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.