First, I'm definitely in favor of increasing the % of our 8th graders who take algebra. Taking 8th grade algebra is virtually the only way (other than doubling up on math classes in high school or going to summer school) to be able to take calculus in high school -- and taking calculus in high school opens many doors to college classes and majors (math, economics, sciences). Again, this does not mean EVERYONE should take calculus ... it means that it would be good if more students had the OPTION to take calculus (which means they need to take 8th grade algebra).

Second, there are districts (some in California most famously) in which people said "let's make them all take algebra in 8th grade" -- and this is, I think, a bad idea. So, increasing the % of our kids in 8th grade algebra does NOT mean just enrolling all of them in that class! It means seeing what skills are necessary to succeed in 8th grade algebra, and then making sure that our entire curriculum (K to 7) prepares ALL kids to get these skills. It may also mean adding a regular algebra class for those who COULD do algebra but aren't ready for HONORS algebra (currently our only option).

One more thing, for those (like me) who like numbers from other districts: As part of my work on the math curriculum council, I contacted math curriculum leaders in other MSAN (Minority Student Achievement Districts) and asked the following questions: What percent of students take 8th grade algebra (and of these, what percent take 8th grade algebra and are then ready to move on to geometry in 9th)? These districts were: Arlington (VA), Brookline (MA), Cambridge (MA), Champaign (IL), Chapel Hill (NC), Framingham (MA), Evanston (IL), Princeton (NJ), Newton (MA), Windsor (CT). Here is what I found.

- In some districts, most or all 8th graders take algebra and move on to geometry in 9th grade (80% in Chapel Hill; 80 to 85% in Princeton; 100% in Brookline).
- In other districts, approximately half of 8th graders take algebra and then move on to geometry (52% in Arlington; 50% in Framingham; 55% in Newton).
- In still other districts, fewer than half of students take 8th grade algebra and move on to 9th grade geometry (43% in Champaign; 34% in Evanston; 26% in Windsor).
- In Cambridge, no 8th graders take algebra.

(Web link: http://www.brookings.edu/reports/2008/0922_education_loveless.aspx)

*The following is a special advanced release of a Brown Center report on eighth grade algebra levels. The full report will be published in February 2009.*

Algebra in eighth grade was once reserved for the mathematically gifted student. In 1990, very few eighth graders, about one out of six, were enrolled in an algebra course. As the decade unfolded, leaders began urging schools to increase that number. President Clinton lamented, “Around the world, middle students are learning algebra and geometry. Here at home, just a quarter of all students take algebra before high school.”

^{1}The administration made enrolling all children in an algebra course by eighth grade a national goal. In a handbook offering advice to middle school students on how to plan for college, U.S. Secretary of Education Richard Riley urged, “Take algebra beginning in the eighth grade and build from there.”

^{2}Robert Moses ratcheted up the significance of the issue by labeling algebra “The New Civil Right,” thereby highlighting the social consequences of so many poor and minority students taking remedial and general math courses instead of algebra.

^{3}The campaign was incredibly successful. Several urban school districts declared a goal of algebra for all eighth graders. In 1996, the District of Columbia led the nation with 53 percent of eighth graders enrolled in algebra. From 1990 to 2000, national enrollment in algebra courses soared from 16 percent to 24 percent of all eighth graders.

The surge continued into the next decade. Eighth-grade enrollment in algebra hit 31 percent nationally in 2007, a near doubling of the 1990 proportion. Today more U.S. eighth graders take algebra than any other math course.

^{4}In July 2008, the State of California decided to adopt an algebra test as its eighth-grade assessment of student proficiency. The policy in effect mandates that all eighth graders will be enrolled in algebra by 2011.

At first glance, this appears to be good news. Transcript studies indicate that 83 percent of students who take geometry in ninth grade, most of whom completed algebra in eighth grade, complete calculus or another advanced math course during high school.

^{5}Research also suggests that students who take algebra earlier rather than later subsequently have higher math skills.

^{6}These findings, however, are clouded by selection effects—by the presence of unmeasured factors influencing who takes algebra early and who takes it late. Schools routinely assign incoming eighth graders to math courses based on how much math students already know. Moreover, it is no surprise that excellent math students want to take the most challenging math courses available to them and that low-achieving students avoid these courses as long as possible. Whether algebra for eighth graders is a good idea, especially for those who have not learned basic arithmetic, cannot be concluded from existing evidence. Studies that test for causality, such as experiments with random assignment of students to treatment and control groups, have not been conducted.

The push for universal eighth-grade algebra is based on an argument for equity, not on empirical evidence. General or remedial math courses tend to be curricular dead-ends, leading to more courses with the same title (for example, General Math 9, General Math 10) and no real progression in mathematical content. By completing algebra in eighth grade—and then completing a sequence of geometry as freshmen, advanced algebra as sophomores, and trigonometry, math analysis, or pre-calculus as juniors—students are able to take calculus in the senior year of high school. Waiting until ninth grade to take algebra makes taking calculus in high school more difficult. From this point of view, expanding eighth-grade algebra to include all students opens up opportunities for advancement to students who previously had not been afforded them, in particular, students of color and from poor families. Democratizing eighth-grade algebra promotes social justice.

1 Remarks by President Clinton, Education Roundtable, Springbrook High School, Silver Spring, Md., March 16, 1998. Available at http://www.ed.gov/inits/Math/timsroun. html.

2 Quoted in Matthew Bowers, “Virginia and the U.S. are Improving Slightly at Math, but We Lag Behind Our Economic Competitors in the Developed World,”

*The Virginian Pilot,*March 28, 1997, p. B3.

3 Robert Moses, “Algebra, the New Civil Right,” in

*The Algebra Initiative Colloquium, Volume II,*edited by Carol Lacampagne and others (U.S. Department of Education, 1995), pp. 53-67.

4 Data available on the main NAEP data explorer: http://nces.ed.gov/nationsreportcard/nde/. See also Jay Matthews, “Adding Eighth Graders to the Equation,”

*The Washington Post,*March 12, 2007, p. B1.

5 Carolyn Shettle and others,

*America’s High School Graduates: Results from the 2005 NAEP High School Transcript Study*(Department of Education, 2007), p. 11. Other than calculus, advanced math is defined as pre-calculus or AP statistics.

6 Julia B. Smith, “Does an Extra Year Make Any Difference? The Impact of Early Algebra on Long-term Gains in Mathematics Attainment,”

*Educational Evaluation and Policy Analysis,*18 no. 2 (1996): 141-153.

## 49 comments:

http://www.nytimes.com/2009/06/08/education/08math.html?hpw

Fyi- in the NYT today

This is an 8th Grade Algebra Argument. For it to be a debate, we'd need an opposing view, which I do not have and so cannot provide.

My 9th algebra teacher at the HS was an Amherst College graduate who was student teaching. He was a good teacher. Half the class was on board and the other half was dedicated to disruption. He and we were able to tolerate the attempts and not allow it to deter our progress. The class moved fast.

I think I would have been ready to tackle algebra in eighth grade. I was not able to tackle Calculus as a senior in high school.

To anon@805

I really hope that our math curricula work, including extensions. But I would like to actually KNOW that they work. This seems like an experiment, one where one does the experiment, but doesn't collect the data or form conclusions (BASED on the date).

Of all the subjects, math seems to be the one that is the simplest to track progress (or regression). It seems that a year's worth of students is a reasonable sample size. A few years comparing student scores (before vs after extensions) on standardized tests ought to provide us with some important information.

I admit the extensions program *seems* iffy to me but my family has yet to experience it first hand. Maybe it is working really well for kids (and all this worry is misplaced). But if the teachers are going to do an experiment on our kids (i.e. trying new curricula), then it ought to be complete (i.e. data collection and analysis).

The iffy bit comes from my impression (and someone correct me if I am wrong) that a functioning system had existed that included an algebra option (i.e. tracking). "Tracking" is evil in Amherst. So to replace this algebra course, we switched to extensions, which consists largely of self-motivated learning outside the classroom (i.e. homework).

Was there a problem with the previous algebra course? Was it NOT working? If my impression is about right (again I welcome correction- honestly) it doesn't seem very progressive. The math teachers that receive students having gone through extensions ought to have an idea about whether their students are as prepared as those previously.

I'd like to know if there is any child who took extensions who enjoyed it and felt they benefited from it? Or is it just the only path Amherst has made for those students to take algebra in 8th grade? Extensions are not taught and allow Amherst math teachers to continue to fool themselves that math doesn't have to be taught, it can be experienced. I'm sorry, math needs to be taught by competent teachers who can explain formulas, concepts and inspire self-direction. Too often the Amherst math departments (at the middle AND high school levels), seem to feel math is just about self exploration and teachers exempt themselves from the one support that can make all the difference in the world: good instruction.

How many economically disadvantaged (free lunch) 7th graders take math extensions?

It would seem that extensions require a knowledgeable, math savvy, at-home parent (or adult) to provide guidance for the extension work. This puts some students at a clear advantage. So, is a student's ability to take and succeed at the extensions biased by their circumstances?

One thing I don’t really get: hasn’t the problem of how and when to teach algebra been “solved”? I mean, if it hasn’t been “solved” after all these years of teaching algebra, I really wonder about the whole education situation in this country.

Why do we have to reinvent the wheel all the time? This is a wheel that should be well known by now.

My observation was that the 7th grade math extensions contributed to the entire sense of malaise that developed that year (three years ago now).

It was fairly clear that the extensions were the "end run" that was necessary to avoid "tracking". If you were an ambitious kid, the extensions were the price you had to pay: you had to do additional work at home that was not integrated into the classroom day. So the work you did last night was not discussed and reenforced in class on the next day. ("Sorry, kid.")

The attitude was: "Here you go, kid. Take this home. You're a smart kid; you'll pick it up. See ya."

And it's been ok to have this shadow curriculum, because the kid being served by it is motivated. And probably has supportive, maybe even wealthy parents, blah, blah, blah. (although THAT may be a self-fulfilling prophecy)

So our ideal of the democratic classroom (different ability levels coming together) becomes the tail that wags the dog. And it's that imposition of ideal on reality that causes us to "reinvent the wheel", as Rick Hood aptly puts it.

Now I'm sure that someone will tell me that I've got it all wrong, but this is where it becomes political: I think that there's a large silent undercurrent of unhappiness among parents in town, about how the 7th and 8th grades go for their children. It's not about beating up on teachers, it's not personal, it's a reaction to the suddenly bummed-out child you meet at the dinner table during those years.

And all the columns bashing Catherine in the Bulletin will not wish it away, although you can certainly intimidate people into silence. Despite that bashing, and the disparaging of blogging as an instrument of leadership, Steve Rivkin then got elected. So there's something real going on there. But it's being expressed right now most forcefully through the secret ballot.

I think 11:24 p.m. has a really thoughtful post. But may I add that encountering bummed-out 7th and 8th graders at the dinner table is partly an age thing. These are the hardest teenage years! It's not always the school's/curriculum's fault.

I've yet to live in a community where people liked their middle school. But it's not always the school's fault - it's a challenging age group.

When a child loves his/her sixth grade experience, and immediately comes home grumbling about 7th grade, and then it keeps on, there's something going on. And then when you engage with teachers and they admit that they can't teach to all the abilities and temperaments in the class, there's something going on.

I'm sick and tired of "those difficult middle school years" being used as an excuse.

Personally, I think that the teachers have been asked to do something impossible.

To anon@855 or anyone with the answer-

why was the math curriculum changed in the middle school to the "extensions" model? What was the rationale? Was it to do away with the "tracking system" or were other faults perceived with the previous model?

Who instigated the change to extensions? Was it the math teachers or was it the administration (principal)?

I agree with anon@824 that having kids of all abilities in one class would be extremely challenging. I would like to know why kids with similar abilities aren't place in specific classes (all with high expectations). Too "tracky", I guess...

I have no idea whether my daughter would be in the "higher track", I do think/know we would doom our future if we dampen down our best and brightest...I see this corralling of students happening already in elementary school.

Kurt Vonnegut wrote a satirical short story on this idea of damping down excellence. "Harrison Bergeron." In HB, society has achieved equality for all...by force and by lowering people's capabilities to the most basic level possible (the only way to achieve true "equality" in skill). The agile and strong are weighted down. The intelligent have buzzing noises forced in their ears. Those with excellent vision are given lenses to distort it. And so on.

It is in society's best interest to have our best and brightest (from wherever they come) succeed. They are the future solvers of the immense problems created by those before them...

My responses:

Anonymous 9:27 - thanks for the link -- interesting article on education (the topic of the day both locally and nationally it seems).

Anonymous 9:30 - I think the Brookings article describes both sides -- I've just chosen my side! Seems like you are a case in point -- you could have handled algebra in 8th grade ... then opted against calculus (but at least had the choice)?

Abbie - I agree with all you wrote -- particularly this line: "But if the teachers are going to do an experiment on our kids (i.e. trying new curricula), then it ought to be complete (i.e. data collection and analysis)." That is all I'm asking for in our schools -- to acknowledge that some of our programs are indeed experiments, and as such, we have to have an open and objective approach to figuring out if they work. Extensions was adopted to replace tracked math in 7th grade - in which kids were placed based on some combination of a placement test and the recommendation of their 6th grade teacher into a "prealgebra" track that led to 8th grade algebra or a "regular math" track that led them to the "regular math" in 8th grade. So, yes, extensions were specifically designed to create heterogeneous classes in 7th grade -- and to provide more students with the option of taking the 8th grade honors class (the assumption was that some students who would not have been placed into the higher track could now choose to do extensions and prepare themselves for 8th grade algebra). This raises two questions for me. First, are more kids in 8th grade algebra now than there were in our earlier system (I haven't seen data on this, but anecdotally, I've heard "yes," so that is a good thing!). Second, is this the best approach to getting more kids in 8th grade algebra (e.g., this is a case in which I haven't found a single other school that uses an extensions model -- and many other schools do have more kids than we have in 8th grade algebra). Again, perhaps more kids are now in 8th grade algebra because motivated parents are pushing their kids to do extensions (and helping them learn the material, hiring tutors, etc.) -- is that, however, a good thing? I'm not sure -- given that it seems like we are potentially creating other problems. I've certainly heard from kids (and parents) that there is peer pressure in some circles to NOT do extensions (and I can imagine this being compelling -- choosing to do extra math homework?!?).

More responses:

Anonymous 7:52 - I hear from some parents/kids that extensions aren't being taught (and yes, extensions are by and large the ONLY way to get into 8th grade algebra -- certainly the most common way BY FAR). I also hear from teachers that extensions ARE being taught, and/or that they are not supposed to be taught (this is the type of self-exploration that they are expecting of kids). Again, this speaks to the need for greater clarity on this program ... and I think an evaluation of how well it is truly working for all kids.

Anonymous 7:57 - you raise an excellent point. I did a review for the math curriculum council two years ago, and, yes, kids on free/reduced lunch are UNDER-represented in 8th grade algebra. I believe that the extensions model probably does require parents who are informed about the benefits of 8th grade algebra (and that this is a necessary path to get there), and may well benefit kids who have math-savy parents and/or wealthy parents who provide tutors. I have two friends with 7th graders who say extensions is working GREAT for their kids -- one of them says her engineer husband works with their chid and the other says they pay for a tutor. This is (obviously) not what the math teachers/MS intend ... but this may well be the reality that follows from extensions. So, perhaps we've replaced "blatant tracking" with "subtle tracking" in a sense?

Rick - excellent point! I think this is a case in which districts, and obviously countries, have different views about how/when to teach math concepts. But I think this is a case in which we should NOT re-invent the wheel (which extensions clearly does) -- how about looking to some districts that are demographically similar to ours but have a greater % of their kids taking 8th grade algebra -- we could then see what they do! For example, most MSAN schools track earlier than we do (e.g., in 6th grade - when MS starts for most other schools - or 7th). And most of these districts have more kids in 8th grade algebra than we do. Thus, we think tracking is bad, so we don't do it, but schools that track have more kids in 8th grade algebra, which I think is good!

Anonymous 11:24 - thank you for your post ... which raises a number of key points. First, I think the MS years have been difficult ones for kids in Amherst for some time -- it is not a new issue for parents, and I hear your experience a lot. Second, I do think the math in the MS has gotten better with the adoption of a textbook (this year) ... and that is a good thing for our district. Third, I think extensions still is creating a lot of concern in our community, precisely for the reasons you point out (and even if these reasons are "inaccurate" -- teachers and principals and superintendents need to understand the perception). Finally, I appreciate your pointing out that a silent majority may well exist. Every week I have numerous people call me and email me expressing their sadness about the bashing I get in the Bulletin, and their support of what I'm trying to do -- people who I don't know, people I've never met. And they say they wish they could write a letter or speak out on my behalf ... but they are worried about being attacked and criticized, as I am. And I get this -- but it really speaks to the power of intimidation in our supposedly liberal community that in theory welcomes all voices ... unless you dare to say that maybe the schools aren't as good as they could be for all kids (and in fact, aren't as good as they USED to be). That isn't teacher bashing ... that is just an honest and candid recognition of what many parents are feeling. But saying that out loud -- on a blog, at a meeting, in an column -- seems to be violating a major taboo.

And even more responses:

Anonymous 8:23 - I agree that these years are difficult ones ... but I also think that kids are pretty nuanced in what they report -- so I hear a lot from parents who say "the German teacher is fabulous' or "the science teacher is amazing" -- it is NOT just kids saying "everything sucks." That suggests to me that it is more than just "the age" in that they are distinguishing quite clearly between classes and teachers in which they feel engaged and challenged and those in which they do not.

Anonymous 8:55 - I agree that the issue in our MS is far, far more than "those are difficult years" (and I believe we do have SOME teachers who can and do teach to multiple levels). But can you clarify your final point? What is impossible for teachers to do?!?

Abbie - I think I have now answered your key question -- extensions was indeed created to eliminate 7th grade tracked math (and I do think there were some perceived problems with this model -- sometimes kids were more capable of higher work than they initially demonstrated, with maturation over time, and then were "doomed" to the lower track -- so extensions was presented as a way to "buy them some more time" to get ready for algebra). I do NOT know who instigated this change ... but this is an example of a change in which I think the SC should have asked for a specific timeline and plan for evaluation of this new and innovative program. Extensions might be a great solution. Or it might not. That is why collecting and analyzing data is essential -- so we can actually have the answer to this qustion.

Budget question: is the School Committee still planning to hire an Assistant Superintendent? Is that position in the budget? At what salary?

Anonymous 9:51 - the short answer is NO -- search was failed. Read my summary of the June 2nd meeting!

writing off middle schoolers' opinions claiming they are in a "difficult age" is just an excuse for not paying this age group the attention they so deserve and need.

I agree with Catherine's opinon that middle schoolers WHEN ASKED can report on quality teaching and bad teaching. Not EVERYTHING is bad. We do our kids a disservice by NOT involving them in these discussions, and by assuming they will not be able to share worthwhile insights.

Actually, I think what's happening is not a "subtle tracking" in the middle school math program with extensions. It is an OBVIOUS tracking, only it's not visible in the classroom since the tracking is happening at home.

For a school system that claims a commitment to equity, how could such extensions be introduced, much less continue to be supported?

Actually, I think what's happening is not a "subtle tracking" in the middle school math program with extensions. It is an OBVIOUS tracking, only it's not visible in the classroom since the tracking is happening at home.

This is argument turns the idea of tracking on its head.

When implented, tracking puts some kids are in the "smart" class, while others are in the "regular" class. By grouping kids heterogeneously, ALL kids are given the opportunity to be exposed to the most challenging material and the most engaging instruction.

I wonder if one of the problems with the middle school is that it's on a trimester system but it's actual daily schedule is based on a semester system. The purpose of the trimester, I'm told, is for students to have fewer classes but more time and depth of material in each course. In high school, the students take 5 courses a trimester. My 7th grader has 8 classes and on Mondays all 8 classes meet, I think, for 42 minutes. Could this be the worst of both systems?

My responses:

Anonymous 12:32 - I think you raise a reasonable point ... we are now tracking by parent/child choice instead of by teacher choice. Maybe that is OK ... but it is still tracking.

Anonymous 1:23 - I think you wisely point out the problem with tracking. But I think there are three key issues here.

First, with extensions, it is possible that some "smart kids" (again, I don't like that term because I think all kids actually can be quite capable, if taught well) don't choose to do the extensions. These might be "smart, but lazy" kids ... or "smart kids whose parents don't understand why kids should do extra mathwork so they don't push them to do so." Thus, your quote implies that in our current extensions model we are challenging all kids ... but isn't clear to me how many kids who are capable of doing extensions opt out (and who might, in the old system, be pushed into the "higher track").

Second, we could decide that all kids are required to do extensions -- and then the class would focus on teaching and reviewing all of the material (not just teaching the extensions part at the end), and then ALL kids would have the same homework. This would prepare all kids for 8th grade algebra -- and not leave the choice up to kids (but still avoid tracking). We could call this approach "math."

One final point -- we do have tracking right now in 7th grade. The "highest" track is for 7th graders who take a placement test and move into "honors algebra" as 7th graders (thereby avoiding the issue of extensions all together). The next track is the group that has 7th grade math and chooses to do the extensions, and the next track is the group that has 7th grade math and doesn't do extensions. So, this is three tracks for 7th graders. We just don't use the word "track" and we have what looks like a pyramid -- a very small % (2 or 3) take 8th grade algebra in 7th grade, then about 35-40% do the extensions, and then a majority do 7th grade math without extensions (many other districts have roughly equal sized tracks, or "diamond" tracks with most kids in the middle model and fewer on each end). Similarly, we track in 8th grade -- the "top kids" are now in geometry (a very small class), the next kids are in 8th grade HONORS algebra, and the remaining kids are in regular math (we just skip the 8th grade regular algebra track that many districts have in favor of two high tracks and one lower track). Again, we are fully, fully tracking at all math levels in the MS.

It seems that “tracking” is a very grey area and pretty confusing.

I take it that separate classes of different abilities are not allowed? But that a heterogeneous class, where kids can take more advanced lessons within the same classroom is OK?

I guess this has all probably been discussed to death over the years…

Sooner or later kids will run into tracking – AP courses in high school or similar in college. Isn’t it really a question of when this should begin? Clearly it should not begin in kindergarten. But equally clearly it’s OK as a senior in high school. Where on the age spectrum do we think it’s OK to have separate paths for kids to pursue?

This whole issue is really critical. On the one hand we want the school system to be as level a playing field as possible – I feel really strongly about that. But on the other hand, it’s a fact of life that some kids are going to excel more than others, and they should be allowed to flourish.

This is a tough problem.

The ideal system to me is one where advanced paths exists, but that plenty of extra help is given to kids who need help to get up to those advance paths. And when I think about that I can’t help but think it all comes back to money. Small classrooms, lots of one on one teaching time – it all costs more money than we have.

It’s really depressing…

Could any of the math teachers at ARMS or ARPS explain why a regular 8th grade algebra is not a good idea -- of if they think it is a good one? Our math teachers deal with the students every day so I am interested in their perspective.

The people on your blog complaining about the extensions are right. It was busy work, and it was the math department head's idea. He was dead set against any kid getting ahead of the group. I had to PLEAD to get the 8th grade curriculum for my son when he was in 7th grade. He had to do both the regular 7th grade math course and attend the class, and then at night he did the 8th grade curriculum. I was able to also get the curriculum for his friend, so the two of them kept each other motivated. Imagine having to do both the 7th and 8th grade work? How’s that for punishment? Then in 8th grade they had a small group of 4 or 5 boys placed in the teacher resource lounge where they were supposed to be doing algebra II. Since the teacher’s aide who was supposed to supervise them didn’t, and after winter break he never returned from India, they were on their own. The math department head didn't give a damn. Before entering Deerfield Academy my son had to take a math placement test. The results showed his knowledge of algebra II were too shallow. So he had to repeat it at DA. Keep in mind he and his friend at the end of 8th grade tested out of Algebra II and were eligible to take Calculus 1 in ARHS. His friend went on to Amherst high school and took Calculus 1. So you have two kids both testing out of Algebra II and the private high school says, not good enough understanding of it, ARHS says fine, go on and take calculus. Why can't there be kids at different levels in the public school? And why is trying to get into an Ivy League College a bad thing? When I tell friends who live in other towns the kind of dialog that goes on in Amherst regarding the schools, they think I’m making it up. You can’t make this kind of stuff up. Keep up the good work Catherine. Ali Burrow.

If you don't have a math savvy parent at home, 7th grade extensions require tutoring and/or helping your child find others to help him/her. 7th grade extensions also force parents to battle with their children about doing "more" work than others in their class. The students see others in their class not doing the extensions but getting better grades. Why should they work harder, they say. A separate math class for those students ready to work at a higher level, with high expectations for all the kids in the class, is what is needed. Perhaps this new acceptance of 7th grade algebra for those students who are ready is the answer.

1:23-- "By grouping kids heterogeneously, ALL kids are given the opportunity to be exposed to the most challenging material and the most engaging instruction."

Is that a joke? This comment in the middle of a discussion of the advantages/disadvantages of extensions repeats one of the things we heard about the benefits of extensions. A statement that has no evidence of proof. There is not one shred of evidence to show that all kids are being exposed to "the most challenging material and the most engaging instruction". Actually in my home, the evidence proves the opposite. Since extensions are not taught, there is no engaging instruction of the most challenging material.

We need evidence. In its absence, I'll rely on the students experiences.

4:56 Ali Burrow, your comment made me think.

"Then in 8th grade they had a small group of 4 or 5 boys placed in the teacher resource lounge where they were supposed to be doing algebra II."

What is the boy/girl ratio for taking advanced math in the middle school? What are we doing to help girls succeed in math? Do extensions affect girls' interests or participation in advanced math?

Equity in math is not only socioeconomic or racial, it also involves gender.

I think that the observation that the extensions system simply farms the tracking of students out to the "learning conditions" in the students' home environments is a very important one. Is that really a better outcome than tracking inside the school? I know that there's some reflexive resistance that arises when this phrase is used, but I think we are in fact talking about "social justice" here.

Once again, students are natural-born critics. But they are NOT natural-born naysayers. They analyze things to death, but they have their enthusiasms like the rest of us. And they should be listened to, carefully.

I checked with my daughter about the statement in Anon 5:15's post that "since extensions are not taught, there is no engaging instruction of the most challenging material." She says that for 7th grade 2005-2006 that statement is absolutely correct.

When I even bring up the memory of 7th grade and math extensions with her, she rolls the eyes, exhales, and says she's tried to forget the whole thing.

Rich Morse

1:23-- "By grouping kids heterogeneously, ALL kids are given the opportunity to be exposed to the most challenging material and the most engaging instruction."

Is that a joke? This comment in the middle of a discussion of the advantages/disadvantages of extensions repeats one of the things we heard about the benefits of extensions.

This is a widely held educational model used throught the State in regards to tracking in general. It is not a joke. It works. It "de-ghettoizes" chronically low-tracked students. The math educational methods in Amherst may need tweaking, but again, in regards to tracking IN GENERAL it is widely accepted throught Massachusetts.

What I would like to understand is whether the material in new Math core course (regardless of the extensions option) is the same as from the "regular" math course that had been offered previously?? Or, as a couple of folks have suggested (eg anon@730), is the new Math class actually more challenging than the previous regular Math (and less challenging than the preAlgebra but with the added extensions is intended to offer the same preparation)? If the answer is no, then I'm very discouraged. If its yes, then at least it's serving some purpose (but perhaps at a cost for those who would have done well in the preAlgebra but aren't doing so well with extensions (for whatever reason)).

I don't think that it is entirely fair to compare ARMS in the last days of the Cavalier regime to what's happening there today. I too had a child there at that time and she hated it. She had been accelerating in math all through elementary school and when she got to ARMS she was completely shut down. In general, those 2 years were lost years for her as far as math was concerned. Her story was not unique. I have to say that I believe that a big reason Mr. Hayes is not the principal today is due in large part to his handling of the math program at ARMS.

This year ALL 7th graders were given the opportunity to place into the 8th grade honors algebra class. My kids are aware of about 8 kids who are in algebra, one girl who is doing some kind of combo 7/8th grade math and 2 girls who are taking geometry. One of my kids is taking the 7th grade class and she generally does not feel very challenged by the content. It seems that there is a lot of review of concepts that she learned in 5th and 6th grade. I have not heard her complain about the extensions being too easy or busywork. My son is in the 8th grade honors algebra class and he finds it challenging in a very positive way.

I would also like to respond to some of the comments I've read on other threads about the amount of reading and writing the 7th graders are doing. I can tell you that my kids, who are on different teams, have both read more than one book, have read ( and written) lots of poetry and have been required to write some pretty in depth essays. There has been much focus on the writing process, and my kids come home with papers that have extensive comments on them.

We have been pleasantly surprised, and, more than a little relieved, at the changes we see at the MS. Much if the criticism of the MS has been deserved but I think that folks need to look at the place as it is today and not keep harking back to those bad old days.

While all the 7th graders could take a test and place into 8th grade honor algebra only a few were prepped for this test in 6th grade by doing extra studying and beng given a textbook to work on over the summer. Pretty random, I think, and hopfully a practice that will not continue.

Also, I think 7th graders experience with extensions varies by the teacher -- another random factor. If a teacher is good at teaching to kids at different levels and juggling the regular math and extension, great. If not, something much less than great for the students.

Anon 8:49- My son did not get any special test prep in 6th grade nor did he get a textbook to help him over the summer. What he did get in 6th grade, along with some other kids in his class, was the opportunity to explore some very basic concepts in algebra. Why is this random? Isn't that what we're asking teachers to do? To differentiate by skill in a heterogeneous classroom? And yes- some teachers are better at this than others. My kids have had teachers who were good at it, some not so good and some who were really bad at it. Is that random? It sounds like real life to me.

Look- my point was and is that lots has changed for the better at the MS and at some point rehashing what was going on 3-5 years ago under very different circumstances gets us nowhere.

My daughter found the concept of extensions in 7th grade math frustrating. There was a huge amount of peer pressure not to do the extensions--both by members of her own grade and by members of grades above her. There also seemed to be little direct instruction relevant to the extensions (although perhaps she wasn't paying attention?) so she needed a lot of help at home. And I think her math teacher was very motivated about math and very enthusiastic, so I think perhaps the extensions just represented "too much to cover."

In contrast, her experience in 8th grade algebra has been great! Enthusiastic teacher again, challenging material, and a lot of peer buy-in to the course. Some of the material comes easy to her, other units are very challenging, but there is adequate support. It has been one of her best courses at ARMS.

I think extensions math has been around only for a few years, so I think most of the parents are talking about the current middle school experience.

I know that another issue with the extensions program was that some parents didn't understand what it was. Kids were not encouraged at home to do them and then found out to late that they would miss out on higher math. This didn't have to do with income/race either, just lack of emphasis on its importance and assuming we all knew the system.

June 9th at 7:30pm: "This is a widely held educational model used throughout the State in regards to tracking in general. It is not a joke. It works. It "de-ghettoizes" chronically low-tracked students."

Show us the other towns that use extensions please!!!! I need to know that our kids are not being used as guinea pigs in an experiment that leaves them dissatisfied, frustrated and feeling ill equipped.

I am pleased to hear that things might be changed from three years ago at ARMS in the math curriculum.

But I'd like to see a show of hands on this blog for this question:

Just how many of you out there are pleased with the writing training your child has been getting in our secondary schools? Do you believe that it is as good as the training you got in those years?

I haven't been seeing much in the way of feedback on writing, i.e. returned papers with constructive commenting from teachers on writing. I know that some children wait weeks or even months for returned papers.

Please don't think that because I think that there has been some improvement in the 7th grade math course that I support the use of the extension model.

I believe that the 05/06 year was the first year that the extension model was implemented across the entire 7th grade. The year before,the model was piloted with a smaller group as part of one of the math teacher's graduate work.

I thought then that the program was poorly conceived and the implementation, especially in that 1st year was poorly executed. And that I think is being generous. I still think it is a poorly conceived program but the implementation has improved in my opinion- based on my small sample size of 2. For example- at least now the kids have a textbook that they can reference.

How successful has this been in improving student performance? Well, I think the fact that once again ARMS did not meet its AYP goals answers that question.

To Anon 4:41

It's hard to weigh in on the subject of the writing curriculum because (and I don't mean to be snarky) there isn't much of a curriculum. My 4th grader has not had a single writing assignment that was more of a long term project (i.e. research a country and write a report) and almost no smaller writing assignments (i.e. write an essay about your favorite hobby).

I know the typical Amherst response is that writing assignments like these may be typical in Newton but are not how we do things here because of all of the economic diversity, but friends, who have same age kids, who live in diverse communities, have rigorous writing programs with long term projects, weekly writing homework assignments and lots of teacher feedback.

My middle schooler (now in the high school) did not read one complete novel the entire 2 years he was in middle school, nor did he receive one paper back with written comments or feedback on his writing. When I asked about it, I was given some explanation about the curriculum which sounded like they didn't really have specific goals that each teacher/student needed to reach. He got to high school, expected to read several novels a trimester and write frequent papers. Middle school had not prepared him at all.

My experience is that the English teachers like to think they're doing a good job at ARMS. But do they consider what is expected from the students in 9th grade and if their program is supporting the student to reaching that goal? I hope that has changed.

I never knew any ARMS student who received written papers back with feedback. I hope that has changed too.

My kids, one at HS and one graduated, were both assigned books and had papers returned with comments. They did not have the same teachers.

My responses:

Rick - I agree that “tracking” is a very grey area, and that the line between "allowing" and "not allowing" is pretty muddy. We do allow right now for tracking in 7th grade math -- some 7th graders get to move right into 8th grade algebra. But then we don't allow any other 7th graders to be in classes in which there is grouping by ability. Relatedly, we allow grouping in math, but in no other subjects in the MS. Then, in the HS, we have some grouping in most subjects (e.g., honors versus regular classes), but then we have no grouped classes in English at all (there are heterogeneous classes in English throughout the high school, even in AP English -- honors students just complete separate independent projects).

For me, I think some grouping by ability/skill makes sense -- in terms of making sure all children are challenged and we don't set impossible demands on teachers (even colleges have some tracking of classes based on skill). But I think the crucial thing is FLEXIBLE and FLUID grouping. The problem becomes when a choice that a child makes in a given year (e.g., I'm nervous about entering the HS so I am not on the honors social studies track) doesn't set his/her path (so that he/she can't rejoin an honors class if he/she wants to in a subsequent year). Similarly, a student might set out to do honors work in a class one year, and find it above his/her ability and need to drop down.

I'm not as convinced that it is money, however -- the MS classes right now are really small (an average of 17 in 7th grade, whereas my 5th grader has 26 in his class). So, if some kids in MS right now aren't getting differentiated instruction with so few kids, I don't think even smaller classes are the issue.

Anonymous 3:45 - I don't think any teachers have stepped up here, but what I've heard from teachers is that having regular 8th grade algebra is tracking -- it adds a third track (honors algebra, regular algebra, 8th grade math). That was stated at the SC meeting on October 14, 2008. Again, as I noted at the time, the distinction seems to be that we are comfortable with two tracks (high/low), but not three (high/medium/low), or (my personal preference), two (high/medium).

Ali Burrow - thanks for using your name! I hear this type of story a lot. Thank you for sharing your child's experience.

Anonymous 5:15 - this is what I hear repeatedly from parents: "If you don't have a math savvy parent at home, 7th grade extensions require tutoring and/or helping your child find others to help him/her. 7th grade extensions also force parents to battle with their children about doing "more" work than others in their class. The students see others in their class not doing the extensions but getting better grades. Why should they work harder, they say." This all raises the question, for me, of whether extensions is a better approach to 7th grade math (that supposedly avoids tracking) than our prior system. I don't have the answer, but again, I have seen no data answering this question nor have I seen a commitment in this district to asking/answering such questions using data.

My responses:

Anonymous 5:18 - I actually looked at the gender issue in 8th grade honors algebra (as part of my work on the math curriculum council). This was only one year of data, but at least in that year, girls were somewhat under-represented in that class (again, I didn't compute statistics on this, though one could, to see if this was statistically significant). But again, you raise a key question--I believe that when the SC agreed to this approach to teaching 7th grade math, it should have been with a specific timeline and plan of analysis for figuring out if this approach works for all kids. That is what I find most discouraging about our district.

Rich Morse - I hear this from a numer of kids/parents -- that extensions were not taught (maybe they are now, or maybe they are now by some teachers). I also think it is distinctly possible that our current system is LESS equitable than our old system. Right now, parents who understand the importance of 8th grade algebra will push their child to do the extensions and provide resources (tutors) if needed (presumably some of these kids would NOT have been placed into the higher track math in the old system). Other parents who don't understand the importance, or don't want to battle their kids about math homework, won't push their child to do extensions (and presumably in the old system, some of these kids would have been placed in the higher track). Again, this is where an analysis of what we are doing and its outcomes would be really, really useful.

Anonymous 7:30 - I am not sure I understand your point -- are you saying that heterogeneous classrooms in math are the best way of teaching math in 7th and 8th grade? You note "This is a widely held educational model used throught the State in regards to tracking in general." But most schools in both the US and MA do track math in 7th grade (sometimes starting in 6th grade). This includes other MSAN schools. And I hear now from parents of color that their kids are told (by peers) to NOT do extensions -- it means they ar "acting white." Again, I think this is why we need to figure out if our approach -- extensions -- is in fact better, the same, or worse than tracking (or another approach) for all kids. I don't have the answer to this because we don't have data that examines this essential question.

My responses:

Abbie - good question -- and I don't know the answer. My assumption (but I could be wrong) is that the extensions are what used to be taught in the higher level course, and that students are now given the option of doing these, and that the other material is the same. This would be a good question to ask at an upcoming SC meeting, however!

Anonymous 8:08 - I think you are right to acknowledge that the MS leadership has changed, and there may be some differences in the MS today compared to a few years ago. I do believe it is good that all 7th graders were given the opportunity to place into 8th grade honors algebra -- and it is clear that those kids really have a great experience (e.g., they avoid extensions completely and will have a very small class -- like 10 students next year -- taking geometry). But that is a very, very small number of kids who benefit in this way.

I'm also glad to hear that your kids are doing a lot of reading/writing and getting feedback. I think this points out that there is a lot of variability ... some kids (on some teams) are getting this ... others are not (from what I hear).

Anonymous 8:49 - I agree - the consistency of the MS experience seems uneven. Some kids have a teacher who really integrates extensions well ... others don't. And yes, I also heard that some kids were given a book to study to prepare for the 8th grade algebra test ... and others were not (again, this varies by school and by classroom in the elementary schools). As a SC member, this points out to me the importance of horizontal alignment across the schools (one of the reasons I was so pleased with the adoption of the Impact 1 book for all 6th graders).

Alison - thanks for your posting -- I hear from many parents about peer pressure from kids to NOT do extensions and about the need for parental help. Ironically, teachers may assume extensions are working for kids BECAUSE these kids are getting a lot of help! I"m glad to hear the 8th grade honors algebra class has been so great!

Anonymous 1:51 - Yes, I think extensions is probably 4 or 5 years old now? These are still recent experiences -- and even if they are not CURRENT experiences, I think they point to the problems with a district creating a program to teach math that avoids tracking (a program that is not used in other districts) and not making a point of collecting and analyzing data on its effectiveness.

Anonymous 1:57 - I have heard this complaint a lot as well ... and I believe the MS is getting better now at clarifying what extensions is and why it might be good for kids to do them. I am still not sure if that is adequate, however.

Anonymous 3:44 - I haven't been able to find a single other town that uses extensions to teach math.

Anonymous 4:41 - great question! And in all honesty, I hear more complaints from MS parents now about reading/writing (especially feedback on writing) than I do about math (I think adding a textbook in math really helped the math experience for many kids).

Catherine- I have to say I find it very difficult to believe that any child in a regular education classroom at ARMS is not required at some point in his/her two years to read an entire novel. I've had three kids go through ARMS on 3 different teams with 5 different English teachers. I can assure you that my kids did indeed read entire novels,plays, shorts stories and poems. And they wrote about them too.AND they got written feedback.

Kumon has recently opened a branch in Amherst - about 3 years ago. Soon, we will start to see those (primarily) elementary students reach the middle school - and they will be way ahead of their peers in terms of their grasp of basic math skills.

That's another form of tracking (parents who are concerned enough to sign their kids up for Kumon, or work on math themselves at home) - that we will have to take into consideration in the next few years. That is also a specific form of tracking that relies on parent involvement, interest in math, AND money (to pay for Kumon) and time (to take the kids to Kumon). This will further increase the gap between the haves and the have-nots.

However, it is the weak math system in the Amherst elementary schools that is forcing all the concerned parents to turn to Kumon. If the elementary school math were better, I would not have to go elsewhere.

My responses:

Anonymous 4:48 - two key points here. First, we still don't know if this program works (and as you point out, there are still AYP issues). That is why we need data. Second, having a textbook (this is the first year) is definitely an improvement.

Anonymous 8:35 - I hear this a lot too ... and I think writing feedback/instruction varies tremendously across schools, grades, and classrooms. A more consistently high quality experience (which some teachers clearly provide) would be good.

Anonymous 8:15 - I hear from current MS parents that the amount of writing, reading, and feeback varies tremendously by teacher. That is a pretty big issue in terms of making sure all kids are prepared for HS, especially when teams loop (meaning some years could have two great years of instruction while others have two very weak years).

Anonymous 10:49 - was this true when your kids were in the MS? I'm hearing now that there are big differences in teacher feedback at this school. I haven't heard this issue in the same way at all from HS parents.

What does AYP mean?

Anon 4:37

This blog chat seems to have wrapped up but to answer your question: AYP is annual yearly progress on standardized test scores, for us it is scores on the MCAS exam.

With an eye on the goal of 100% proficient scores by the year 2014, a certain amount of improvement in the proficient scores is expected each year, so it is an annual yearly progress.

I know that the middles school has made progress each year on MCAS scores but has sometimes fallen short of the amount prescribed. So, for example, if they make 6% progress but it was supposed to be 8% then they haven't met AYP.

Also as a whole school the MCAS scores are very good when compared around the state and AYP is regularly met as a whole school. It is actually only in two subgroups that the AYP is not being met.

Many schools do not have to worry about measuring subgroup's progress because they do not have enough students to have to count them as a group. You must have 40 in a subgroup, I believe, to make it count. Subgroups can include groups like low-income, special ed, english language learners, as well as different racial or ethnic categories. So, in a couple of ARMS" subgroups while there has been progress shown it has not been quite enough to meet AYP.

The funny thing about AYP is that they are not measuring the progress for one group of students, but are actually comparing entirely different groups. For example the scores of this year's 7th graders will be compared to the scores of last year's 7th graders to look for progress. I guess I don't understand how you can measure progress between two totally different groups. it might just be the makeup of the group that changed the scores. The only way to measure how the schools are doing, it seems, would be to follow one consistent group from year to year and see how they are progressing.

Thank you for your answer on AYP. The whole thing sounds very complicated. I appreciate you taking the time to explain it.

Anon 4:37

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