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.

Friday, October 22, 2010

Math: A Few Updates to The Bulletin

I know there is considerable interest in math in this district, so I was pleased to see the brief piece by Nick Grabbe on the upcoming math review in this week's Bulletin (, and in particular the publicity for the presentation of the math review by Dr. Chen on Monday, November 1st, at 6:30 pm in the middle school. But I'd like to point out a few things that I wished had been noted in this important story.

First, the piece points out the rise in 6th grade math scores, and that is indicated as evidence that the Investigations curriculum is effective. However, Investigations is a K to 5 curriculum only; our 6th graders use a new curriculum called Impact, which a number of parents (including myself) pushed for for two years. Thus, any improvement in 6th grade scores is due to the new curriculum, which was adopted last year for the first time, and not to Investigations, since 6th graders don't use Investigations.

Second, I'm surprised the story didn't mention that the 3rd grade math scores (the first math scores collected by MCAS, which follow 4 years of Investigations) in Amherst are below the state average. To be precise, only 18% of the 3rd graders in Amherst scored at the Advanced level in math, compared to a state average of 25%. That really suggests that our district is not helping kids to achieve at the highest level. However, even more concerning was the finding that 14% of the kids in Amherst scored at the warning level in math, compared to the state average of 11%. So, our district has more kids at the very bottom level than the state average AND fewer kids at the top.

Third, it is not that "some parents and School Committee members" express concern about Investigations; there has been long-standing concern about Investigations among parents AND teachers in Amherst since at least 2007 (see for the math program report which I assisted with under the direction of Jere Hochman and includes negative comments by parents and teachers about Investigations) and there is a large national debate about this curriculum. You can read about the concerns (including petitions to eliminate Investigations) across the country simply by googling "Investigations" and "math". You will find many links showing concerns. In other words, the Amherst debate isn't really an Amherst debate; it is a national debate (and frankly, a very important national debate).

Finally, and most importantly, I think the key piece of information that should have appeared in the story is not opinion - mine, parents, teachers, School Committee members - but data. Because frankly, I'm not interested in having a curriculum simply based on what some people like (whether those people are parents, teachers, SC members, etc.). I want a curriculum that works to teach math. And I've attached a link to an article reporting a random assignment study published last summer (funded by the US Department of Education) showing that Investigations was the weakest of the 4 elementary math curriculum studied ( Here's a brief summary:

Achievement Effects of Four Early Elementary School Math Curricula: Findings from First Graders in 39 Schools reports on the relative impacts of four math curricula on first-grade mathematics achievement. The curricula were selected to represent diverse approaches to teaching elementary school math in the United States. The four curricula are Investigations in Number, Data, and Space; Math Expressions; Saxon Math; and Scott Foresman-Addison Wesley Mathematics. First-grade math achievement was significantly higher in schools randomly assigned to Math Expressions or Saxon Math than in those schools assigned to Investigations in Number, Data, and Space or to Scott Foresman-Addison Wesley Mathematics. This study is being conducted as part of the National Assessment of Title I. The report cleared IES peer review on February 2, 2009.

I believe that elementary kids in Amherst deserve an excellent math curriculum that will provide them with a thorough basis in mathematics so that they can build on this knowledge in MS and HS math and science courses. If the best curriculum for our kids is Investigations, that's great -- we already own it! And I believe we all need to focus on the facts, and not ideology, and I have serious concerns about both our 3rd grade math scores (again, following 4 years of Investigations) and the results of this randomized study showing Investigations is the worst of the 4 curriculum. I really hope Dr. Chen's report can provide useful information to the district moving forward, and I hope all those interested in this topic will try to attend his presentation on November 1st.


Abbie said...

So I just quickly read the K-12 curriculum program evaluation report 2008 and Hockman's recommendations.

I still don't understand why the school district chooses to follow everything "NCTM" (Focal Points, standards). NCTM = national council for teachers of mathematics. FYI this is not a governmental body, it is a teacher's association. What are the reasons for not following the the National Mathematics Advisory Panel's standards, which by the way is a governmental body (don't confuse NCTM).

While there are similarities, clearly there are differences (see NCTM Response to National Mathematics Advisory Panel Report:

I just wonder why the NCTM is preferred?

Anonymous said...


I would agree that the Investigations curriculum is worhty of serious reconsideration.

However, I would be cautious about saying, "Thus any improvement
in 6th grade scores is due to the new curriculum" before you talk to 6th grade teachers. You might find there are other explanations.

Catherine A. Sanderson said...

My responses:

Abbie - you raise a very good question, and I have to answer honestly: I have no idea. I was on this curriculum council, and at the time, I frankly didn't know much about the broader math debate and assumed that the NCTM was a governmental body. This seems like a reasonable question. Perhaps it would be a great question to ask Dr. Chen at his presentation!

Anonymous 8:18 - good point re. teachers -- my mistake. Clearly it could be many things -- Impact, 6th grade teachers, etc. But clearly it wasn't Investigations. Thanks for raising this point I missed.

ed said...

This is all getting close to the research question that is driving me crazy -- not just what do kids in the lower grades know, but how did they learn it - via school or via parents....

At least some of the parents in town are helping teach math -- how many and to what extent? And the alleged racial gap may really be the gap between those parents who help their kids and the single parents who don't...

Anonymous said...


I'm wondering where the data is the proves your statement:

"Thus any improvement in 6th grade scores is due to the new curriculum"

Just because you think it doesn't make it so.

Anonymous said...


I really am tired of you equating single parenting to bad parenting in terms of educating their child(ren). I am a single parent and I have read to my 5 year old every night since he was born (and he knew how to read before he entered kindergarten). I have also worked on math skills with him and he can not only count to over 100, he can count to 20 and beyond in Spanish (no, I do not know how to speak Spanish - just a little that I have picked up here and there) and he can do simple addition as well.
So, please stop equating single parents with the idea that we do not care about our kids education and we do not work with them just as much, if not more, than some 2 parent families.

Anonymous said...

Catherine, while I'm not necessarily for or against Investigations, I think that one of your statements about 6th grade scores is inaccurate.

Investigations has to have an effect on 6th grade math scores because 6th grade isn't the first year these kids are learning math - and the material on the 6th grade MCAS test is not ALL new...there's a lot of material that students would have had to learn in earlier grades and build upon in 6th grade. My point is that 6th graders learned a bunch of stuff via Investigations for 5 years PRIOR to entering 6th grade and switching curriculum.

I'm not at all defending Investigations, but, again, to say that Investigations "clearly" has no effect on 6th grade scores is inaccurate.

Anonymous said...


we really need you. please say that you are running for School board again this year. (When is the election?)

Catherine A. Sanderson said...

My responses:

Ed - I think it is always difficult to tell where kids are getting instruction on math - parents, teachers, Kumon, etc. But I certainly feel that public schools need to educate ALL kids, because if that isn't happening, parents with means (education, money, connections, etc.) will supplement in ways that others can't.

Anonymous 2:48 - I answered a version of this question earlier -- my point is that since Investigations ENDS in 5th grade, 6th grade MCAS scores aren't attributable entirely to Investigations (in contrast, 3rd to 5th grade MCAS scores would be a better measure of the effectiveness of Investigations). What we can see by using these scores is that Amherst kids do worse than the state average in 3rd (as noted in my blog post), about the same as the state average in 4th (15% advanced versus 16% in state; 7% warning versus 11% in state), and better than the state in 5th (36% advanced versus 25% in state; 14% warning versus 17% in state). BUT where you really see the big jump compared to state averages is in 6th (42% advanced versus 27%; 11% warning versus 16% state). Now, there are definitely various explanations - maybe 6th grade teachers are better than 3rd & 4th grade teachers, maybe Impact is a better curriculum than Investigations, etc. But I think it is very tenuous to imply, as this article does, that Investigations (a curriculum that ends in 5th grade) is responsible for the 6th grade scores.

Anonymous 3:54 - I think you make a very important point. Thank you for adding your voice.

Anonymous 5:07 - you raise a good point - and you may be right. HOWEVER, it is very hard to prove that Investigations is a good curriculum (which the article seems to imply) based on 6th grade scores, since the 6th grade scores are presumably influenced by the 6th grade curriculum (and, as you correctly note, the 6 years of Investigations they had previously). However, what we do know is that 3rd grade scores are below state average, and this is after 4 years of ONLY Investigations, and the 4th grade scores are about state average, and this is after 5 years of ONLY Investigations. That is my concern about Nick's representation -- surely we can tell more about the influence of Investigations on math scores based on 3rd through 5th grade data than 6th grade data, but he only points on the 6th grade data.

Anonymous 6:30 - thanks for the kind remarks about my school board service. As is probably clear from my work on this blog, I'm devoting a huge amount of time to serving on the SC, including this blog, attending meetings, doing research/reading in preparation for meetings, attending subcommittee meetings, and meeting individually with parents and teachers who reach out to me with various concerns. I therefore need to really think through whether I have the time/energy to devote to the SC for another 3 years, and I therefore just haven't decided whether I can make this level of commitment to the SC for another 3 years (and I won't run if I don't believe I can make this type of commitment). The election will be at the end of March, so all candidates (and I'm sure there will be several other candidates for this seat) will have to announce by early February (6 weeks before the election). I will certainly announce my decision on my blog once I've made up my mind -- but again, this likely won't be for several months.

Anonymous said...


"maybe Impact is a better curriculum than Investigations"

It's important to note that 6th grade scores were fairly strong for many years before Impact came into play. To attribute any improved scores to Impact may be a huge mistake.


"maybe 6th grade teachers are better than 3rd/4th grade teachers"

Do you really want to throw out that divisive little tidbit?

Catherine A. Sanderson said...

Anonymous 8:54 - I think my point is pretty clear: it is quite tenuous to attribute 6th grade scores this year, or last year or in any other year, to the Investigations curriculum, since that curriculum stops in 5th grade. So, you have to attribute the 6th grade scores to something different - which, yes, could be Impact, or the quality of 6th grade teachers, or something else that would impact 6th graders in Amherst and not across the state (e.g., it can't be hormonal changes since that would impact kids across the state). If you have other ideas, feel free to share them.

ken said...

As always, you emphasize the negative in the math discussion, Catherine. You surely know that in 2009, our 5th grade MCAS scores (i.e., with Investigations) were HIGHER than 6th grade scores on both CPI and SGP. While you say the curriculum YOU pushed for is largely responsible for 6th grade scores being high last year, you NEVER say that Investigations is responsible for 5th grade scores being just as high or higher than 6th grade scores in the past. You also know that 6th grade scores were just as high with the math program in 6th grade that preceded Impact. You also know that in every year since 2006, 4th grade scores have been better than 3rd (with one exception), and 5th grade scores have been visibly better than 4th, and 6th has usually been slightly higher than 5th. You also know (because I've written it several times) that each of our subgroups improves well above the state average as they move from 3rd, to 4th, to 5th, to 6th. While you highlight the scores from 1 year to make a general point, you know that statistically, data is much more reliable as a trend over time, and the TREND since 2006 has been quite clear, which is that math as taught in Amherst steadily improves student performance as students go through the grades. While some math programs are standards-based on a grade-by-grade basis, others focus on the long term growth of conceptual understanding. This may be one reason that the study you note (an interesting one to be sure) has Investigations lower at a first grade level. I'm hypothesizing this, not stating it as fact. (About the study, you also misrepresented the data a bit in what you concluded, but we'll leave that for now.) There is also one undeniable trend that Amherst needs to pay attention to, which is that math as taught in Amherst generates inequitable results across subgroups, which is something I've never shied away from saying (both now and when I was a teacher in the system). But this is a nationwide problem, not one specifically tied to investigations, but rather to knowledge of students and teacher training.

Catherine A. Sanderson said...

Ken - I appreciate your long and detailed post. I'll just add a few points.

1. My point was not whether Impact in 6th is better than the prior math program. It is that it is tenuous to describe the 6th grade scores as caused by Investigations, which ends in 5th, as the article implies.

2. As you note, MCAS scores have risen from 3rd to 4th to 5th. However, I believe that having low 3rd grade scores (after 4 years of Investigations) is a problem. You don't seem to feel this is a problem, because you focus on the improvement. I believe it is at least plausible that you could still get this improvement with higher 3rd grade scores, which clearly other districts are seeing (so all scores would be lifted at each grade).

3. A new version of Investigations (supposedly an improved version) was implemented in Amherst 2 years ago, so the scores we are now seeing clearly represent some impact of that new curriculum. I believe you would agree that the early signs are that the new curriculum have not led to big improvements, as the scores now are worse in 3rd than they have been previously, which calls into question whether the growth we've seen in the past to above proficiency by 5th will be true for the current 4th grade cohort (in which I have a child).

4. I certainly agree that it is hard to make a definitive conclusion about the effectiveness of a curriculum based on one study. However, I continue to be surprised that there isn't a single well-done research study showing that Investigations is in fact effective. I know you believe it is effective, based on your experience as a teacher. But other teachers (including teachers in Amherst who read this blog and contact me privately) have serious concerns about its effectiveness. That's why research really is important -- this isn't about my opinion, or your opinion. This is about what objective, independent data reveals -- and again, this objective information provides no support for Investigations, and suggests that this curriculum may be less effective than others. That does concern me, as a researcher, a parent, and a SC member.

ken said...

Catherine, thanks for your reply. But I think you didn't understand a couple of my points, and I'd like to reiterate them.

First, of course I am concerned that 2010's 3rd grade scores are lower. But 3rd grade from 2006-9 was still a culmination of 3 previous years of Investigations math, K-2, and it is ONLY last year that scores fell. In addition, 2009's 3rd grade scores were quite high, using the SAME edition of Investigations that "yielded" lower scores last year. Logically, the changing factors between better and poorer performance with the SAME math program are students most obviously, and possibly teachers. That is why I keep saying that a focus on programs is a red herring and misleading, because a more complex student body will STILL be an issue regardless of math program. It just diverts attention from the probably main cause of disparate performance, and what the district does about it.

When I wrote about judging off one year, I didn't mean off 1 study, I meant generalizing a trend from one year (2010) rather than contextualizing 2010 as the last in a series of years starting in 2006 (when MCAS scores on DESE are first reported). I believe you are drawing VERY general conclusions about the overall effectiveness of the program based on just one out of many sets of data (i.e., 5 years worth of trends and figures), and even then, you are highlighting the negative without looking at all the data, even from 2010. As I've written before, I do not believe that preconceptions or philosophical preferences should inform one's analysis of data, but rather that data analysis should confirm or deny one's preconceptions. Perhaps we just disagree about this. But all along, I have not been supporting Investigations so much as trying to insist on a THOROUGH analysis of the rich data available BEFORE one's decision about the effectiveness of Investigations IN THIS DISTRICT (not somewhere else that a study was done, but studying OUR data, HERE). I think it's in the best interests of a district to do it that way, and I would hope you agree.

Catherine A. Sanderson said...

Ken - I think I agree with basically everything you write - thanks for persisting with the clarifications. I would just add one thing (and you may or may not agree with this) and that is that I'm interested in learning not only how things are working in Amherst, but how given curricula have worked in other places. I believe kids learn math in similar ways in different places, and therefore I find experiences of other districts (good or bad, with Investigations or another curriculum) useful.

Steven said...

Hi Catherine,

Just a comment about Impact Math, which is used in Newton, MA public middle schools: The Algebra curriculum (8th grade) is regarded as so weak that most of our middle school math teachers fully supplement with a different Algebra text. An estimate I've heard from a handful of 8th grade math teachers regarding how much material is taught from the Impact Math text in 8th grade: 10%.

Abbie said...

So what happened to the expected preliminary report by Dr. Chen? I went the meeting last night fully expecting a preliminary report by Dr. Chen (as POSTED on the ARPS website). Who changed the agenda?

I was already familiar with most of the material covered last night by Dr. Chen. What I expected and wanted to hear was about Amherst's Math program!

I feel cheated and feel like someone (the Administration?) is being less than open.

I want my 2 hours back from last night and I want to see that report posted IMMEDIATELY on the ARPS website. It is OUR report and we deserve to see it as soon as the Administration and faculty see it. This is not a way to treat the consumers, it breeds distrust...