In December, Ariel and Dawn hosted an information session for parents on grouping in math. This is a topic that our staff has researched and debated for the past couple of years. A number of us have been taking an on-line course with Professor Jo Boaler through Stanford University on the most current research on mathematics teaching. As a staff, we have also read Carol Dweck’s book, Mindset, which is about the role that one’s perceptions of intelligence can influence learning in surprising ways.
Students’ academic success may be influenced not only by their actual ability, but also by their beliefs about their intelligence. Studies have found that students enter a classroom with one of two distinct conceptions of their intellectual ability: some students believe their intelligence is expandable (growth mindset), while others believe their intelligence is a fixed trait (fixed mindset). A review of the research suggests that students with growth mindsets outperform their classmates who hold fixed mindsets. In addition, the adoption of a growth mindset may decrease or even close achievement gaps. —Christie Blazer
As a result of this study, we have refined our understanding of the implications of grouping in mathematics and have reaffirmed our commitment to heterogenous mathematics instruction. Jo Boaler talks about the implications of grouping and the role of mindset in this video clip. (You can search youtube for more videos by Professor Boaler on this topic. These video clips are part of the course of study in which the teachers and I are participating.) In addition to Dr. Boaler’s work, we have found several other important research studies on this topic.
Carrol Burris from Southside High School in New York, with Columbia professors Jay Heubert and Hank Levin, conducted a study of a detracking innovation in mathematics. They found that ALL Students from detracked classes (including students across the achievement range) benefitted from heterogenous classes. Their pass rates were significantly higher, they passed exams a year earlier than the average student in New York State, they had higher scores on various achievement tests, and they developed growth-mindsets.
Research has also shown that tracking has negative impacts on high and low achieving students. High achieving students feel pressure to always get the correct answer, often feel that classes are too fast and students don’t want to admit they don’t understand something. If students need to grapple with a problem, they can feel that they are not “smart.” As a result, students begin to dread or hate math classes. Lower achieving students are also negatively impacted by tracked classes. In lower tracked classes, students are given low level work and therefore fail to achieve at standard level. Because they know they are labeled as low-achieving, students give up. We don’t want these outcomes for any of our students.
Rather than sorting students into math tracks, we offer an accessible curriculum that provides challenge for all learners. Our teachers use heterogenous (mixed) groups most of the time, with some small groups being taught in homogenous groups. Heterogeneous groupings allow for diverse perspectives, which lead to richer conversations and achievement of high standards for all students. As an added bonus, accessible structures lead to greater racial/socioeconomic equities and the development of respect among classmates.
Features of accessible curriculum at 276 include tiered tasks in which teachers pose problems that have multiple levels of challenge embedded in them, small group instruction and open-ended tasks.
So how does this impact our scheduling and programming? We continue to provide and refine our program in grades K through 8. This program teaches big mathematical ideas through context rich problems, games, and discussion. We continue to offer Algebra 1 in 8th grade which culminates in a Regents exam. Students are selected for Algebra 1 through consultation with students and parents as well as an assessment of mathematical work habits, confidence and skill as evidence in state test scores, math grades, and teacher assessments.
A more detailed explanation of our math curriculum, a summary of Common Core Learning Standards in mathematics, the powerpoint that Ariel and Dawn presented to parents, and other math resources, can be found on our school website.
Blazer, C. (2011). How Students’ Beliefs about their Intelligence Influence their Academic Performance. Information Capsule Vol 1012: Miami.
Boaler, J. (2016). Mathematical Mindsets: Unleashing Students’ Potential Through Creative Math, Inspiring Messages and Innovative Teaching. Jossey-Bass: San Francisco.
Boaler, J. (2009) What’s Math Got To Do With It? How Parents and Teachers Can Help Children Learn to Love Their Least Favorite Subject. Penguin: New York.
Burris, C.C., J.P. Heubert and H.M. Levin (2006), Accelerating Mathematics Achievement Using Heterogeneous Grouping. American Educational Research Journal, Vol. 43, No. 1, pp. 105-136.
Dweck, Carol S. (2007). Mindset: The new psychology of success. New York, NY: Random House.