{"id":175,"date":"2019-07-18T11:20:02","date_gmt":"2019-07-18T15:20:02","guid":{"rendered":"https:\/\/blogs.harvard.edu\/siams\/?p=175"},"modified":"2019-07-18T12:55:56","modified_gmt":"2019-07-18T16:55:56","slug":"notes-on-how-a-detracked-mathematics-approach-promoted-respect-responsibility-and-high-achievement","status":"publish","type":"post","link":"https:\/\/archive.blogs.harvard.edu\/siams\/2019\/07\/18\/notes-on-how-a-detracked-mathematics-approach-promoted-respect-responsibility-and-high-achievement\/","title":{"rendered":"Notes on “How a Detracked Mathematics Approach Promoted Respect, Responsibility, and High Achievement”"},"content":{"rendered":"

Boaler, 2006. \u00a0“How a Detracked Mathematics Approach Promoted Respect, Responsibility, and High Achievement”. \u00a0\u00a0<\/span>Theory Into Practice, 45:1, 40-46<\/span><\/p>\n

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”. \u00a0The students in this study developed “extremely positive intellectual relations” with peers across culture, social class, gender, and attainment “through a collaborative problem-solving approach”.<\/p>\n

The article describes a problem solving approach that was used ad the school and that enables these outcomes. \u00a0The problem solving approach (“complex instruction”) involved “additional strategies to make group work successful”. \u00a0The 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.”<\/span><\/p>\n

 <\/p>\n

Ingredients in the approach:<\/p>\n

(1) Multidimensionality: \u00a0In some classrooms success is about “executing procedures correctly and quickly”. \u00a0Here, 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'”. \u00a0Giving students “group-worthy problems”: “open-ended problems that illustrated important mathematical concepts, allowed for multiple representations, and had several possible solution paths (Horn, 2005).” \u00a0Students 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.<\/p>\n

This breadth was key: that there are multiple paths to an answer, with interaction and explanation central to the work.<\/p>\n

(2) Roles: “facilitator, team captain, recorder or reporter, or resource manager”. \u00a0If each student has something important to do in the group, they are needed for the group to work. \u00a0The teachers reinforced the centrality of each role by pausing to ask facilitators to help with answer checking, etc. \u00a0This helps with the reliance of students on each other.<\/p>\n

(3) Assigning competence: “public, intellectual, specific” feedback that is also relevant can lift students up. \u00a0This can reinforce the breadth of contributions that are valued. \u00a0I 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. \u00a0Specificity is important so that students know what is being praised.<\/p>\n

(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). \u00a0In 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). \u00a0That will then be the grade on the test for all of the students in the group. \u00a0Another 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.<\/p>\n

Justification and reasoning were also centered. \u00a0They emphasized to students the responsibility “to help someone who asked for help, but also to ask if they needed help”.<\/p>\n

(5) High expectations: complex problems with high-level follow-up. \u00a0“Teachers would leave groups to work through their understanding rather than providing them with small structured questions that led them to the correct answer”.<\/p>\n

(6) Effort over ability: math success is about hard work and continuing to try. \u00a0This message needs to come through.<\/p>\n

(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).<\/p>\n

 <\/p>\n

Outcome:<\/p>\n

Relational equity: this was a learning outcome of being in the classroom, where students developed respectful relationships.<\/p>\n

 <\/p>\n

For more on Complex Instruction, see:<\/p>\n

\n
\n
\n

Cohen, E. (1994). Designing groupwork. New York: Teachers College Press.<\/p>\n

\n
\n
\n

Cohen, E., & Lotan, R. (Eds.). (1997). Working for equity in heterogeneous classrooms: Sociological the- ory in practice. New York: Teachers College Press.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Boaler, 2006. \u00a0“How a Detracked Mathematics Approach Promoted Respect, Responsibility, and High Achievement”. \u00a0\u00a0Theory 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”. \u00a0The students in this study developed “extremely positive intellectual relations” […]<\/p>\n","protected":false},"author":8032,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[157887,1010],"tags":[],"class_list":["post-175","post","type-post","status-publish","format-standard","hentry","category-learning-and-teaching","category-math"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p7E5LF-2P","jetpack-related-posts":[{"id":32,"url":"https:\/\/archive.blogs.harvard.edu\/siams\/2017\/08\/25\/reading-student-learning-objectives-and-mathematics-teaching\/","url_meta":{"origin":175,"position":0},"title":"Reading “Student learning objectives and mathematics teaching”","author":"siams","date":"25 August 2017","format":false,"excerpt":"I am working to write learning objectives for multivariable calculus this Fall. This article helped distinguish between overarching goals (that students are able to fit the math in the course into a greater understanding of math and of the world) and the learning objectives, of what I hope students will\u2026","rel":"","context":"In "Learning and teaching"","block_context":{"text":"Learning and teaching","link":"https:\/\/archive.blogs.harvard.edu\/siams\/category\/learning-and-teaching\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":173,"url":"https:\/\/archive.blogs.harvard.edu\/siams\/2019\/07\/18\/reading-high-school-algebra-students-busting-the-myth-about-mathematical-smartness-counterstories-to-the-dominant-narrative-get-it-quick-and-get-it-right\/","url_meta":{"origin":175,"position":1},"title":"Reading “High School Algebra Students Busting the Myth about Mathematical Smartness: Counterstories to the Dominant Narrative \u201cGet It Quick and Get It Right\u201d”","author":"siams","date":"18 July 2019","format":false,"excerpt":"Dunleavy 2018, \"High School Algebra Students Busting the Myth about Mathematical Smartness: Counterstories to the Dominant Narrative \u201cGet It Quick and Get It Right\u201d\". \u00a0Education Sciences. I'm reading a paper about a high school Algebra I course that uses the principles of \"complex instruction\" (which I still need to look\u2026","rel":"","context":"In "Learning and teaching"","block_context":{"text":"Learning and teaching","link":"https:\/\/archive.blogs.harvard.edu\/siams\/category\/learning-and-teaching\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":226,"url":"https:\/\/archive.blogs.harvard.edu\/siams\/2020\/06\/05\/notes-on-worldmath-curriculum-fighting-eurocentrism-in-mathematics\/","url_meta":{"origin":175,"position":2},"title":"Notes on: “Worldmath Curriculum: Fighting Eurocentrism in Mathematics”","author":"siams","date":"5 June 2020","format":false,"excerpt":"SE Anderson, 1990: \"Worldmath Curriculum: Fighting Eurocentrism in Mathematics\". \u00a0The Journal of Negro Education Section one: \"A few grim statistics\" The manuscript starts with \"A few grim statistics\", looking forward to 2000 and to 2010 and providing numbers about low numbers of Black, Latino, and Native American scholars receiving PhDs\u2026","rel":"","context":"In "Learning and teaching"","block_context":{"text":"Learning and teaching","link":"https:\/\/archive.blogs.harvard.edu\/siams\/category\/learning-and-teaching\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":83,"url":"https:\/\/archive.blogs.harvard.edu\/siams\/2018\/03\/03\/the-vector-calculus-bridge-project\/","url_meta":{"origin":175,"position":3},"title":"The vector calculus bridge project","author":"siams","date":"3 March 2018","format":false,"excerpt":"Reading about \"The vector calculus bridge project\" (Tevian Dray and Corinne Manogue at Oregon State). http:\/\/math.oregonstate.edu\/bridge\/talks\/OSU.pdf http:\/\/physics.oregonstate.edu\/~tevian\/bridge\/papers\/FEdgap.pdf Their takeaways: * key calculus idea: the differential (not limits) * key derivative idea: rates of change (not slopes) * key integral idea: total amounts (not areas\/volumes) * key curves\/surfaces idea: \"use what\u2026","rel":"","context":"In "Math"","block_context":{"text":"Math","link":"https:\/\/archive.blogs.harvard.edu\/siams\/category\/math\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":88,"url":"https:\/\/archive.blogs.harvard.edu\/siams\/2018\/03\/05\/calculus-made-easy\/","url_meta":{"origin":175,"position":4},"title":"Calculus made easy","author":"siams","date":"5 March 2018","format":false,"excerpt":"S.P. Thompson.\u00a0 Calculus made easy: Being a very-simplest introduction to those beautiful methods of reckoning which are generally called by the terrifying names of the differential calculus and the integral calculus. (1914). \u00a0 It is interesting to take a look at this 1914 approach to calculus. \u00a0","rel":"","context":"In "Math"","block_context":{"text":"Math","link":"https:\/\/archive.blogs.harvard.edu\/siams\/category\/math\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":81,"url":"https:\/\/archive.blogs.harvard.edu\/siams\/2018\/01\/03\/grading\/","url_meta":{"origin":175,"position":5},"title":"Grading!","author":"siams","date":"3 January 2018","format":false,"excerpt":"I'm reading Effective Grading: A Tool for Learning and Assessment in College, by Barbara Walvoord and Virginia Johnson Anderson. To think about grading, they emphasize that building learning objectives is core to the process.\u00a0 They break these into a few categories: the vocabulary and content and concepts that students should\u2026","rel":"","context":"Similar post","block_context":{"text":"Similar post","link":""},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]}],"_links":{"self":[{"href":"https:\/\/archive.blogs.harvard.edu\/siams\/wp-json\/wp\/v2\/posts\/175","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/archive.blogs.harvard.edu\/siams\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/archive.blogs.harvard.edu\/siams\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/archive.blogs.harvard.edu\/siams\/wp-json\/wp\/v2\/users\/8032"}],"replies":[{"embeddable":true,"href":"https:\/\/archive.blogs.harvard.edu\/siams\/wp-json\/wp\/v2\/comments?post=175"}],"version-history":[{"count":4,"href":"https:\/\/archive.blogs.harvard.edu\/siams\/wp-json\/wp\/v2\/posts\/175\/revisions"}],"predecessor-version":[{"id":183,"href":"https:\/\/archive.blogs.harvard.edu\/siams\/wp-json\/wp\/v2\/posts\/175\/revisions\/183"}],"wp:attachment":[{"href":"https:\/\/archive.blogs.harvard.edu\/siams\/wp-json\/wp\/v2\/media?parent=175"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/archive.blogs.harvard.edu\/siams\/wp-json\/wp\/v2\/categories?post=175"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/archive.blogs.harvard.edu\/siams\/wp-json\/wp\/v2\/tags?post=175"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}