Strands of Mathematical Proficiency
1. Write a short personal reflection on some aspect of the executive summary and chapter one of Adding it Up. In the executive summary, I particularly found the section on the strands of mathematical proficiency interesting, as it gives a clear and concrete definition of what it means to know mathematics. In doing so, it expands the definition beyond procedural fluency to include four additional strands of proficiency. As a math leader, I will have to help other teachers to see these additional aspects of what it means to have learned mathematics. I will have to also come to terms with the fact that i mostly learned procedural fluency in school, and will have to acquire conceptual understanding, strategic competence, and adaptive reasoning myself in order to be able to teach it to my students and to help educate my fellow math teachers about it.
Furthermore, preschool children start with the ability to “formulate, represent, and solve simple mathematical problems and to reason and explain their mathematical activities. They are positively disposed to do so and to understanding mathematics when they first encounter it. For the preschool child, the strands of mathematical proficiency are especially closely knit” (p.6) As we discussed in class, as early as kindergarten we start to teach kids that it’s only about procedural fluency and the rest of their mathematical skills start to atrophy.
In Chaper 1, I particularly liked the section about research methodology. First, the study authors pointed out how both instructional decisions and research must be guided by values. In my my paper on research methodology, I propose that an author having a value-based theoretical commitment is an important part of the validity of a research project… meaning that, I contend, any research claiming to be value neutral is fundamentally flawed in terms of attempting to critically analyze and transform society. I also like Adding It Up’s focus on how “the conditions of practice make the success of any procedure contingent.” I was talking to the educator the other day about my research work, and he observed that a lot of times researchers try to import a solution they saw work in one classroom directly into another classroom, only to have it fail miserably once the researcher leaves the picture.
Third, the authors observed, it can be hard to control irrelevant variables. I see this as kind of a red herring — of course we can’t control the variables in education, and that’s okay – education practice is messy, and research can inform the work we do, but it’s always going to be a guide to be shaped in the hands of an experienced teacher. Finally, the authors contend, “information obtained from research therefore is particularly useful when it goes beyond the sought-after effects.” (p. 26). This is something that my approach to research is particularly useful at — digging deeply into what’s going on in a situation using a value-based theoretical modality in order to give researchers and practitioners new tools and frameworks to interpret reality.
2. Explore these websites: Mathematically Sane and COMET.
Mathematically Sane is a blog and resource site about reform approaches to mathematics education. Although the site hasn’t been updated in a while, I could see it as being potentially useful for educating teachers and parents about the true nature of reform mathematics. It has some guides for administrators and families that were developed by NCTM, for example. There’s also background information on the common core and some philosophy documents on teaching mathematics.
COMET is a newsletter produced by the California Mathematics Project. I’ve been on the list for the past year, and it gives regular updates on what’s going on with the State Board of Education, the Commission on Teacher Credentialing, the Common Core, and various other projects and initiatives within and outside California. The headline story for the current issue is about how the SBE has restored individual district’s ability to make decisions about placing students in Algebra 1 in 8th grade. One of the students in my class related about how parents push to have their students in high school geometry in 8th grade (perhaps to be in multivariable calculus by their senior year?) Another article that particularly intrigued me, given that I serve on the Advocacy Committee of the California Association of Mathematics Teacher Educators (CAMTE), is the article about teacher preparation and possibly requiring a mathematics pedagogy class to add mathematics to an existing multiple subject or single subject credential.
3. Think about the issues in mathematics education; choose one or two issues
that you’d like to explore in more depth. Write them down….
I’m interested in a number of issues in mathematics education:
- technology/MOOCs/calculators/computer algebra systems/khan academy for one
- gender and race in math, and how it relates to both geek identity and the notion of being good at math
- teacher preparation and what it will take in order to prepare teachers for the Common Core
- multicultural mathematics and ethnomathematics
- should we assign homework, and what place should it have in the curriculum?
4. Generate a few topics that you might be interested in exploring further in your
Field Study. Write them down……
I’ve already done a Master’s thesis, so I won’t be specifically enrolling in a field study for mathematics education. However, I’m working on a concept for a culminating project that will be a theoretical piece about taking a queer approach to mathematics disability. Right now i’ve written it up as a 10-page conference paper and have submitted in abstract form to the DC Queer Studies Symposium. I’d like to continue to work on this project throughout the summer, and coming into Fall have about 20-30 pages — and really elaborate on both the queer theory aspects, the disability studies aspects, and also connect it to issues faced by English language learners in mathematics as well.
I would also like to find a way to distill the key information from the project into something that I could present at the mini-conference that my math leadership class is putting together for May, and possibly even turn into an Asilomar workshop.