Grouping in Mathematics

Growth Vs. Fixed Mindset 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

Video Clip While you are watching the video clip, think about how tracking impacts achievement for all students.

Tracking Vs. Accessible Curriculum Homogeneous groupings ALL of the time Heterogeneous groupings most of the time/homogenous groupings sometimes High standards set for SOME students High standards set for ALL students Fixed Mindset Growth Mindset Homogeneous groupings lead to right-answer thinking and less-rich conversations Heterogeneous groupings allow for diverse perspectives, which lead to richer conversations Leads to racial/socioeconomic inequities and segregation Leads to greater racial/socioeconomic equities Leads to a lack of respect among classmates and categorization of others in negative ways Leads to the development of impressive levels of respect amongst classmates

Effects on ALL Students 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. Their findings: ALL Students from detracked classes (including students across the achievement range): Pass rates were significantly higher Passed exams a year earlier than the average student in New York State Higher scores on various achievement tests Development of growth-mindsets

Disadvantages of Ability Grouping Effects on higher-ranking students Effects on lower-ranking students Students feel pressure to always get the correct answer. Students feel classes are too fast and don’t admit they don’t understand. Students feel that they are not “smart,” if they need to grapple with a problem. Students begin to dread or hate math classes. Students given low level work and therefore achieve the lowest. Students afraid to take risks because they fear being unsuccessful. Students give up because they know they are labeled as a low-achiever.

Third International Mathematics and Science Study Collected a wide range of data of 8th grade students in 38 countries. The United States came in 19th. The United States had the most tracking. Korea, the highest ranking country in the study, had the least tracking and the most equal grouping. Countries with the least ability grouping have the highest achievement.

Ways to Make Curriculum Accessible for All Students Tiered Tasks Open-ended Tasks Small Group Instruction Projects

Changes at PS/IS 276/The Battery Park City School 2015-2016 School Year All 5th and 6th grade students are being taught in heterogeneous settings 7th and 8th grade tracked with Algebra 1 offered 2016-2017 School Year All 5th, 6th and 7th grade students will be taught in heterogeneous settings 8th grade is tracked with Algebra 1 offered 2017-2018 School Year All 5th – 8th grade students will be taught in heterogeneous settings. Algebra 1 will still be offered as an option for 8th graders

Resources Blazer, C. (2011). How Students’ Beliefs about their Intelligence Influence their Academic Performance. Information Capsule Vol 1012: Miami. http://files.eric.ed.gov/fulltext/ED536502.pdf 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. http://www.jstor.org/stable/3699404?origin=JSTOR- pdf&seq=1#page_scan_tab_contents Dweck, Carol S. (2007).  Mindset:  The new psychology of success.  New York, NY:  Random House. http://www.mindsetworks.com https://www.youcubed.org/parents/