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.

The second approach to conceptual understanding is an effort to challenge students with material they may not yet know how to solve, material just beyond their reach.  Hiebert and Grouws label this approach ‘Work and wrestle’.  Here’s the Marshall Memo again:

  • Teachers should pose problems that are just beyond what students can handle – they have most of the prerequisite skills, but something extra is needed.
  • The teacher should resist the tendency to jump in and help when students show signs of uncertainty.
  • Students should be asked to present their solution strategies for peer review of mathematical validity.

Hiebert and Grouws’ ‘Work and wrestle’ approach is of particular interest and is relevant to the Quantile Framework for Mathematics.  The Quantile Framework places both students and math skills and concepts on the same developmental scale, allowing us to identify both prerequisite and impending skills for any skill with the  Quantile Framework taxonomy of math skills and concepts.  This becomes especially actionable when a teacher has access to a student’s current mathematical level through his Quantile measure.  Knowing the student’s Quantile measure allows a teacher to identify gaps in a student’s learning and then target that student at just the right level – with the prerequisite skills essential to the current lesson.

But the teacher can do more than that.  Knowing a student’s current level also allows a teacher to target a student at the right level of challenge, to apply Hiebert and Grouws ‘Work and wrestle’ approach.  A teacher may target a student with an impending skill that may be just slightly out of reach, but one where the student has the necessary prerequisite skills.

Quantile Framework tools, like the Quantile Teacher Assistant, make that task even easier by allowing teachers to choose both the state standard they will be teaching and the range of the students they wish to target.  For students at a higher level – students needing enrichment activities – teachers may choose skills and concepts just ‘beyond what students can handle’ and then match them to resources and work at that level.  Doing so not only introduces them to the new concepts and skills, but may deepen and enrich their understanding of the skills they currently possess. 

If you have not yet tried Quantile Teacher Assistant, be sure to give it a try.

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