When Response to Intervention (RTI) was first introduced in 2004, districts began looking further into the impacts of small group instruction as part of their second tier support services. Our grade level teams would look at assessment data and determine which groups of students were struggling on specific concepts. We would use this data to create small instructional groups for targeted instruction.
As students use Cube (place value, decimals and money) and Glow (addition, subtraction, multiplication, and division) to explore, build, solve, and/or compare numbers, teachers are provided with reports that include the data and time of session. They also can see what skills students worked on, as well as the number of questions they completed correctly on the first try, which they answered incorrectly, and the number of tries they made that produced an incorrect answer. 
These teacher reports are an excellent resource in guiding teachers to determine topics of instruction and creation of small groups. During this small group intensive instruction, students have the opportunity to engage in math talk. For decades, research has supported the notion of engaging students to talk about the strategies and ways in which they are solving problems. As educators, it is essential that we take the time to listen! I have often spent my small group instructional time listening to how students solve problems; it has helped me to identify misconceptions in their thinking. It is only by engaging our scholars in this process… that we can help fill in the gaps or clear up misconceptions in the mathematics classroom.
For example, the template image below is a data collection tool to organize and keep record of students in tier 2 math interventions. Keep in mind that this tool could also be used in a more targeted tier 3 RTI intervention, or even whole class to help determine small group instructional topics.
Click here to make a copy of the template.
In this first example from the spreadsheet, detailed below, the student was using Cube and working on the skill of making numbers using place values up to the hundreds place. The student was receiving a tier 2 intervention and has been asked to practice with Cube 3 times a week for 10 minutes each session. Since the student made 2 out of 5 errors, they were pulled into a small group for further analysis on the skill.
While the student made only one error when decomposing the number 907, they made two errors when given the expanded form (100 + 50 + 9) of the number. During small group instruction, I asked the students to engage with math talk to help discover any misconceptions they might have. As the student was working with Cube, it became apparent that they were reversing the numbers they were putting in the tens versus hundreds place value. The power in watching students place the cubes in the tower was that I could see where they were placing the cubes and listen to their thinking. This helped me to uncover the misconception. I had this student go back to working with unifix cubes with the tens blocks and hundreds blocks to help fix the gap in understanding.
As educators, we must advocate for the tools that help us identify the gaps in understanding. Both Glow and Cube can be essential in helping teachers identify and then close these gaps.
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!
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