This article focuses on the upcoming math review (K to 12), which I know is of interest to many parents (http://gazettenet.com/2010/07/22/amherst-begins-math-review-plan). I would also encourage interested readers to check out the Amherst SC meeting last night (on ACTV), in which we discussed this review for some time, as well as the summary of the scope of the review that is posted on the ARPS website (http://www.arps.org/node/1660). As we discussed at last night's meeting, the present review (as commissioned by our current interim superintendent) will include surveys of teachers (but not parents), and no comparison whatsoever to the experience in other districts, which I find concerning. In addition, the focus of this review is to see how well our curriculum align with the NCTM (National Council of Teachers of Mathematics) standards, which are somewhat controversial (they are very much in the "reform math" camp, not the "traditional math" camp -- which you can read more about at: http://en.wikipedia.org/wiki/Math_wars). That also seems to me to be less than ideal -- I would prefer, and indeed expect, that all evaluation of our curricula and programs be done using an objective lens, as opposed to the lens of a particular ideology (Steve spoke to this point at length at last night's meeting).
However, I'm very glad to hear that the Chair of the Regional SC supports a rigorous evaluation, so that we don't have to just rely on anecdotes to evaluate our programs and curricula (which has been the approach for far too long in this district). That is precisely my view, which is why I asked at last night's meeting for the review to expand to include three additional components (as specified in the evaluation policy unanimously supported by the SC earlier this year): comparison to benchmark districts, surveys of parents, and review of empirical data on the effectiveness of different curriculum. I hope that these three components will indeed be added, which would indeed help us gain a fuller understanding of the strengths and weaknesses of our current K to 12 math program.
Wednesday, July 21, 2010
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17 comments:
Fyi link
Thank you TomG for posting that link!
akab
Catherine,
The NCTM standards have been around for 25 years. Here is a good statement of the vision provided by the standards:
NCTM Vision
Can you point to something in that statement that you consider "ideological"? I'm not even sure what you mean by that word. If it's ideological to believe that all students deserve access to a curriculum that helps them develop higher-order thinking skills and a rich repertoire of problem-solving strategies, then I guess I am ideological. And proud of it.
You have advocated several times for the adoption of Everyday Math, which is a K5 curriculum designed to meet the NCTM Standards. You liked it, I believe, because of the studies that were posted on the What Works Clearinghouse. Are you now saying that you no longer support adoption of Everyday Math because it's ideological?
I don't think we need to be encouraging people to take positions in a math war. Let's just talk about what we want our kids to learn and to be able to do after they graduate from high school. The NCTM Standards articulate that very well and I think most people who read the basic principles will agree with them. It doesn't mean you are choosing a side. It just means you are thinking about teaching and learning.
It is now a common practice for school systems to use the NCTM Standards along with the state framework to shape vision and to set a high bar for mathematics teaching and learning. Keep in mind that they are standards. The whole point of standards is to provide a yardstick for measurement. That's why it's appropriate to use them when doing a program review: you measure your program against the standards.
Here is where Newton states its commitment to the NCTM Standards
Newton
and here is where Brookline presents its vision for math education, based on the Mass Framework and the NCTM Standards
Brookline
and here is where Chapel Hill posts its mathematics principles, taken directly from an NCTM document:
Chapel Hill
Nina - the NCTM has been a strong supporter of reform math, which is one view on how math should be taught. It is not the only view that is respected within the math/science community. I believe that when we undergo evaluations, they should be rigorous and objective, and thus they shouldn't start with the premise of "how well are we doing with meeting the accepted reform math standards?" but rather "how are we doing teaching math?" I believe we should evaluate the data, and then make a decision about a curriculum -- which could be our current curriculum, or Everyday Math, or Singapore math, etc. I don't believe we should ask for an evaluation to be conducted to validate the math world view that we have adopted, but rather to take a more objective and scientific approach.
Catherine,
I am curious at how you arrived at your opinion that the NCTM Standards are ideological. As you read through them, what did you see in them to lead you to that conclusion? Can you point to an example, with a specific reference to the standards themselves?
I think most people would find themselves nodding their heads as they read the standards. For example, here is what the standards say about Reasoning and Proof:
Instructional programs from prekindergarten through grade 12 should enable all students to—
• Recognize reasoning and proof as fundamental aspects of mathematics
• Make and investigate mathematical conjectures
• Develop and evaluate mathematical arguments and proofs
• Select and use various types of reasoning and methods of proof
It's not a manifesto. It's a statement of what students should be able to do. That list above looks like Mom and apple pie to me. Do you see anything there that you disagree with? Proof is at the core of mathematics. If students aren't learning about proof, they are not really learning mathematics. In my view, we need to improve in this area.
I think it would be most helpful for you to point to something specific in the standards that you find problematic. Is there something in there that we should not be asking students to do? I don't think it's helpful to try to tie the document to one faction or another and to decide by association whether you like it or not. Why not just read the document itself and respond directly to its content?
Nina - what I want, and what I have to assume you want, is an objective and thorough review. That should include the three things stated in our policy on evaluation and which I asked for: parent surveys, review of empirical data on the effectiveness of different curriculum, and comparison to other districts. Those were the changes I requested, and I hope that those changes are made. I didn't request a change in the standards used, although if you read about "math wars" (as I imagine you have done), NCTM is clearly identified as being in one "camp". But again, my big issue, as is clearly stated in my post and as I clearly stated at the meeting, is that I will be satisfied with this review as long as it includes those three additional components.
Have we tapped the experience and understanding of the many mathematics professors we have living within the town borders?
I'm wary of what we will get from surveys of parents and comparisons with other school districts.
I would like to know what professionals in the teaching of mathematics at both the secondary and higher ed level WHO LIVE RIGHT HERE think about what our schools are currently doing. Is there some consensus to reach or would such a discussion result in endless debate? (I've heard at least one math professor suggest that there should be much more teaching of statistics in high school.)
Although it sounds parochial, it's not. I'm suspicious of what constitutes "proficiency" in math as it is tested nationally, and of what is thought to be "effectiveness" in the teaching of math in the US. I think math is more than working through processes or responding to multiple choice questions.
For me, it's not about performance on tests as much as it is about teaching a deeper understanding of the beauty and relevance of math. And I think the experts about this deeper understanding live amongst us in Amherst.
Rich Morse
But is Amherst's perception about a "deeper" understanding of math consistent with the rest of the world? Does basically understanding the math to build a bridge cut it at a civil engineering firm? Or will solid math foundation cut it?
Rich,
What you describe in your last paragraph sounds exactly like the vision presented in the NCTM Standards:
"All students deserve an opportunity to understand the power and beauty of mathematics. Students need to learn a new set of mathematics basics that enable them to compute fluently and to solve problems creatively and resourcefully."
In response to your comment about teaching more statistics in high school, the ARHS math department agrees that it needs to increase and has established it as a department goal. Quite a few of our teachers are attending a week-long institute this summer toward that end. The Mass framework, the NCTM Standards, and the Common Core Standards all call for a stronger emphasis on probability and statistics throughout the K12 curriculum. We recognize that we need to do more to meet those standards.
Also, to answer your other question, there are local mathematicians on the K16 Mathematics Curriculum Council, so their input is indeed being sought.
Ms. Sanderson,
Now you are distancing yourself from the national professional organization of math teachers in the United States because they are moving more into one camp of math teaching than another? Would you have the same response to this professional organization if they were moving more into the camp you prefer?
For a school committee member to call into question such an organzation is appalling. They have been thinking about how to teach math for a lot longer than you have been thinking about how to teach anything, let alone something way outside your area of expertise.
This value laden approach to the evaluation of math programs in our districts is not going to help us get a clear sense of the data. Your judgments muddy the waters.
Of course, this is your MO, whether you realize it or not.
Nina,
How does the high school math department assess whether or not its students are meeting the standards the department has set for them (be they NCTM, MCAS, SAT or internal standards)?
How does the department assess if its classes and programs are working?
Janet McGowan
I went to the meeting on Tuesday and spoke my peace that I am concerned about NCTM as a basis for review. As it states in the survey request:
“Our goal is to have a K-12 Mathematics Program that supports the National Council of Teachers of Mathematics (NCTM)’s Process and Content Standards of School Mathematics and includes the following:”
Over the past 4 years at the ES level I have come to understand why we have moved to a heavy reform model. I feel the implementation is failing our students. From the reading in the math wars it is discussed that the originators of reform math wanted to teach math in a different way to reach a broader audience. Certainly this is an admirable goal. Upon reaching that broader audience a more traditional approached would be used to continue the education of math.
Where I think we are missing the mark is that at the ES school level we spend to much time (at least 2 years too much) doing reform math. The students need to move on to a traditional memorization approaches at least as it relates to addition, subtraction, multiplication, and division. While students of the reform method can figure out the answers to questions from the math tables it takes them, from my experience, 10 times longer to get the answer. The problem comes when these students have to move onto fractions and long division. If you have a student that takes a long time to figure out individual components of a long division problem they are going to fall far behind when given multiple problems to complete.
Now if think that it should be ok that these students will be on pace with one another consider the bigger picture. Our students don’t just complete with each other. Someday they will have to complete on a National or International arena. To be fair this issue may not be as much a problem with reform math but the Investigations curriculum used in our schools. A complete survey may flush that out.
To Anon 7:44
I was an engineer, and no, basically understanding mathematics does not cut it at any engineering firm or company I have ever worked for.
To Albert E.
I share Catherine’s concern but I don’t have it in for reform math. I want someone to prove to me that this path my two children are going down, while different from the one I went down, will not leave them behind when they compete in a larger arena. I can not stress this enough. I don’t know if reform math works. I know that all of the very smart international students I went to college with that breezed through math learned a traditional approach on steroids. They did problems over and over again. They worked very hard, harder that most American students and their edge in math was clear.
So parents like me really want an outside, honest, and complete evaluation not only that we are following our hybrid NCTM standards but that those hybrid NCTM standards are up to par when compared to other forms of teaching math.
Nina,
I would be most delighted for the math department K-12 to put on a presentation or multiple presentations that show the difference from our traditional style math to our new hybrid reform / traditional style math that we use today. I would also love to see a set of standards written in non curricular speak that shows the expectation that each student should achieve at each grade level.
Sorry for the long post, but it feels good to just get it all out there.
FYI for any parents interesting in the math program.
K-12 Math Review - Visit from Dr. Chen
Place:
Professional Development Center - Amherst Middle School
Date:
Wednesday, July 28, 2010 10:00am - 4:00pm
Schedule for Dr. Chen's Visit on July 28, 2010
10:00 - 11:30 K-16 Math Council
11:30 – 12:00 Working Lunch
12:15 - 1:00 School Committee
1:10 - 2:10 Principals
2:15 - 3:00 Community Group I*
3:00 - 3:45 Community Group II*
3:45 - 4:00 Reflections/Next Steps
*If you would like to attend one of the Community Group meetings with Dr. Chen please RSVP before July 27th to Sharon Gross at GrossS@arps.org.
Hi Michael,
I think having presentations to the public is a great idea. I know that some schools have had "Family Math Night" but I don't think it's happening at every school every year and I would like to see that. I think it's really important to do more outreach and give people a sense of what it feels like to learn math in a different way. It would enable us to have a more productive dialogue.
As for the grade by grade standards, can you tell me if this document has the kind of language you are looking for:
Elementary Math Summaries
Also, I was trying to hear what you said at the July 20 meeting, but it seems like the mike wasn't hooked up to the TV feed or something.
Nina-
I find the idea of needing a night to 'sell' the way we teach math disturbing. It won't change what happens in the classroom and it won't change what happens at home with homework. Nina seems to think the only problem with our math curriculum is that parents just don't understand or appropriately appreciate the wonderful way that math is being taught, the way that kids are invited to 'discover' math.
The problem we have faced and many families that I have spoken to is not perception, it is the very structure of math education that has been embraced by Amherst schools (with little or no input by the consumers (ie families)). In the elementary schools Investigations is used (and sometimes kids get 'challenge' math). In both cases, the approach to math education is very different from what parents were taught and since kids don't get to take home their workbooks, parents have no background to the arcane problem solving methods so they are largely unable to offer help to their children. But, perhaps, this is exactly as you'd like it- kids have to struggle and 'discover' the concepts and answers all by themselves with little or no direction.
Believe me, this problem (as viewed by many families) is not about perception, it is very much about substance.
Nina,
Your link was very helpful. That is exactly what I have been looking for. It will give me a basis to continue this discussion in person with our administration / curriculum director. I would highly recommend that everyone reads it. Please pass on the idea of a math night to whomever could make that happen.
I don't perceive it as a selling night. Certainly someone could try to use it as such. I would hope that those who put on the event would be people able to hear concerns and seriously consider modifications to curriculum based on our experiences with our students that have gone through this process. On the flip side it gives the teachers / curriculum administrators a chance to explain why we teach in this manner and order, describing what greater achievements they believe occur from this process.
As for the July 20th meeting I was speaking to the math survey criteria that describes us with math standards that fully embrace NCTM. This issue was fully addressed by the entire board later in the meeting. My comments were not only repeated but expanded on in great detail by those better informed to continue that discussion. I would recommend to anyone who is interested in the math survey to watch that meeting from about 8:40 on.
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