When I first began my teaching career, the focus was on the Madeline Hunter lesson plan template, as seen below. It was all about the teacher being on the stage and providing students with the knowledge, skills, and processes they needed. It’s ironic that this pre-internet lesson plan template used the word ‘input’, as the word ‘input’ typically refers to the items we put into a computer. In this case, ‘input’ refers to the knowledge, skills, and processes that teachers provide to their students.
According to UK’s Science and Media Museum, the internet grew from 130 websites in 1993 to over 100,000 at the start of 1996. As the internet grew, my lesson plan format moved from the ‘sit and get’ to a more inquiry based model.
Then, my district brought in trainers for a curriculum called the Connected Math Project, developed by Michigan State University – and my connections to math just ‘clicked’. The CMP teacher materials are organized around an instructional model that supports this kind of “inquiry-based” teaching. This model is very different from the “transmission” or “direct instruction” model, in which teachers tell students facts and demonstrate procedures, and then students memorize the facts and practice the procedures. Instead, the CMP model looks at instruction in three phases: launching, exploring, and summarizing.
Problem-centered teaching and learning opens the mathematics classroom to exploring, conjecturing, reasoning, and communicating. Both the teacher and student take on more responsibility for the learning process. When teaching a whole class lesson using Cube and/or Glow, students can apply the concepts as you are teaching them individually or with partners. This creates an exploration out of what was once just an explanation (or lecture).
For example, if you are teaching CCSS 1.NBT.B.3: Compare two two-digit numbers based on the meaning of the tens and ones digits, recording the results of comparisons with the symbols >, =, and < using Cube, you would first select the ‘Tens’ mode and then select the ‘Compare’ mode. Rather than do problems on the board for students to see, students could work along with you to build numbers, such as a number with 9 in the tens place, individually or in partners.
Students can then compare the number they build to another number by dragging and dropping the correct answer into the box. Cube allows for students to show their thinking with both word explanations and symbols. Being able to show their thinking in both modalities allows educators to look for misconceptions. Sometimes students can understand the written language answer, but struggle to make sense of the symbols. This allows teachers to provide assessments that are differentiated to the learning needs of students. For example, on an assessment the instructor could put a guide that has the written words next to the appropriate symbols.
You can use Glow for teaching CCSS 4.NBT.B.5: Multiply a whole number of up to four digits by a one digit whole number, and multiply two two-digit numbers, using strategies based on place value and properties of operations. Illustrate and explain the calculator using equations, rectangular arrays, and/or area models. The beauty of using Glow is that students will be able to see the equation and build the array using Glow’s orange dials.
Tune in next time to explore how Cube and Glow can be used in math centers.
Heidi Williams is the Computer Science Curriculum Specialist for Marquette University in Milwaukee, WI. Her focus is on the K-8 integration of computer science and computational thinking within all core content areas. She is the author of ISTE’s No Fear Coding: Computational Thinking Across the K-5 Curriculum, as well as a facilitator of ISTE-U’s Computational Thinking for Every Educator course.
Within this Blog, Heidi will be posting on how Cube and Glow can help educators to support their students’ mathematical thinking. Over the course of the next three months, you will hear about best practices in pedagogical use, CRA – concrete, representational, abstract connections, visualization of partial products, connections to mathematical standards, and MUCH more!
Within each post you will find detailed explanations, links directly back to the components and resources of Cube and Glow, as well as external links that will provide you with more background information and support in teaching a variety of mathematical standards. As you continue to read her posts, week after week, we hope you fall in love with Cube and Glow. We also hope you enjoy the wealth of mathematical pedagogical content and strategies she shares.
Heidi has an extensive background in mathematical pedagogy, with over fifteen years of experience as a 6th – 8th grade math teacher, as well as a K-8 mathematics specialist. She has had extensive training in differentiation, coaching within a Response to Intervention (RtI) framework, as well as inquiry based instruction. Birdbrain is tapping into her understanding and passion for helping K-8 teachers with mathematical thinking in the classroom. Please join us and follow Heidi’s Hoots!