Boaler, 2006.  “How a Detracked Mathematics Approach Promoted Respect, Responsibility, and High Achievement”.   Theory Into Practice, 45:1, 40-46

This article is about a high school math program with high and equitable math achievement, where mixed-ability approaches led to “higher overall attainment and more equitable outcomes”.  The students in this study developed “extremely positive intellectual relations” with peers across culture, social class, gender, and attainment “through a collaborative problem-solving approach”.

The article describes a problem solving approach that was used ad the school and that enables these outcomes.  The problem solving approach (“complex instruction”) involved “additional strategies to make group work successful”.  The author identifies seven factors: “The first four (multidimensional classrooms, student roles, assigning competence, and student responsibility) are recommended in the complex instruction approach; the last three (high expectations, effort over ability, and learning practices) were consonant with the approach and they were important to the high and equitable results that were achieved.”

Ingredients in the approach:

(1) Multidimensionality:  In some classrooms success is about “executing procedures correctly and quickly”.  Here, success requires a range of abilities where “no one student ‘will be good on all these abilities’ and … each student will be ‘good on at least one'”.  Giving students “group-worthy problems”: “open-ended problems that illustrated important mathematical concepts, allowed for multiple representations, and had several possible solution paths (Horn, 2005).”  Students were able to identify: “asking good questions, rephrasing problems, explaining well, being logical, justifying work, considering answers, and using manipulatives” as contributing to success in mathematics.

This breadth was key: that there are multiple paths to an answer, with interaction and explanation central to the work.

(2) Roles: “facilitator, team captain, recorder or reporter, or resource manager”.  If each student has something important to do in the group, they are needed for the group to work.  The teachers reinforced the centrality of each role by pausing to ask facilitators to help with answer checking, etc.  This helps with the reliance of students on each other.

(3) Assigning competence: “public, intellectual, specific” feedback that is also relevant can lift students up.  This can reinforce the breadth of contributions that are valued.  I suppose I can imagine naming that a student has done a great job questioning how the problem worked or digging deeper into the underlying concept.  Specificity is important so that students know what is being praised.

(4) Student responsibility: creating responsibility for each other’s learning, and taking that seriously by “rating the quality of conversations groups had”, or giving “group tests” (this comes in multiple flavors).  In one version of a group test, the students work through the test together, but write it up individually, and the instructor grades only one of the individual write-ups (at random).  That will then be the grade on the test for all of the students in the group.  Another way to create inter-student responsibility is to ask a follow up question to one student in the group, and if they can’t answer it, give the group more time to talk together before returning to that same student with the question.

Justification and reasoning were also centered.  They emphasized to students the responsibility “to help someone who asked for help, but also to ask if they needed help”.

(5) High expectations: complex problems with high-level follow-up.  “Teachers would leave groups to work through their understanding rather than providing them with small structured questions that led them to the correct answer”.

(6) Effort over ability: math success is about hard work and continuing to try.  This message needs to come through.

(7) Learning practices: point out the process of what students are doing (things like fully formulating a question that they want to ask, or thinking about whether their answer is reasonable).

Outcome:

Relational equity: this was a learning outcome of being in the classroom, where students developed respectful relationships.

For more on Complex Instruction, see: