I’m not a Missourian by birth nor have I ever taught history or geography, but I’ve found the state motto to be one that’s served me well in teaching mathematics. It’s only two little words “Show-Me”, but oh what power they hold.
Dictionary.com defines show as to explain or make clear. So I would often say to students, “We live in the Show-Me State, so show me – show me what you did and/or what you’re thinking. The Common Core State Standards for Mathematics (CCSSM) convey the same message. The Standards for Mathematical Practice: Commentary and Elaborations for K – 5 (2014) state that mathematically proficient students should be able to justify their conclusions, communicate them to others, and respond to the arguments of others.
To be able to justify your conclusions and communicate them to others, you must have a good understanding of what your conclusions are and how you arrived at them. From my experience, students can often describe a process or procedure they’ve carried out, but they have difficulty explaining their thinking and the mathematics behind it.
If you and I really want students to be able to do the math and understand it well enough that they can clearly explain or show it, then we have to make sure that we’re presenting them problems and learning experiences that convey the different ways that mathematics concepts can be represented. For these kinds of problems, Illustrative Mathematics is the go to source.
Illustrative Mathematics is a discerning community of educators directed by Dr. Bill McCallum, one of the lead authors for the CCSSM, dedicated to the coherent learning of mathematics. Illustrative Mathematics examples are vetted problems that serve in illustrating the CCSSM. Relevant information and clarifications of important math concepts make these problems perfect for classroom investigations and discussions.
LearnBop has partnered with Illustrative Mathematics to link the illustrations in our teacher intervention resources for easy access and downloading for whole class instruction, interventions for instruction with small groups of students, or instruction with individual students. Our data reports pinpoint the concepts that students have not mastered. As shown in Figure 1 below, only 37% of these sample students are reading and writing decimals correctly, 36% finding wholes, and only 38% mastering fractional side areas.
To find out which students are struggling with the concept, simply select the number of students who need help for a specific concept. If we select the 3 students that need help with Fractional Side Areas, we find that Jordain, Lakin, and Riken could benefit from interventions with this concept.
As you can see in Figure 3 below, there are two Illustrative Mathematics tasks that I could use in interventions with these three students. Each task comes complete with a commentary including sample solutions and discussion points that help clarify the concept.
With the end-of-the year assessments on the horizon and some of your students still needing to learn math concepts they’ll be assessed on, it’s the perfect time to take advantage of a free LearnBop trial. LearnBop helps you quickly pinpoint students’ knowledge gaps. And the automated step-by-step guide complete with critical thinking questions, hints, and visuals, informed by Illustrative Mathematics, assist students in the conceptual understanding and learning of mathematics.
It’s this understanding that enables students to justify their thinking and communicate it to others, which many will be doing on upcoming assessments and need to be able to do as they progress in their study of mathematics. So sign up today and show your students the math they need to know and learn!
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