SUDDS Ratio Study: Takeaways for Teachers

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As a follow-up to our design study of a sixth-grade ratio unit at Highland Middle School in Harnett County, NC, we analyzed student responses to several assessments that teachers administered over the course of the unit. The assessments included: A pretest administered before the beginning work on the SUDDS ratio curriculum that included items from cluster 4, Finding Key Ratio Relationships, and cluster 5, Comparing Ratios and Finding Missing Values. A Cluster Assessment of Progress (CAP) was administered for cluster 4 after completing the cluster 4 curriculum. A CAP was administered for cluster 5 after completing the cluster 5 curriculum. A SUDDS-designed posttest containing items from both cluster 4 and cluster 5 was administered after completing and reviewing the cluster 5 curriculum. An independent assessment containing ratio items, was administered…
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NC Mathematics Educators Speak Out on Standards Debate

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Math Education Leaders in North Carolina Criticize Math Sub-Committee Report from Academic Standards Review Commission and Co-Chair Covil's Criticism of ASRC Decision In light of the recent discussion and review of mathematics standards in North Carolina, we feel it is important for the voices of mathematics educators be heard. We represent NC mathematics education organizations and individuals with considerable expertise in the issues at stake. We applaud the Academic Standards Review Commission (ASRC) decision on December 17 not to replace the current standards and are committed to join any effort to improve the quality of these standards for the benefit of our students, teachers, and stakeholders. We have three critical observations in response to the report of the ASRC mathematics working group and the subsequent comments by ASRC Co-Chair, Tammy…
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Writing Assessments to Diagnose Student Thinking Stimulates Discussions among Experts

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by Dr. Jere Confrey The examples that follow came from working with my team, comprised of Tammy Baumann, Takeema Evans, Alvaro Rodriguez, Debra Cheap, and Jennifer Neel. Opinions offered are my own, but examples and discussions came from members of this delightful team. Two weeks ago, I spent a week with 22 middle grades teachers writing assessments for the related learning clusters in our SUDDS middle grades learning map. Our goal was to identify a student’s proficiency level within a learning trajectory stack for each construct in our map. We all worked steadily for four days, 8 hours a day. Writing items to measure an exact student behavior and its variations for the purpose of diagnostics is hard work. Lots of issues surfaced during this week. I thought I would share…
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Unpacking a Learning Trajectory for Ratio Reasoning

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by Dr. Jere Confrey In the last blog post on ratio, I presented ratio as the “über” concept under which fraction and rate are located. All three constructs share the fundamental idea of expressing the relative size of two values, but fractions require the comparison to be within a single dimension or quantity; rate requires it to be between two quantities, and ratio encompasses either type of comparison of relative size. In this blog, I introduce the key components of a learning trajectory for ratio, ratio equivalence, base ratios, and unit ratios, and discuss how unit ratios relate to the term “unit rate” as it is used in the Common Core State Standards. I will also use the analysis as a context to compare and contrast learning trajectories and standards. In…
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Co-Design

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by Basia Coulter The interdisciplinary team at Scaling Up Digital Design Studies (SUDDS) was brought together last November by Jere Confrey to build a learning map web application with an accompanying assessment and reporting system for middle school math. The team was new, and we were yet to gain a deeper understanding of the project and to learn how to work together. As a UX/UI and visual designer, I was looking forward to being part of a team. Several years of freelance work prepared me to handle and to enjoy wearing many hats on the job, but I yearned for an experience of teamwork where ideas are born and brainstormed through a collective effort. And that was exactly what I was going to get! Several months after the SUDDS project…
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Clarifying Definitions: Fraction, Rate, and Ratio

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by Dr. Jere Confrey What does it mean to be a fraction versus a ratio or a rate? Let’s start with the simplest and most common distinction. Perhaps the simplest explanation is that a fraction is a comparison involving one quantity (miles, pounds, cents) or one dimension (length, area, volume). Thus, to have ¾ of a banana means that the banana is divided into four equal parts and one has three of them. There is one quantity: amount of bananas. By contrast, a rate is a comparison between two different quantities. Most commonly known is the concept of miles per hour, as rate or speed. It is important to keep in mind that it is unwise to define a fraction as the relationship of a part to a whole, because…
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Why We Display Data

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In this second post in a three part series on data and statistics let’s begin by considering the following CCSS-M standard: CCSS.Math.Content.6.SP.B.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots. Like many of the standards, this looks so easy at first glance. You think “Ok, there are three ways to display numerical data so I’ll just tell my students how to create these three.” But, where did these three come from? Who, if anyone, invented them? What choices did they make about the data to create them? Are they all equally valuable? Is one better than the other? Is there a fourth way? These are just a few of the questions that kids might ask. As usual, there is a lot more…
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