Tag Archives: research

The “Math Wars” still rage on

What amazes me about working in schools is that when I walk into one I am immediately transported back to being a student.  The clothes may be different and the hairstyles may have changed, but in the over twenty-five years that has passed since I was a student in an elementary school the model for teaching math still looks very similar in a lot of classrooms.

The teacher stands at the board (maybe now it’s a smart board), models an algorithm and the students practice it at their desks.  Now I’m not saying that this happens in every school.  I’ve had the chance to visit classrooms that use very different approaches and I like to think that when I was a teacher, I pushed for an inquiry-based way of teaching as much as I was able to at the time.

But it’s perplexing to me that 25 years of research haven’t been able to change the traditional model in a lot of schools.  Imagine if the hospital I went to 25 years ago still used the same methods today.

However, after reading the recent op-ed piece in the New York Times that argues against math education reform, I see why it is so hard to enact change.   There are still many people who don’t buy into new methods of teaching math, hence the so called “math wars.”   The fact that this debate between traditional and reform methods of teaching still wages on is shocking to me because we know that our traditional ways of teaching are failing lots of students.

After reading the piece in the Times, you should check out Professor Keith Devlin’s thoughtful paragraph- by-paragraph critique of the article.   It makes a number of good points that I won’t rehash here.

The thing that bothered me most about the op-ed was that there was no connection to what we know about how students learn.  There is no attention given to what the research says about student learning.   There has been plenty of work (see the references at the end for some of it) that demonstrates that students learning math in reform-based classrooms outperform students in traditional classes and these students report stronger motivation and interest in math.  What’s more, the reform approach has been shown to be successful with students of diverse backgrounds.

It just doesn’t make sense to me to keep doing what we’ve been doing and expecting different results.

What do you think?

Want to know more? Check out some of the research below.

Boaler, J. (2002). Experiencing school mathematics: Traditional and reform approaches to teaching and their impact on student thinking. Mahwah, NJ: Lawrence Erlbaum Associates, Inc.

Knapp, M. S., Adelman, N. E., Marder, C., McCollum, H., Needels, M. C., Padillia, C., Shields, P. M., Turnbull, B. J., & Zucker, A. A. (1995). Teaching for meaning in high poverty schools. New York: Teachers’ College Press.

Silver, E. A., & Stein, M. K. (1996). The QUASAR project: The revolution of the possible in mathematical instructional reform in urban middle schools. Urban Education, 30, 476–521.

Van Haneghan, J. P., Pruet, S. A., & Bamberger, H. J. (2004). Mathematics reform in a minority community: Student outcomes. Journal of Education for Students Placed at Risk, 9(2), 189–211.

How do you know? Part II

In a previous post, I talked about why it might be important to ask a student “How do you know?” when they give an answer to a problem.  What I neglected to talk about was the research that supports this recommendation.

Luckily, Education Week recently published an article about several research studies that claim asking students for explanations can deepen their understanding.

Although the research mentioned does not talk specifically about learning math, it does lend support to the idea that asking students for explanations is important.  Furthermore, one study suggests that asking for an explanation focuses a student’s attention on what the underlying concept is as opposed to other aspects of the task.

What I did not see addressed in the research presented was how we can better foster explanations in our students.   It cannot be enough to simply ask them for explanations or to focus their attention on figuring out how something works.  It seems to me that we need carefully designed tasks that allow them to develop an understanding of why something works so that they can explain it.

Asking for an explanation is a good suggestion, but what do we do when students can’t explain?  I’d love to hear your thoughts.

Want to know more?

Access the article (which includes links to the accompanying research papers) here.

My Summer Reading List


Ever since I was a child, the summer was my favorite time of year.  One reason was because it allowed me uninterrupted blocks of time to read.  Even today, I keep a list of books I plan to read over the summer.  Since Memorial Day is around the corner, I thought I would share some of the books I have on my summer reading list that relate to research and education.

What’s Math Got To Do With It?  How Parents and Teachers Can Help Children Learn To Love Their Least Favorite Subject by Jo Boaler

I had the opportunity to hear Jo Boaler speak about her research at a conference this year.  A professor of math education at Stanford University, she researches mathematics teaching and learning.  I’m interested to read about how her research informs the solutions she proposes for improving math education.

How Children Succeed:  Grit, Curiosity and the Hidden Power of Character by Paul Tough 

In my last blog post, I talked about the research on grit.  This book explores the importance of character traits like grit and how to promote them in children.  While it’s not specific to mathematics, I’m interested to learn more about why some students succeed and think about how I might apply this to teaching and learning mathematics.

Knowing and Teaching Elementary Mathematics: Teachers’ Understanding of Fundamental Mathematics in China and the United States by Liping Ma

This is the only book on the list that I already read but I think it’s worth a reread.  Liping Ma researched the differences between teachers in China and the US and she reports on what she observed.   When I first read the book, I was amazed by how the Chinese teachers understood elementary mathematics in a profound and deep way.  I want to go back and take a deeper look at how these teachers thought about teaching specific concepts.

I’m excited to read these books (hopefully while sitting on the beach somewhere) and I’ll be sure to report back on what I learn after I read them.

What’s on your summer reading list?

Learning Trajectories: A research-based tool you can use right now


In an earlier post, I talked about the gap between the work being done by researchers and the work being done by teachers in classrooms.  Today, I’d like to talk about a resource that I think is a good example of a tool that connects research and practice.

The Common Core Standards have received a lot of attention lately.   I often struggle when trying to unpack the Standards in order to develop a lesson.  A research team from NC State has created an interactive tool, available at http://www.turnonccmath.net/, which I have found very useful in designing lessons.  The researchers developed 18 learning trajectories for the K-8 Common Core Standards for Mathematics.   These learning trajectories describe how students develop an understanding of a particular concept, or set of concepts, over time.

The hexagon map allows you to click on one of the trajectories or on an individual standard and get detailed information about how students might move from prior knowledge and informal ideas to sophisticated understandings of various concepts.  Also included throughout are common student misconceptions and a variety of models and representations that have been shown to foster particular understandings.   What I love about the trajectories is that they include the research that was used to build them.

So how do I use them?  Recently, I needed to prepare a lesson for fourth graders on angles so I went to the site and clicked on the Shapes and Angles Trajectory.  I was able to view suggested activities, such as the angle game where students stand and follow directions to rotate a half turn or quarter turn.  I also read about common student misconceptions, such as the fact that students sometimes think that an angle with longer rays is larger than an angle with shorter rays, and viewed questions that assess this misconception.   The references were also included in case I wanted to go back to some of the original papers and explore any of the ideas further.

Of course, it wasn’t the only resource I used when I was preparing the lesson.  I used my prior experience of teaching angles and other resources I have collected over the years.  But it was nice to have place to go that summarized the major research in a way that allowed me to think about how the students might develop a concept and the challenges they might face along the way.

I’d love to know of any resources you use that connect research and teaching.