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The first time I ever saw a teacher using Unifix cubes in the classroom, it was not in an elementary school. I was coaching a middle school teacher who was introducing the concepts of mean, median, and mode to her students. They were using the cubes to “graph” the data and then find these measures of central tendency. Since then, I’ve seen Unifix cubes in classrooms at every grade level, used in a variety of ways to teach number sense, data, measurement, patterns, and an array of topics. They were never as useful a tool for Geometry… until now.

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"Would you rather have half of one chocolate bar or a quarter of a different chocolate bar? Most popular answer: It depends on the size of the chocolate bars! As teachers know, the relative size of fractions depends on how the whole is defined. Authors Jim Callahan and Marilynn Varricchio address these common problems with fractions in their new book Fractions Made Easy (Didax, 2016). Drawing on material from the book, we will focus on how visual models can be used to support a solid conceptual understanding of fractions in third grade.

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"With current math standards' emphasis on number lines as a visual math model, number lines are being used in nearly all primary grades classrooms for learning such things as counting and early operations. However, research has shown that number lines are conceptually too difficult for young children to understand and instead we should be using number paths, at least until second grade (Fuson, et. al., 2009). A number path is a visual model for counting, addition, subtraction and more. Experts say that the number path is superior to the number line as a visual model for early math learning. We caught up with Educator Margaret McGinty to learn why.

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Kathy Richardson, one of the leading authorities on elementary math, has spent years educating children in the early grades. Her recent book, How Children Learn Number Concepts, is a wonderful introduction to the Critical Learning Phases that elementary children move through as they are developing a sense of number. This concise book is full of information to guide teachers of all levels as they help students through the phases.Read More

When I was teaching high school, place value was a concept that just seemed to exist; it was inherent in everything I taught, yet received little attention. I simply took it for granted. As I transitioned to working with students and teachers in the elementary grades, I realized that this was a mistake because place value was a concept that many of my students probably never fully understood. Place value is far more than just ones, tens, and hundreds. To really understand the concept of place value, we need to understand the relationship between the places.

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My Preschool-age son likes to read with us, and one of the books in his “favorites” rotation teaches shapes and colors. On the page with the rhombus, I always use the term “rhombus” rather than “diamond,” which is what is printed in the book. While reading with his mother last week, she read the term on the page rather than substituting “rhombus.” My son quickly corrected her; he shared what his preschool teacher taught him: “Diamonds are shiny things in jewelry. That is a rhombus.”Read More
While on hall duty during my first year of teaching, I was surprised to see our math department chair leading her Calculus students to a large common area in the school. Curious, I checked in on them a few minutes after the class had started and found that they were plotting “points” by standing on a large coordinate grid mat on the floor. After watching the teacher use those mats over and over with students in Algebra 1 all the way through Calculus, I realized the value of this kinesthetic learning experience. Her students understood the concepts better, and were more engaged, because they were out of their seats and actively creating a life-sized visual model.Read More
As a teacher for over 15 years, I recognize that the kinds of experiences that teachers offer their students play a major role in determining the extent and quality of students’ learning. For example, rich problem-solving activities help students build understanding by actively engaging in tasks and experiences designed to deepen and connect their knowledge. Playing math games affords students the opportunity to build understanding while encouraging strategic thinking as students will have different approaches for solving problems. Using classroom activities and games is also a great way to check in on their progress as well as to provide reinforcement of key concepts. I like problem-solving activities that are easy to put together, fun, and require all students to participate.Read More
One of the things I really enjoyed about my Geometry classes in college was that they were very hands-on. We used a variety of manipulatives to explore geometric concepts, and the lessons have stayed with me for a long time now. I carried many of these ideas into the classroom when I started teaching, using ideas as simple as nets and tools like marshmallows and toothpicks. While these models are adequate for teaching the general ideas, they lack the consistency and formality that Geofix shapes offer.Read More

When working with math teachers at any level, one of the complaints I've heard over and over begins with the phrase, "If they only knew their facts..." Fluency with basic facts, however, is only one part of a bigger picture, and I always encouraged teachers to think about the conceptual foundation they were building rather than how quickly students can rattle off some facts. As we consider the increased emphasis on rigor, we need to keep in the back of our minds what rigor is: a balance between conceptual understanding, application, and procedural fluency.

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