studies Curriculum Review Committee and there are very similar issues. There are terrific teachers, but no horizontally or vertically aligned curricula.

I don't want to take the focus away from Math and Science, but I think it's important for people to know that Amherst's schools had either no or very weak or even very bad leadership in the recent past from SC's and superintendents and those people's actions have really hurt our schools and made life difficult for many of our teachers.

Anonymous said...

You are to be commended. Would you consider a career change and become our Super? Lord only knows you're needed. For you, I would be happy to come out of retirement.
Someone I could look up to.

Anonymous said...

Wow, I was thinking the exact same thing. Would you think about being a super? We could use your expertise.
Ali

Anonymous said...

Glad to see this discussion happening! Among the many questions that will be addressed, I hope will be questions about the IMS math program in use at the HS. I like the program, I just wonder how college admissions offices look at it relative to the more standard paths, how ARHS students who have gone through the program have done once in college, how easy is it to opt out of it after a year or two and then what?

Anonymous said...

Not to take away from the poor curriculum issue, but most of the teachers I see at my kids' elementary school are focused on reading/writing. They'll ask the district, the school, the principal AND the PTO/PGO to pay for reading/writing workshops, trainings and materials, and some will even pay out of pocket for training at Teachers' College in NYC during the summers.

Very few are as passionate about teaching math. What do you do about that?

Abbie said...

to anon@624:

this was part of a comment on the earlier blog. I agree with you:

"Who's decision was it that the vast majority of the instructional time (almost the entire day as we've experienced for 1-3rd grade) would be spent endlessly composing at the expense of math, among other subjects. This seems to be an intentional pedagogy. Who thought it up and is there any rationale for it?"

While I think its really important that kids learn how to write, it seems like this is the TOP priority, by far, in the elementary schools. Why?

I looks like lots of folks are in agreement on this one (for a nice change). I wonder whether having a lot of folks show up to the next ES SC mtg and voice their support (or demand) for a change in the math curriculum would be productive? I for one am already planning on it.

Ed said...

Three things:

First, yes, Catherine for Superintendent. This actually is exactly what a Superintendent ought to be doing, summarizing the state of the profession and asking the community to make choices.

Second, I've had parents of color tell me their kids are told by peers that doing this extra work is "acting white."
I know of a very real situation about 15 years ago now - others may as well - where there was a Black UM professor with a national reputation in one of the sciences. Children tend to be interested in things that their parents are interested in and his son was in the Middle School at the time.

And his son was being beaten up with frequency because of his interest in Math & Science. Subjected to physical violence.

Now I don't know how you address this issue, but you aren't going to have young men of color interested in these things if they are forced to choose between their physical safety and self actualization....

I can certainly imagine that stereotypes about girls being bad at math lead some 7th grade girls to opt out of extra math homework.

Knowing how insecure girls are at that age and just how important it is to fit in with the (female) peer group as well as to be sexually attractive to the boys, I wonder how many opt out as a means to accomplish goals more important to them.

I have seen college women with MENSA-level IQs pretend to be stupid so that they didn't appear smarter than the young men whom they were interested in. This is reality, we can get into why but the reality is that it is an *is*....

Which goes to my third point - forget political correctness, the teachers should be encouraging ALL the kids with abilities (and they know who they are) to try to get into the upper level classes.

They need to give students plausable denialability as well as a low-stakes opportunity to see if they can do the work. Sorta like saying "why don't you stop by next Wednesday after school and we will see if you can do the work - tell your boyfriend it is detention because I caught you smoking dope in the hallway or something, tell your boyfriend whatever you want to tell him, I won't say anything." "And if you really can't do this kind of work, I won't tell anyone - but I really think you can and I think you need to know you can't before you start saying that you can't."

Likewise to the young man, tell him that he can say that "the computer messed up" or that "I put you in the accelerated class to punish you" or whatever -- give the kid some excuse, some way to say that he is in the upper level class or a reason other than wanting to be there.

It is a terrible thing to have to give bright and gifted students excuses for taking classes at the ability they are able to perform at, but this is reality. The reality is that when forced to choose between peer acceptance and academics, they will not choose academics!

And we have to deal with the reality in which we live, not the society that we wish existed....

Ed said...

Very few are as passionate about teaching math. What do you do about that?

This is in general regarding elementary teachers statewide and there are specific exceptions -- but in general, elementary school teachers are really weak in Math & Science and they know it. No one is good at everything, and teachers are human beings.

One approach is the carrot - find some grant money (NSF perhaps) to offer PAID summer training in Math & Science. Even if this is in remedial math, we need to be adult about this and encourage people to seek help where and when it is needed - without judgment.

I think you will find that a lot of teachers would quietly admit how insecure they are in their knowledge of Math/Science and the absolute first thing they tell you in teacher training is to "teach what you know." And there is a whole lot more comfort in learning more about something you already feel comfortable with than running the risk of humiliation of it being found out how weak you are in another area that you are supposed to know...

Second, the district needs to target elementary teachers with strong Math/Science in its recruitment and hiring efforts. There are a variety of ways in which this could be done.

Third, administrative fiat....

Anonymous said...

Really? We're pushing to adopt a whole new curriculum (which is thousands of dollars!) after teachers have only all been using it for a year and half when the budget crisis is so bad that we are losing teachers and closing a school???? And talking about closing the middle school altogether???? We're going to spend money on something new when we can make what we have work until we are out of this crisis?

This just doesn't seem like a reasonable use of the little money we have. It seems like it would tax the teachers who are left after the cuts, and changes of buildings and students and whole staffs to have to learn a whole new curriculum when they've been working hard to learn and use the one they have.

Any certain curriculum doesn't make good teachers. Aligning, yes. Professional development, yes. A good teacher can make any curriculum work.

Caren Rotello said...

Anon 8:27: Yes, the ES math curriculum is bad enough that it needs to be changed now. In my view, that's more critical of a need than, say, continuing to offer 6 foreign languages. And I suspect it's a lot cheaper. (I don't have personal experience with the MS or HS math options, but I'm not looking forward to that given the information on this blog.)

You really should read the study of Investigations that Catherine mentioned -- the study is well-done and the results definitive (and disturbing).

Anonymous said...

I'm sure some of you will jump up and down, but teachers at the high school are being riffed and being told that, even with an override, they won't come back. Teachers in the music department and some of the electives, teachers with 10+ years experience there, marvelous people with great relationships with students. And they've only just begun.

Abbie said...

to anon@8:27 PM

can you explain how switching from Investigations to another workbook series would cost a lot of money? Are the workbooks for Investigations that much cheaper than the others? I guess maybe they might be cheaper since they are so bad (maybe that's why they were chosen in the first place). If you know this is the case perhaps you can provide a link of the costs?

While my experience of Investigations is only of 2nd and 3rd grade, I can't see how a teacher would need much preparation to change to another workbook. I imagine that is also the case at 4-6. We are not talking partial differential equations, this is pretty straightforward stuff. If a 2-6th teacher can't manage simple addition, subtraction, multiplication, division, and fractions, then maybe they should reconsider...

"Any certain curriculum doesn't make good teachers. Aligning, yes. Professional development, yes. A good teacher can make any curriculum work." Why would you want to tax teachers with the burden of a crappy workbook? Their work might actually decrease with a system that has actual merit. Are you a teacher? Do you have kids in the Amherst elementary schools?

Sorry, but I don't see things improving economically for some time, years. I refuse to have my daughter's (or any Amherst kid) entire math education sacrificed because there are some people desperate to stick with the crappy status quo. If you don't get a solid foundation early then its really hard, if not impossible, to catch up. If you want to handicap your own kid with the mental equivalent of a tremendous pair of headphones or a pair of glasses with wavy lenses for 4 years then fine. I guess if we were to stick with it, as more and more elementary students only math experience consists entirely of Investigations it may gradually do away with the MS extensions program as no one would be prepared to take them. Oops, except for all those kids whose parents pay for Kumon lessons. What's the social justice in that! Our public schools ought to provide to EVERYONE a math curriculum that promotes achievement.

Anonymous said...

What a fine report! How quickly can the work be done and a decision be made?

Anonymous said...

I just thought it was worth mentioning that there is a 2nd grade teacher who won a state award for her methods of teaching math. Catherine, would it be possible to consult her about the elementary math curriculum? I hear she does great things!
I know this thread's topic is the elementary math curriculum, but have you looked at IMP at the HS? Luckily my daughter did not choose IMP, but has friends who did and ended up completely unprepared for calculus.
As an aside, my daughter excels in both math and sience, and has no problems socially ;).

Alison Donta-Venman said...

I agree that the math curriculum is so bad that it should be changed immediately. My two oldest kids went through Fort River and neither was prepared enough in basic math skills (i.e. multiplication tables, long division). In addition, the Investigations method turned them off math; they felt as if they had to spend as much time writing about why/how they got the answer as they did making the calculation. That was frustrating to them. Frankly, they would have been happier with the old-fashioned drilling of 50 addition problems on one piece of paper, day in and day out, gradually increasing in complexity! I didn't know about Kumon (unfortunately) but in the end I ended up drilling both at home by the fourth grade (which they were not happy about).

Rick said...

This is a great discussion and very important issue. Thanks Catherine for all the research and for pushing the discussion!

Perhaps there are three separate problems with math:

1. Oversight of curriculum K-12 (coordination) – this would include whether or not 8th graders take algebra.
2. Exactly what curriculum is used
3. Do teachers know math well to teach math (elementary)?

#1 is the probably the easiest to address, and I noticed this on the ARPS site which is moving in that direction: http://www.arps.org/node/1073

#2 is extremely confusing to me. The reason there is a math war to begin with is that there is a huge disagreement about what the right thing to do is. Investigations and Everyday Math are both in the reform math camp, with Saxon Math as perhaps the favored one in the traditional math camp.

First, which is the right way to go: reform or traditional, and can one know this simply by measuring how many schools do which?

Here’s a video showing that reform math (both Investigations and Everyday Math) is not the way to go which apparently the state of WA has decided: http://www.youtube.com/watch?v=Tr1qee-bTZI - that's one person's view.

My (limited) understanding about the two camps is this:

• Traditional math is what most of us old folks would recognize. It teaches methods (algorithms) for doing multiplication division, etc., without necessarily understanding why those methods work.

• Reform math tries to teach students why the methods work, the idea being that this teaches them to think better than just memorizing methods does. But in the process also introduces other methods, which may increase understanding, but are inefficient methods. This may have come about in part because with the advent of calculators and computers, being efficient at calculation is not as important as it once was.

Second, within each of these camps, which is the best curriculum?

The Dept of Ed study that Catherine linked to indicates these two are the best: Math Expressions and Saxon. Is that what we go by or do we go by what schools in our comparison group uses, where apparently none of the comparison schools use the above two curricula? See how confusing this is?

We are not the only ones struggling with this:http://blogs.wickedlocal.com/newton/2009/09/27/does-newton-have-a-math-problem/
…where people are complaining about Everyday Math, and Newton math in general.

It’s very frustrating that there is not more of a consensus across the country about this. One would think that teaching math would be “figured out” by now.

#3 Do elementary teachers know math well enough to teach it?

I “hear” this may be a problem (as Anon 6:24 and Abbie above points out) but what do we really know about this? I can see this as possibly being a larger problem that curriculum – or not – we somehow need to find out.

At any rate, I certainly applaud the effort to dive into this and try to figure all this out. Thanks again Catherine.

Joel said...

I want to thank Catherine again for this, but it's important to remember that the SC doesn't make curricula.

We have a new superintendent and it's his job to get going on this. Where does he stand on elementary school math? What is he willing to do NOW about?

He told me in a private meeting that he was concerned about various curricula and wanted to move forward, but that was in the summer. Does anyone know if any progress has been made?

Anonymous said...

I just wonder how many of the folks on this blog who are clamoring for cutting languages, music and other electives at the HS actually have kids who go there? My guess is that if they get cut now- you all will be clamoring when your children get there in a few years about how bad the HS is because they DON'T offer these things.

Anonymous said...

I agree that the Investigations curriculum is a problem. I can attest to its difficulty for children with an LD. My son (now in fifth grade) has an LD (severe problems with processing and reading) and although is much stronger in math until this year had to be pulled out of the classroom for math as well as "the math curriculum was so heavy in reading and writing" He can do the math just not this math. This created a problem as he was more advanced (in math at least) than his peers in the pull out but not allowed to be in the classroom due to the heavy reading and writing component. Contrary to popular opinion about SPED in many cases there is no differentiation in SPED classes either. In spite of being pulled and consequently not learning all the grade level content (because he was not taught it) he did well enough in the MCAS to be placed in the regular classroom this year however there is a para who helps him and other students with math which is great as he can not always do the reading but usually can do the math. Give him worksheets of math facts and he slogs his way through. The problem at the beginning of the year this year was that he had gaps where he was not taught the math last year as the pull out group does not do all the grade level math. If the curriculum was more standard I think he would have been a. more successful in the area of his strength and b. in the regular classroom for math earlier in his career with his friends...which is the goal and which helps his self esteem.

One note of caution....before we moved here my children were in a school with Every Day Math which is equally as problematic. The parents in that school were lobbying for a change. It also does not focus on basics....it is a spiraling curriuclum so each lesson deals with multiple functions which may work for some children but for others it is confusing and a program where you focus on one area until mastery and then move one is much better. Call me old fashioned but if you do not know the basics how can you do the more advanced math? I am still suffering from being the product of an experimental math curriculum way back when....

Jan Kelly

Anonymous said...

to Rick 7:42: your points are well made but I'm concerned you're only looking at the problem from the school system and teacher perspectives. I think we also need to start asking students what they think, and make sure they have the safety to answer honestly. I think if we had the resources (or volunteers from UMass or Mt Holyoke-- one of the places where our school system offers student teacher placements)to survey high schoolers or conduct some focus groups with high schoolers about their math experiences in Amherst, we (as in the adults in this community) would learn a whole lot more about how the math program is perceived by its students, what they see as its weaknesses and strengths and where they have continuing persistent needs.

As the people most impacted by the program, why don't we ever involve the students in the assessment process? and I mean doing more than just looking at the data surrounding their achievement and what college they end up going to.Why don't we ever ask them what they think?

Rick said...

Anon 8:12

Yes I agree that asking student is always a good thing to do.

The main point I was making is not about determining whether what we are doing now is good or bad; I can imagine we can figure that out and surveying students would be a part of that I would hope. It’s what to do instead - if we determine we need a change - that is very confusing since there seems to be such a lack of consensus out there as to which is the best method and curriculum.

Anonymous said...

My suggestion: Align the minimum level of mastery of basic math facts required in grades 1-3 DISTRICT-wide.

A big complaint from 4th-5th-6th grade teachers is that the kids do NOT know their basic facts.

How about a temporary fix (which in my mind does not require picking an official curriculum): Include a separate 15-minute drill period that involves timed tests for addition, subtraction, multiplication, and division. Have specific goals per grade that ARE DISTRICT-WIDE (e.g., master addition/subtraction facts up to 20 by the end of first grade, master double- or triple digit addition/sub by the end of second grade, get all your multiplication/division facts memorized (yes, I said memorized)(up to 9x9 or 12x12) by the end of third grade.

And yes, let kids who've mastered addition/subtraction in 2nd grade move on to multiplication facts. If the teacher doesn't have time to explain what multiplication means to a 2nd grader - let the parents take care of that if the kid is doing advanced work. Just give the advanced kids the option to practice advanced basic facts.

I know some teachers do "drillsters" but it's not consistent throughout the year, or even across the grade or the school or the district.

AND INFORM parents whose kids are not on track to reach the district goals that they MUST work on the basic facts at home with their kids. The kids in 1st-2nd-3rd get almost no homework anyways. Make the parents accountable too. Anyone who's done Kumon knows that eventually EVERY kid gets it, if they do the practice sheets.

I think math in the lower grades (1-3) is REALLY weak, in part because rote memorization is really frowned upon. I agree that investigations is nice in that you can understand the 10 ways to add up to 10, and you can write an essay on how to do that, but you don't have any of those facts easily accessible (memorized).

These worksheets/timed tests are probably out there, probably not too expensive to purchase. Or we could have some old-school volunteers, math-minded teachers, or Kumon-experienced parents make up a series of worksheets and timed tests for the entire district for grades 1-3 - so we can start aligning the minimum level of basic facts mastery across the district.

Speaking for myself - I am not worried about my own kids as we work on the basic facts at home. But I see that my kids can't get better math (or differentiated math) in the classrooom because so many of the kids do not know their basic facts. And the ones that do are frequently bored (and fooling around) because they have to teach to the lowest level.

Anonymous said...

Maybe one of the reasons that so much time is spent on the reading and writing of math is that this is an MCAS requirement. The open response questions do ask the kids to expalin in detail how they solved a problem.

Anonymous said...

I agree with anon 10:30 am. Kids don't know the basics. Eventually you have to know the basics.

This is a great site for math fact practice. You create your own worksheets online and print them. Both my kids used these - it was part of their "homework".

http://www.mathfactcafe.com/

Thanks Catherine for all your work in this area. You are spot on.

Anonymous said...

About the comments re: how hard is it to teach Investigations.

In the fifth grade, Investigation methods of multiplying and dividing 2- and 3-digit numbers are so complex (and novel) that they handed out a textbook FOR THE PARENTS. This is a textbook for the parents if they want to help their kids in math because the ONLY method that NOT allowed is the old-fashioned method of long division, or long multiplication. Kids are ONLY allowed to use the old-fashioned methods to the check their work.

They only handed the textbook out to one of the three fifth grade classes, so this is just another example of how math is NOT aligned across a grade, a school, or the district.

Anonymous said...

Some aspects of math just flat out require memorization. Not understanding it, but just memorize it. Like multiplication tables. You cannot move on to division unless you have those down pat. To try to explain the concept to third grade kids might be a waste of time. Just memorize it for now and you'll see why you need to know it later. Ali

Abbie said...

to anon@11:25 AM:

the point I wanted to make was that it might not be too onerous for teachers to switch. You point out that it might make teaching actually easier!

Anonymous said...

Rick 8:56-
"that is very confusing since there seems to be such a lack of consensus out there as to which is the best method and curriculum."

This is true. But not as true as there seems to be consensus that the curriculum our town is currently using is known to be NOT the best method. seems to me our choices are clear, and that getting together a group of really good math teachers to pick from the remaining curricula would be helpful.

Rick said...

...getting together a group of really good math teachers to pick from the remaining curricula would be helpful."

Yes, agreed.

Caren Rotello said...

Anon 11:25
When solving problems at the board, my child has been told that he is not allowed to use the traditional "algorithm" method of solving problems (this involves, for example, adding from the right and carrying). The reason he was told not to use this method at the board -- which is guaranteed to produce the right answer in a short amount of time -- is that the teacher does not want the other children to learn that method. How awful is that?

Anonymous said...

Is there another method then adding from the right and carrying???? Why are we always trying to reinvent the wheel? I am in my 50s, have been using that algorithm since I was in grade school and it continues to serve me well when I must add large numbers together and do not have a calculator handy.

I don't get it! What are they teaching kids in school these days?

Anonymous said...

This talk reminds me very much of the new math vs. old math discussions from when I was a kid back in the 60's. I can vividly remember my mother saying "what are they teaching you anyway? What do you mean you don't know long division?" The more things change.....

Caren Rotello said...

Anon 3:08:
These days, they teach kids to add from the left and create intermediate sums, which are then added. They also do a lot of work with the number-line, though it's not clear to me how that helps kids' understanding.

Anonymous said...

I'd be curious to know how many of our comparison school districts use IMP.

Anonymous said...

What is IMP?

Rick said...

IMP: http://www.mathimp.org/

IMP at ARHS

Anonymous said...

The elementary schools offered a free (for the participant) hands on workshop for educators of math at Greenfield Community College called Math for the 21st Century. I suggest all teachers of grades K-7 take these workshops and start teaching the same curriculum throughout the grades so that as a child's ability to understand mathematical concepts grows s/he continues to be challenged and prepared for the next grade.

Rob Spence said...

Great analysis of the issues facing our district with math curriculum, Catherine. Spot on. I agree that considering a more effective elementary math curriculum should be a priority. Maybe along with ThinkMath and Everyday Math, Saxon Math could be looked at as an option as well. This analysis also reinforces Dr. Hamer's report highlighting the need for more consistency in our curriculums, across classrooms and schools and vertically through the grades, as well.

I do think is is important to consider that the ARHS science department was likely also attempting to formulate a new curriculum that would get the largest possible number of ninth graders excited and interested in science, especially more rigorous lab and field science, when they developed the current program; and that they were not simply reacting to the variable levels of math preparedness of incoming students. That said, I would very much like to see expanded science offerings and options, especially for the high achieving, highly motivated students interested in science. I think that this is going to be very important for students in a world of increasing globalization and competition in the technological fields. It is interesting that the Mathematics Program of Studies at the HS allows even well-prepared students different options for proceeding through their studies, at least giving them the option of the Interactive Math Program (although I don't know enough about it to know how many highly-prepared math students pursue this course). For the student who is motivated to do well and take multiple AP courses in the core sciences, there really seems to be one obvious pathway: 9th grade Honors Environmental Science, 10th grade Honors Chemistry, 11th grade Honors or AP biology, and 12th grade Physics (Honors/AP). I have heard that these Honors-level courses are rigorous and rewarding. This pathway does not, however, include an option for AP Chemistry; and it precludes an option for students to take both Physics, and, say, AP Environmental Studies.

The three-term AP Biology/Honors Biology combo intrigues me, and I wonder if that could become an option for AP Chemistry? I also wonder how it was determined that 9th-grade biology required the prior completion of algebra? I ask this because Catherine's analysis of comparison districts indicates that really only Brookline is trying to have all 8th graders take algebra; yet all of the other comparison districts have either 9th-grade biology, or 9th-grade physics. So it seems to me that they can't have the requirement of pre-requisite algebra. I understand that the "physics first" model includes a 9th-grade intro to physics that does not require higher-level math. I personally think that this would be much easier to achieve with a biology course and still be able to cover major topics. I worry that "math-light" physics would have to leave out a lot of physics. However, it may also be good to get as many kids exposed to some physics as possible.

That said, I think that there is a real opportunity to work with the HS science department to come up with some ways that strong science students could have some increased options along the way.

Anonymous said...

By way of Rick's link to information on the IMP Math program I noticed that the Math Program of Studies indicates that we do not offer any Statistics courses to our students, never mind AP Statistics. Is this true?

It seems odd to me that we don't offer statistics at all.

Rick said...

Rob,

Very thoughtful post; I really like your balanced view of things and the attitude expressed here: “there is a real opportunity to work with the HS science department to come up with some ways that strong science students could have some increased options along the way.”

On AP Chemistry, the problem is that according to the College Board, an AP Chemistry course has to be a second chemistry course – or at least that is highly recommended. Perhaps a 4 trimester (or 3 semester) course would suffice - I don’t know - but perhaps that could be looked at along with all other options.

Anonymous said...

Math and science go hand in hand. You HAVE to be strong in math to do well in science. I wouldn't attempt to find wiggle room with the APs. The last thing you want, after all this research, is to find out the option you've decided on isn't going to get the kids the highest score possible on AP exams. Ali

Catherine A. Sanderson said...

My responses:

Ali - thanks for the kind remarks. I take my SC "job" very seriously -- whether people like or hate what I'm doing, I am working hard!

Jennifer - I agree that our issues are in a sense universal (e.g., ones that other districts are also struggling with). However, I see the solutions arrived at in Amherst (e.g., extensions in 7th grade, ecology in 9th grade, no AP chem or stats) as less universal, which is one of the things I find concerning -- it doesn't seem like we are looking to see how other districts have solved these universal problems, but rather are trying to create our own solutions. Seems like a good K to 7 math curriculum would go a LONG way towards helping all kids take 8th grade algebra, which does seem like a very reasonable goal (and I'm glad your daughters have been able to do that in Northampton!). The low graduation requirement in the Amherst schools for math and science (as well as the absence of prior core AP classes) I think speaks to the lack of focus on these areas in our curriculum -- and I share your hope that we can make some important changes.

Joel - yes, the problems in math/science in our district aren't unique to math/science ... just perhaps more salient in some ways. I very much hope the review committees (for math, for social studies, for all fields) will have a more focused mission in the future and will actually help make some much needed progress. We are reviewing a new evaluation of instructional programs at the SC meeting this Tuesday which I think is a good step towards making this happen.

Anonymous 5:24 - thanks for the kind remarks! I am just hopeful that I am making a difference -- sometimes it seems I am, and sometimes it seems like banging my head against the wall.

Ali - I believe we have a good super now in Dr. Rodriguez who I hope is committed to making the types of changes we need to see in the Amherst schools. I look forward to hearing more about his vision and the direction he'd like to see in our schools in the weeks/months ahead.

Anonymous 5:58 - very good question re. IMP -- I had thought about posting about that as well in my summary, and then thought it was just going to be too long. For those who don't know, IMP is an interactive math program that is an alternative to the traditional math sequence (algebra-geometry-algebra II-trig-calculus). This program started in ARHS in 2005 ... and to the best of my knowledge, its effectiveness has never been evaluated. I believe such an evaluation is very important, since it may well be costly to offer two separate math tracks and it is not clear whether kids who have this type of math preparation are equally able to access math in college (a concern I've heard from U Mass math professors). It is possible to move from IMP after three years to calculus in the senior year, but not possible to move before that point (e.g., after 1 or 2 years), so it is a track that in a sense can reduce flexibility of other courses. Some MSAN schools offer IMP, but not most -- the only schools, other than Amherst with this track in MSAN are: Brookline (MA), Cambridge (MA), Columbia (MO), Madison (WI), and Montclair (NJ) -- so 6 of 23. Similarly, Northampton, East Longmeadow, Longmeadow, Framingham do not offer IMP, although Newton and Hadley do. I think a review of whether this program is working would be very important.

Catherine A. Sanderson said...

My responses:

Anonymous 6:24 - I think it is likely that elementary school teachers are GENERALLY more interested in reading/writing -- I believe there are nationwide statistics showing that fewer people with math/science majors go into elementary school teaching. So, to me, that is ALL the more reason that we need to choose a really strong and good curriculum -- and one that is easy for teachers AND students to use. I don't think we've found that in Investigations, and I think it would be very useful to have elementary school teachers review, and even pilot, some alternative math curriculum to see what might work better. I teach an intro to psychology class, and that covers the WHOLE field of psychology. I'm pretty good at some of this stuff, and I'm pretty bad at others of this stuff (e.g., the brain, the eye, neuropsychology). For the stuff that I know well, I can pretty much wing it since it is in my field and my comfort zone. For the other stuff, I really, really need a good textbook to review before I teach so that I can make sure I'm conveying the information clearly. Again, good curriculum are probably more important for those areas in which a person is less personally strong/comfortable.

Abbie - I think math, but especially science, have been under-valued in the Amherst schools for a while -- probably for many reasons -- and I think that is unfortunate. I believe it would be useful for the SC and the superintendent to hear from parents about their views about the focus of our curriculum in general, and their experience with Investigations in particular -- at a meeting or via emails.

Ed (at 7:02) - I think the situations you are describing can and do occur in our schools, and I love the creativity ways you suggest for getting some kids into advanced math!

Ed (at 7:19) - I agree that math/science are probably subjects that many elementary school teachers find less interesting/accessible. This points to me to the need to (a) have a really strong curriculum, (b) have appropriate teacher support (which, yes, could include summer training programs), and (c) trying to hire teachers with these backgrounds (although I bet the pool is small here).

Anonymous 8:27 - my guess, and this is really a guess, is that a new elementary school math curriculum would cost about $200,000. And yes, that's a lot of money, particularly at tight budget times. Then I look at what having a bad curriculum costs us: we pay math coaches in all of the elementary schools to teach teachers how to teach our non-intuitive curriculum, we hire intervention teachers to work with kids who don't understand math since we are using such a weak curriculum, and we pay for afterschool intervention support for kids who fail the math MCAS. Gosh, that sounds REALLY expensive -- plus, those expenses are on-going, year after year after year, whereas buying a new curriculum is a one time expense. Sounds like a new curriculum could in fact be a cost saver! And although I agree that great teachers can make any curriculum work, we don't only have great teachers (how about the new teacher?!?), and is it FAIR to ask teachers to do so much extra work to supplement a bad curriculum? I'd rather have teachers work on teaching, giving feedback to kids, etc., then writing their own math curriculum.

Catherine A. Sanderson said...

More from me:

Caren (at 9:20) - I agree that we need a new elementary math curriculum ASAP, and believe that moving to a new curriculum could actually result in cost savings for the district.

Anonymous 9:46 - I haven't received any proposed budget cuts yet, but I do know that the superintendent has asked principals to make tough decisions involving staffing. I believe we will hear about these cuts at the Tuesday meeting. Do you have suggestions for other things to cut in the district? It is clear that cuts are going to have to be made -- the question is just where. I also think the teachers union has the OPTION to re-open the contract and reduce the wage increase -- I'm not suggesting they should do that, but I do believe it would be a way to save jobs since 80% of the school budget is people.

Abbie (at 11:31) - as I've noted in an earlier post, I think having a new curriculum would be good for kids and teachers and would actually be cheaper for the district, since it would reduce the money we are spending on intervention and coaches. I believe this would be money very, very well spent. I also agree with your point re. Kumon -- paying for coaching/tutoring is how parents with means supplement a weak math curriculum ... hardly in line with the district's commitment to social justice.

Anonymous 3:40 - this report is just one SC member's opinion. For anything to happen, other SC members and the superintendent need to support such changes. I'd recommend coming to an SC meeting or emailing the SC and the superintendent. SC members are elected to represent parents/community members, so the only way most people have any voice is by sharing their thoughts with their elected officials.

Anonymous 6:08 - Lauren Mattone is an EXCELLENT 2nd grade math teacher at Crocker Farm and did receive an award for her work. If a committee was put together to study elementary math, she would be a logical choice! I know there are other teachers in the district who also have a real talent for teaching math -- and would be a great resource as well. I have posted already about the IMP program -- and I share your belief that it is important to understand how well this program is preparing kids for calculus (this has not been done as of yet). Glad that your daughter is good at math/science and socially skilled!

Alison - I've heard this story from many parents ... and it points to the problems with having a very weak math curriculum (and the problems that must cause for the MS math teachers).

Catherine A. Sanderson said...

And still more from me:

Rick (at 7:42) - thanks for the thanks! In terms of your three issues:

"1. Oversight of curriculum K-12 (coordination) – this would include whether or not 8th graders take algebra."

I think the oversight of curriculum is not as easy as you think -- because I think the Amherst system has been designed so that each teacher has almost total autonomy in what he/she teachers. I believe there is some resistance to the idea that there should be alignment, since that in a sense interferes with teacher choice (that is what I hear). We also likely then need an assistant superintendent in charge of curriculum, and that is $$! But I do believe there may be some movement on this front in terms of SC policy -- a new one will be reviewed this Tuesday which really focuses on doing good evaluation (this is based on Brookline's model).

Then, you have "2. Exactly what curriculum is used." And yes, this can be confusing (e.g., there is a math war!). But there are a finite number of curriculums out there, so I think a place to start would be gathering 3 or 4 different options (based on research/other districts' use) and having our teachers review them -- and perhaps even pilot them in their schools (this is exactly what Framingham, MA did -- reviewed 8 curriculum, then piloted two, then chose 1). Similarly, when the math curriculum council (group of teachers/administrators) chose a MS math book 2 years ago, they got books from lots of publishers, reviewed a bunch, chose 3 to examine in depth, let parents/community members see and comment on those, and then recommended 1 to the superintendent (which we adopted - Impact - and I hear is GREAT). So, we could certainly do such a process here -- and that could include reviewing a variety of textbooks (and considering what research says about their effectiveness AND calling our peer districts to learn about their experience with other curriculum).

I also think that even within a given camp, there are "better" and "worse" choices. So, I think a lot of teachers in Amherst and elsewhere have seemed to feel that there were advantages to reform math (I may be wrong, but this is what I've now heard). But within reform math, there are better and worse choices, and that Investigations is really on one end (perhaps with Everyday Math more in the middle and Think Math! -- the newest curriculum -- on the less reform end). I would think these are two we should consider, along with Math Expressions and Saxon (based on that study -- but that study was with 1st graders, which means it is a pretty limited sample in terms of exposure to any curriculum).

In terms of your final point:
"#3 Do elementary teachers know math well enough to teach it?" - to me this means we have to choose a good curriculum that is teacher-friendly. And although I believe this is somewhat of a problem (e.g., elementary school teachers are less likely to have majored in math/science), it is NOT a uniquely Amherst problem -- I think it just means we need a good curriculum that our teachers can teach. Our teachers are plenty smart enough to teach math using a good curriculum (in reform or traditional math) ... they just may not always have the time/energy to make a bad curriculum work!

Catherine A. Sanderson said...

Me, again:

Joel (at 7:46) - I do not know where the superintendent stands on the issue of elementary school math. However, this is one of his goals for the year (one of the district goals), so I believe we will hear what he thinks sometime this year! I would very much hope that some real progress on this front could be made in time for the start of the 2010 school year.

Anonymous 7:51 - I haven't read any comments on this blog clamouring for cuts to music/electives/languages. What I've read is people concerned about why our HS offerings in math/science aren't the same as those in other districts, and people having a recognition that in times of tight budgets, some things have to go. What things would you suggest be cut instead?

Jan - thank you for sharing your experience with Investigations ... I think it is quite clear that this curriculum doesn't work for many kids at all, and is very difficult for teachers to teach. Thanks also for sharing your experience with Everyday Math -- it will be important to make sure we are choosing a BETTER curriculum if a move is made, and I would hope that we would carefully review several curricula, talk to districts that are using these alternatives, and review the empirical research on effectiveness.

Anonymous 8:12 - as I put in my original post, a survey was done of kids in our district involving math in 2007. This survey revealed that kids in both elementary and middle school see the teachers as focused largely on those who don't understand math and that the math curriculum lacks challenge. This seems quite problematic to me.

Rick (at 8:56) - again, I think the issue is less about choosing which new curriculum to use (since SC members really don't have any clue about elementary school math!) and more about trying to figure out the PROCESS by which we make a decision (since SC members actually do control district policy in terms of how decisons are made). What would you propose as a good process for making the decision about a new curriculum?

Rick said...

Yes great point, I totally agree: "trying to figure out the PROCESS by which we make a decision"

Joe said...

Catherine,

In response to Rick's point #3, you said:

Do elementary teachers know math well enough to teach it?" - to me this means we have to choose a good curriculum that is teacher-friendly. .... I think it just means we need a good curriculum that our teachers can teach. Our teachers are plenty smart enough to teach math using a good curriculum (in reform or traditional math) ...

I believe the curriculum is crticial and should be evaluated and changed if needed. However, I think your comments put to little weight on the teacher and their teaching skills. I know plenty of "smart" people that have exceled in math, but are horrible teachers. Given a choice, I would much rather have an excellent teacher than a "stronger" math curriculum. Obviously having both an excellent curriculum and excellent teachers are ideal. So, let's improve the curriculum, but let's not forget the importance of hiring, honestly evaluating and retaining excellent teachers.

Anonymous said...

some ideas for cuts:
1) reduce languages in middle school to the basic 3: spanish, french and latin. offer additional languagues in 9th grade: german, chinese, and I'm not sure what the #s are in russian these days.
2) review to name cuts to all vocational oriented electives at the high school.
3) review elective choices at the high school- identify potential cost savings per course/student value
4) view music and art as academics and don't touch
5) protect dance and theatre
6) ASK HIGH SCHOOL STUDENTS FOR SUGGESTIONS

Anonymous said...

Well Catherine- then I guess it's just a matter of how one interprets comments like: "Do we really need to have 6 languages?" or "Do we really need to have music/art? Those kids can go to PVPA" or 'Do we really need to have .... " fill in the blank with anything other than an AP science or math class. "Just have those kids who might not be so academically inclined go to Smith Voke." All of those comments have been made at one time or another by you or others on this blog.

Anonymous said...

The reason for the discussion is because rigor in science and math has been so sorely lacking in Amherst schools. That's why so much focus on it in this blog. There is no place in the schools for the kids who do want AP classes.

Anonymous said...

Catherine,

Didn't you do a post a while back on the importence of having extra years in math and science, like how it effected performance in college?

I think it had a colored graph from Scientific American or something. Can you repeat the post so people can talk about it? That would be great.

Thanks for all you do.

Rick said...

Catherine, I realize I didn’t answer your question: “What would you propose as a good process for making the decision about a new curriculum?”

I would suggest something like this:

A committee for each area of study (math, science, etc.) would be created, made up of teachers, administration, parents, students and one or two SC members. Perhaps like this:

1x ARPS Curriculum Coordinator
4x teachers (one being the department head at ARHS)
3x parents
3x students
1-2x SC members

That’s 12-13 people – perhaps too many – but you get the idea.

The ARPS Curriculum Coordinator would be responsible mainly for making sure these meetings happen, that everyone is heard, that good minutes are taken …generally coordinate the process.

The parents there would be charged with collecting input from other parents; ditto for the students. It’s not just about their input only – they need to help with gathering input from others.

I see any SC members there as mainly observers – reporting back to the full SC to say how they think the process is going.

Then having formed these committees, you start off at the very beginning. For example, with math:

1. Background: Review what has happened over the past 20 years or so, what traditional math means, what reform math means, what IMP means. What seems to have worked and what hasn’t. I might bring in outside people to talk to the committee on these subjects.

2. Data collection: #1 leads into collecting as much data and study as possible.

3. Then with background, data and study in hand, you start to discuss all the options, laying out pros and cons of each using the data collected. A website (or section of ARPS website) should be created where anyone can go and see what’s going on with the committee as it does its work and can comment on it.

4. Finally, when everyone feels they have researched this enough, the committee makes a recommendation, including a detailed report of why the recommendation is being made. If it is not unanimous, you would also include a report from people not agreeing with the recommendation.

5. Then present this recommendation to the public and SC at one or more public forums.

6. Finally a vote is taken.

This is at least a 6 month process – probably more like 9-12 months.

Rick said...
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Anonymous said...

To Anon 3:52 -To say that there is no place in the schools for kids who want to do AP classes is beyond ludicrous. Let me- see last time I looked a student so inclined could take AP calc AB or BC, AP Physics, AP BIology, AP Euro, AP Latin, French or Spanish and or, AP Environmental Science.

Rick said...

I was talking to my son this morning, who is a junior at McGill.

He mentioned that he thought it was important to have had calculus in high school, that most of the international students have had it, and recommended looking at the International Baccalaureate program: http://www.ibo.org/

But it was interesting to hear why he thought this was important. It wasn’t so that he would have some kind of a head start on calculus upon entering college. It was because he didn’t get turned on to math until he took calculus. He might not have taken calculus in college had a friend not pushed him to do so. He is very glad he did as he in now majoring in Economics, which of course requires lots of math.

He also mentioned this:

When he was at ARMS, he said kids were in different tracks in math and he thought that was bad as they were really locked in to a path all the way through high school and thought they were way too young to be locked in like that.

He thought there should be some kind of heavy duty counseling of kids to make it very clear to them what classes they need to take for certain career paths. While most kids may not have clue about what they want to do for a career, they may be thinking about a handful of careers and so do not want to get locked out of those careers if they go down the wrong path.

Anonymous said...

I have heard the same comment about tracking in math from other ARHS students. They said because of what they didn't do, or didn't know, at ARMS, they were locked out of certain math courses at ARHS. For all of you who think that tracking is a preferred educational tool, I think you should listen to these students AND answer this question: What does a classroom look like that is full of students in a low-tracked course? I have not heard one person on this blog discuss what happens to those children, but I know, from personal experience, that students in a low-tracked classroom have low expectations of themselves and their future. Many of them are dumped there for a variety of reasons, most of which has nothing to do with their ability, intelligence or skill. I'm not talking about tracking in theory. I'm talking about the reality of what happens in a low-tracked classes, at ARHS and across the state.

Anonymous said...

Rick, I agree with what you said about the counseling. Right now there is only one guidance counselor to cover both grades at ARMS. How many at the HS? I think it would be important to add the 2nd counselor back in. It would also help to really explain it to the PARENTS what the kids need to do now that will help in HS. Not everyone is thinking ahead or even understands that. Some of us didn't go to college but want our kids to.

Rick said...

Anon 9:02
Absolutely. Sometimes I think this is the single most important thing we should be doing – making it crystal clear to students and parents what the road map is.

Joel said...

Rick,

Your proposal for reviewing curricula is interesting and could work. As I've mentioned, I was on such a committee and Catherine was on another. What I saw from the leadership of the committee (and I believe Catherine had the same experience) was an interest in doing politics. What are the politics of reform? How can we craft something that is unique?

One thing you forgot is that we're a college town. The Mass. Dept. of Ed is very interested in having institutions like the UMass History dept. play a lead role in developing Social Studies curricula. I got nowhere with that idea. One of the two leaders of the group was much more interested in the politics and pedagogy of social studies than in content.

We spent zero time reviewing what's done throughout the Commonwealth. While the teachers were eager for UMass and AC to play a role, the leaders of the committee did absolutely nothing to facilitate that.

Rick said...

Joel,

I guess like anything it can be done well or not done well. Probably the key to that is a no nonsense Director of Curriculum overseeing the whole process and heading each meeting.

That position is perhaps just about as important as the superintendent?

Joel said...

RIck,

True enough. I think it's also all about basic principles. If you start with a desire to embrace best practices, you'll gather information from other successful schools. If you start with a desire to be unique and different, you'll spend a lot of time spinning your wheels and developing curricula that no one else wants (our 9th grade science requirement) and practices that are either illegal or against government guidelines and best practices (ethnic/racial clustering and our ELL program).

So, I guess we agree that such a curriculum coordinator would end up being a key person. The SC would have to decide if they want the best practices person or the we're super-unique person. I know you want to bring all sides together, but this is pretty much a deep divide and I'm not sure there's a lot of room for compromise.

Given it's about my kids' education, I would always opt for best practices over experimentation and innovation for innovation's sake.

Anonymous said...

I'm with you Joel on Best Practices. I don't want them experimenting with my kid's education.

Ken Pransky said...

I've noticed that frequently, individual anecdotes substitute in this blog's discourse for 'proof' of things. But Catherine's data analysis is equally flawed. Only using AYP to determine math (or any) program effectiveness is a discredited way to view data nowadays. AYP is the law, so it can't be ignored, but that's different than using it to measure program effectiveness. About 50% of districts in this state are now not meeting AYP, including some of the HIGHEST scoring districts on MCAS. Each year the % grows, not shrinks, and that's true across the nation. According to Catherine's AYP logic, pretty soon nearly every district will need to change every program, and probably multiple times if the law doesn't change.

The problem is how arbitrary the AYP system was originally designed (under NCLB). For anyone who may not know, AYP at the elementary level is figured as the average of 3rd-5th graders in one year compared to next year's 3rd-5th graders; a predetermined increase on state testing must be made each year or that district/school did not make AYP.

There are 2 big problems. First, it's statistically unreliable because each year, 1/3 of the students being compared will change, as 5th graders move to 6th and new 3rd graders enter in. Second, it's a sledghammer view of data whereas now there are so many finer ways to examine data. FYI, the MA Department of Ed already encourages districts to use a growth model, not just AYP, to determine program effectiveness. The state is moving rapidly toward the day where individual student's (and demographic groups of students') MCAS scores will be tracked for improvement, and determinations of school effectiveness made on that basis.

Catherine already knows, because I sent her the data, that a growth model (comparing the same students from 3rd grade in 2006 to 6th grade in 2009) yields a far different view of our elementary math program. We "outgrew" the state growth average in EVERY demographic subgroup category, sometimes very substantially. This means low income, non-low income, White, African-American, Asian, Latino, SPED, ELLs, males, females, Title I... Translated, our students' math performance improved relative to the state average on what is universally recognized as one of the most challenging state tests in the nation. If you use MCAS data to measure learning, it means that our students learned math better between 3rd and 6th grade than the state average in every demographic category--in several cases by a huge amount.

This data is freely avilable to anyone who wants to look on the DESE website. It is a complete distortion of reality to call our elementary math program "weak" based on MCAS results.

It is true that Investigations is more challenging for second language learners, and indeed, in Amherst, the ELL subgroup grew the least--yet even our ELLs grew at a greater rate than the average of all students in the state, and greater than every subgroup average in the state except Asian students! The improvement question that an appropriate look at the data generates is NOT, "Our program is weak, so what should it change to?" but rather, "Our math program is quite strong. Now how do we train teachers to be even more effective teaching math to African-American students and ELLs (the 2 lowest growing groups)?"

It is also true that it's challening to teach Investigations well, and some teachers may not. There is also no inherent conflict to learning math facts well and the Investigations program. Some teachers just need more training.

To further contextualize our MCAS growth results, Massachsetts 4th graders score at the TOP of the nation in math (on the NAEP test). That means that within the context of the highest achieving state in math, our students--in every group as well as all students as a whole-- grow at a higher rate (i.e., learn more math) than the state average. "Weak?!"

Excuse the long post, but there was a lot to respond to.