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by Kelly Paulson, TERC

August 2014: Early Algebra at TERC

I don’t want to make any of the old jokes about “new math” and whether you’re smarter than a third grader. But you would think helping my young kids with their math homework wouldn’t be too hard for an adult with a graduate degree. But it can be. Sometimes the challenge is not that I don’t know how to add two digit numbers, but it’s that I don’t speak the same language of adding that my children speak with their teachers. “Addends” and “regroup”... what happened to “borrow” and “carry the one”? Their translations can be suspect or non-existent, and suddenly I’m missing the piece that allows me to help or at least reinforce what they’ve done at school. Once, my daughter had to “dice” a problem… dissect, illustrate, calculate, and explain. Luckily, she was able to translate that one; she’s a good listener in a consistent classroom with a consistent voice… and everyone was speaking the same language. Now, imagine being in a classroom, learning math, where you hear the same consistent, thoughtful voice for three years… the same teacher, the same language, and with this consistency you are also learning algebra.

This is happening in the Impact of Early Algebra projects spearheaded by Maria Blanton, Principal Investigator at TERC. Traditionally, elementary school math has been arithmetic, with algebraic thinking beginning at the secondary level. But Dr. Blanton and her colleagues at TERC and the University of Wisconsin Madison have been looking at how an early introduction to algebraic concepts might allow students more time to develop an understanding that would help solidify concepts in middle school and beyond. Their research is following the same students over time as they are introduced to algebra concepts prior to middle school.

Blanton’s work, funded by the National Science Foundation and US Department of Education, focuses on two lines of early algebra research. One of these lines of work, Project LEAP (Learning through an Early Algebra Progression), began in 2009 and is now starting its third iteration. The first part developed the tools necessary to teach algebra at an early age. A curriculum based on an early algebra learning progression developed by the team was created and tested with students. Still ongoing, the second piece of the project uses this curriculum to test student’s middle-school readiness for algebra after three years of researcher-led teaching in the elementary classroom.

Angela Murphy-Gardiner, Senior Research Associate at TERC and lead teacher for this ongoing project, will begin her third year with the same students exploring early algebra concepts. “I think consistency helps because I am using the same terminology from year to year, so when I say ‘organize your information’ when we are working on a function task, they know they need to start a function table to collect and organize their data,” Gardiner explains. Next year, in the sixth grade, the students will be tested, and compared to a control, to determine the impact of this early algebra curriculum on their middle school algebra success. Still over a year from wrapping up, this second iteration of the project is already showing evidence of success and statistically significant improvements in students’ understandings.

And now funding has come through for a broader, larger scale, third early algebra project that puts the teaching in the hands of the classroom teacher, not the researcher. Instead of a researcher in the classroom, teachers in North Carolina will be trained to implement the curriculum developed by Blanton and her team. The study will follow approximately 4,500 students at 45 schools in North Carolina. In this ethnically and socio-economically diverse community, 450 elementary school teachers will receive professional development throughout the year in which they implement the curriculum. The progressive intervention will take place in grades 3, 4, and 5 and students will be given a follow up assessment in grade six.  

This project not only encompasses a much larger sample population, it puts the responsibility in the hands of the classroom teachers. Ms. Gardiner is confident that the teachers will do well. She believes the curriculum is clear and easy to work with, but more importantly, she believes they are working with an enthusiastic and positive group of teachers and administrators.  The hope is that this commitment will translate to effectiveness in the classroom.

In addition to the Project LEAP line of funding, Dr. Blanton, along with her colleagues at TERC and Tufts University, was recently awarded an NSF grant for the proposal, Learning Trajectories in Children’s Understanding of Algebraic Relationships. This project is a continuation of another NSF-funded project that looks at very young students’ (K-2) understanding of functional relationships. Both projects focus on the “how” of the children’s understanding of algebraic concepts at the start of formal schooling. Researchers talk to students as they explore ideas that are the foundation for algebraic thinking. Students actively explain their thinking, and videos and written work are analyzed. Researchers are finding that even very young children – as early as Kindergarten – can talk about algebraic concepts in very sophisticated ways and seem to exhibit less of the difficulties that adolescents have with these same concepts.

When I look at the tasks that the K-2 students have been working on, the progress from the understanding of an ABAB pattern to an understanding of functions, or at least a way to think about functions, begins to make sense to me. The concepts are presented as questions to be thought through… how many legs on 4 dogs? How can we figure out how many legs on 10 dogs? The answers are not as important as the thinking students use to get to the end. Discussion is encouraged. Variables are slowly added. A language is learned.

So I will watch closely as my daughter makes an ABAB pattern with dry pasta and Cheerios as she works on a summer math calendar challenge. Right now, the language she knows is “pattern,” but someday this will translate to “rule” or “variables” or “functions.” I hope she will learn the language early and be able to translate for me.