Two Different Worlds

I started my Ph.D. program thinking I knew a lot about teaching and learning.  After all, I spent 7 years in a classroom, went to many professional development sessions, attended courses, and read a lot of books and articles on education.   However, having the luxury to step away from the classroom and really immerse myself in thinking about teaching and learning exposed me to a whole new world.    I realized that there was all this research out there that would have helped me when I was teaching.

Here’s an example.  Recently, I was looking through the research on algebra.  One of the things I learned after reviewing the literature was that researchers have known since the 80’s that elementary students develop misconceptions about equality that cause major problems later on in algebra.  For example, when most elementary school students see the equal sign, they view it as a signal of where to write an answer or as a direction to work out an equation.  So “5 + 3=__” becomes a direction to add 5 and 3.  They don’t see the equal sign as relating two equivalent quantities or amounts.  Therefore, when they see a number sentence like:  5 + 4 = __ + 2, they often write 9 as their answer.   Various researchers have offered teaching interventions, such as using balance beams when first introducing the equal sign, to avoid this misconception.

What amazed me was that the research community documented this problem years ago and yet, I never heard about it when I was teaching.  Now maybe my fellow teachers were secretly reading lots of journal articles and not telling me about what they were learning, but I have a feeling that I was not the only one who was unaware of the research.

Why was this work that was being conducted in universities by people who had the time and money to study these things not being relayed to the teachers who needed it?  This seemed ridiculous to me.  Imagine if doctors in hospitals weren’t using the research that scientists did in the 80s.

I’ll mention this in other posts, but I want to make it clear that this lack of communication goes both ways.  Some researchers are completely disconnected from what goes on in classrooms today.   Just as I was surprised to learn about the research world, I would imagine some of these researchers would be surprised at what they would learn if they went into a classroom today and had to teach full-time.

So why does this happen?    Why is there this gap between these two worlds?  I’d love to hear your thoughts.



5 thoughts on “Two Different Worlds

  1. michaelhfelberbaum

    I know at my mom’s school in Fairfield, CT they incorporate research from Teacher’s College in a partnership with a few professors there, though I’m not sure how it works. I’d be interested to know more about University-school, or Researcher-School partnerships and whether they’re effective at bringing best practices into the classroom. It seems to me there needs to be a good partnership in place between administration, teachers, and University researchers/Faculty to bring these worlds together.

    1. Post author

      That’s a good point. There are some great collaborations going on between universities and schools. I’ll have to write about some of those partnerships and what lessons can be learned from them in a future post.

  2. Pingback: Learning Trajectories: A research-based tool you can use right now | Bridging The Gap

  3. Ken Kosgraff

    Can you provide citations/link to studies referenced in these posts? I’d like to read up on the research myself.


  4. Nicora Placa Post author

    Hi Ken-

    Here are some citations to start with. Let me know if you would like more info.

    Kieran, C. (1981). Concepts associated with the equality symbol. Educational studies in mathematics, 12(3), 317-326.

    Knuth, E. J., Stephens, A. C., McNeil, N. M., & Alibali, M. W. (2006). Does understanding the equal sign matter? Evidence from solving equations. Journal for Research in Mathematics Education, 297-312.

    Alibali, M. W., Knuth, E. J., Hattikudur, S., McNeil, N. M., & Stephens, A. C. (2007). A longitudinal examination of middle school students’ understanding of the equal sign and equivalent equations. Mathematical Thinking and learning, 9(3), 221-247

    Baroody, A. J., & Ginsburg, H. P. (1983). The effects of instruction on children’s understanding of the” equals” sign. The Elementary School Journal, 84(2), 199- 212.

    Falkner, K.P., Levi, L., & Carpenter, T.P. (1999). Children’s understanding of equality: A foundation for teaching algebra. Teaching Children Mathematics, 6, 56-60.