Minds On Mathematics Book Study

In Chapter 3, Hoffer takes us through the importance of challenging tasks, and what a challenging task looks like in the workshop model. She offers up 3 key beliefs (Hoffer, p. 35):

  • Understanding, not coverage, ought to be our goals as teachers.
  • Challenging tasks generate and demonstrate an understanding.
  • We need to devote out class time to making meaning of those juicy tasks to cultivate comprehension.

In theory, these sound great. I want  my classroom to be filled with rich, meaningful tasks that get kids thinking and understanding. I want practice to be secondary, and easy for my kids because they already know how to do the work. Hoffer says that as a facilitator of the workshop, the job of teachers is to ask good questions, promote connections to prior knowledge, and encourage conceptual thinking rather than to rescue students when they begin to struggle by simplifying problems or offering algorithms to follow (p. 39).

Wow. Again, great. How do I do this? I’m a full-time teacher. I don’t have time to reinvent the wheel and redo every single assignment I’ve ever made. I am reading this book for practical strategies on how to create a workshop model in my classroom, and thankfully, Hoffer provides them.

  1. Find better tasks if yours stink. 😉
  2. Change the learning tasks by changing the order in which you give assignments. If all of the challenging tasks are in the back of a chapter in a book, they might get skipped because of time. Move them to the beginning of a unit or learning target — save the easy stuff for homework and additional practice.
  3. Modify the assignments you already have by:
  • increasing complexity
  • introducing ambiguity in questions
  • synthesizing strands of mathematics
  • inviting conceptual connections
  • require explanation and justification for answers
  • propose solutions that reveal misconceptions and common errors

Keep Bloom’s Taxonomy in mind when changing what you’ve got.

My favorite chapter so far has to be chapter 4, which is all about creating a community in your classroom. As teachers, we all know what “creating community” means, and I personally believe it to be an overused term in our profession, but through this book, I’ve been given a better definition, and one that I feel that I can better work towards.

” A learning community is a culture, not a structure. What matters most is not how we arrange the tables and chairs or assign the groups, but how we create that invisible classroom landscape the provides intellectual safety and camaraderie, promotes serious academic pursuit, and celebrates the acuity of complex content” (p. 50).

Basically, a community is one that supports the learning of others, not just one that has fun together. What good will it do to have fun together if there’s no learning happening too?

I love this line, also from page 50: “all students can and should see each other as allies on their learning journey.” School needs to be a place where it’s cool to be smart, cool to be engaged in your work, and cool to try even if you aren’t sure of yourself and your thinking. And, it needs to be a place where it’s cool to help others when they struggle, not mock classmates behind their backs.

There are ways to create this community. Hoffer makes the following suggestions:

  • develop a vision and work purposefully toward said vision by establishing short and sweet expectations and demonstrating confidence in the learning and work of all students and building relationships with individual students (intention)
  • emphasize opportunities for learners to co-create [their norms, for example, the norms of group work] and promote discourse (interdependence)
  • balance all socioemotional forces as they shift and change by holding all students accountable, providing meaningful consequences, giving immediate feedback to students, facilitate and encourage self-reflection and monitoring (homeostasis)

There are plenty of examples for how to do these in Minds on Mathematics.

Mrs. K