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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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As an undergraduate education student, I was challenged to write my personal mission statement that would help me define myself as a teacher. I don't recall the entire statement, but I know that it included something along the lines of "helping students think critically about mathematics." Looking at this from an experienced perspective, I'm not convinced that I knew what critical thinking was, let alone how to help my students become critical thinkers. With time, I've come to understand that there is no one way to accomplish this task, but there are strategies we can implement that will help students develop these skills.Read More
From a very young age, children learn and develop using all their senses. As infants they are surrounded by the stimulation of shape, color, lines, numbers, patterns, and textures. By the time they reach preschool, they are engaged in stories and imaginative pursuits that build on these sensory explorations. Thanks to the materials they have explored in their first five years, children already have a strong foundation for mathematics when they start kindergarten.Read More
Success in school, the workplace, and society increasingly depends on our ability to comprehend informational text. Yet, despite current language arts standards, informational text often gets short shrift in primary grades classrooms. One study of 20 first-grade classrooms showed that nonfiction books constituted less than 10 percent of the classroom library and that students spent less than four minutes per day reading informational text. (Duke, 2000)Read More
According to the American Statistical Association, "Effective prediction is essential to improving medicine; monitoring climate; providing sufficient, safe food supplies; and much more." To make educated predictions as adults, children need to understand probability -- and start learning about it at an early age. Prediction is an adult skill used in many professional fields, including science, medicine, finance, and insurance. Underlying prediction is the notion of probability: whether a given event is certain to happen, likely, unlikely, or impossible.Read More
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