Targeting for Success in Math

Over at Scholastic’s Math Hub, Carolyn Kaemmer has an interesting interview with Harvard psychologist,  Dr. Jon Star on conceptual understanding in math.  In the interview, Dr. Star tackles the controversial distinction between ‘knowing versus doing’ in mathematics, e.g. does the math student really understand what they’re doing or just following a process.  Star argues that a student’s math performance can, in fact, be determined through various modes of assessment, including multiple choice tests, though he qualifies his argument with the requirement that the assessment prompts need to be carefully designed.

The Quantile Framework is directly relevant here.  Unfortunately, assessments often fail to inform classroom teachers of their students needs or of their progress in mathematical development.  When summative assessments offer a Quantile measure for the test-taker, however, the teacher has information that is instructionally actionable.  The Quantile Framework for Mathematics helps the educator to determine the material that various students in the classroom are ready to learn when the Quantile measure of the student closely matches the Quantile measure of the skill or concept. When such a match occurs, students will perform more successfully and develop more confidence in their mathematics ability. (more…)

Work and Wrestle: Targeting Students with the Quantile Framework for Mathematics

Hat tip to Marshall Memo for pointing to the latest edition of Better for James Hiebert and Douglas Grouws’ article, ‘Which Instructional Methods Are Most Effective For Math?’ (subscription required).  Hiebert and Grouws argue  that when it comes to teaching math skills and concepts, there are a number of essential elements in ensuring students gain conceptual understanding of the skills and concepts being taught.

First, teachers should continually draw relationships between what is being taught and past material covered.  Here’s the Marshall Memo summarizing what Hiebert and Grouws label the ‘Work and talk’ approach:

  • Examining relationships among facts, procedures and ideas within a lesson and across lessons.
  • Exploring reasons why procedures work as they do.
  • Solving problems using different procedures and then looking at similarities and differences between them. (more…)
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