Concrete, Pictorial, Abstract: Students first learn concepts concretely, manipulating physical objects. Students then move to the pictorial stage where they use visual representations of concrete objects in order to model problems. Lastly, students use numbers and symbols (+,-, etc.) to model and solve problems.
Number Bonds: When introduced to addition and subtraction, students are taught how to see numbers as various parts that make up a whole through drawing number bonds. For instance, when adding 5 and 7, we can see the 7 as 2 + 5, making it easier to first add 5+5 to get 10, and adding the 2 after. This strategy fosters strong number sense that can be help students with mental math. Bar Model: This essential component of Singapore Math uses rectangles to represent numbers in a problem. This is strategy is particularly powerful when solving word problems, as it helps students pull out key information and organize it in a visual way. Metacognition / Thinking Visibly: Another key component of Singapore Math is metacognition, or "thinking about thinking". We encourage students to become aware of their approaches to math through asking question, having class discussions, or individually reflecting in our journals.
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Monday/Tuesday: 9:10-9:30 - Whole Class Problem Solving 9:30 - "Free Five" (A short break to get outside, move our bodies, breathe fresh air, and reset) 9:35-10:00 - Independent Work in Workbooks
Wednesday/Thursday: 9:10-9:35 - Independent Work in Workbooks 9:35 - Free Five 9:40-10:00 - Math Games Friday 9:10-9:30 - Independent Work in Workbooks 9:30-10:00 - Weekly Reflections
The Culture of Math in 3/4
Math as Open, Creative, and Visual: In 3rd and 4th grade our goal is to nurture students' excitement and enjoyment of math through exposing them to the multi-dimensional nature of the subject. To do this, we engage in activities that demonstrate the open, creative, and visual nature of math. We stand against the idea that there is one "right" way to do math. Rather, we believe that math is open in nature and embrace all approaches to problem solving that students bring to the table. Sharing a multitude of perspectives allows us to see the creative nature of math, shedding light on each student's individual expression and their own unique ways of recognizing and creating patterns. Another way we highlight the creativity and openness of math is through visualizing numbers, the relationships between them, and the computations we may be working on at the time. Representing abstract numbers and symbols visually has many benefits, drawing on multiple parts of the brain and strengthening number sense in a beautiful, fun, and exciting way. Embracing Mistakes: One major obstacle for students, especially in math, is their relationship to mistakes. When the focus of math is solely on arriving at the correct answer, students can struggle. Failing to recognize how their process in approaching a problem matters they can adopt a series of behaviors to compensate, which eventually hinder their progress. Some refuse to engage in any challenging problems without explicit guidance while others erase the written work they used while solving, believing that solving the problem “in their head” is a true sign of intelligence. Our focus in class is on making thinking visible, not only as a strategy for understanding problems but as a learning tool, a way for students to think of themselves as sense-makers and understand how they understood and problem or concept at the time and what steps they need to take to further their understanding.
Tied to this is the concept of “Growth Mindset” popularized by Carol Dweck. In math class, we try to focus on the importance of engaging in challenging problems and embrace the idea that it is only during these occasions that real learning is taking place. When students begin to see their brain as similar to a muscle, that only grows when pushed, they are more likely to push through the more difficult parts of a problem and see their struggles as part of the path to who they will become as learners and not as representative of their identity and potential.
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