Mathematics

Illustrative Mathematics by Imagine Learning

Penn Hills has adopted Illustrative Mathematics from Imagine Learning as the backbone of their K-8 Math curriculum because of how well it draws on the strengths of established educational practices and standards. Dr. Bill McCallum and a group of math experts designed Illustrative Mathematics (IM) with the objective to improve students' mathematical achievement. Expertise and research from organizations such as the National Council of Teachers of Mathematics, the National Research Council, Smith & Stein, and others provide the foundation of the problem-based curriculum.

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Learning Mathematics by Doing Mathematics

A problem-based instructional framework assists teachers in designing mathematics lessons such that students are responsible for problem-solving and learning. The exercises and routines allow teachers to assess what students already know—what they can see and surmise introducing new ideas and processes.

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Balancing Rigor

Mathematics requires three dimensions of rigor: conceptual comprehension, procedural fluency, and the capacity to apply these concepts and abilities to problems with and without real-world settings. These components are taught concurrently to facilitate student comprehension.

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Purposeful Representations

Mathematical representations are utilized in the materials for the following purposes:

• To aid students in developing an understanding of mathematical concepts and approaches
• To aid students in solving problems. 

Students are systematically exposed to representations and encouraged to utilize ones that make sense to them throughout courses and modules. Students build links between various representations and the topics or procedures they represent as their learning progresses. With time, students will see and comprehend more effective approaches of problem representation, which will aid in the development of procedural fluency.

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Instructional Routines

Teaching procedures establish frameworks within which all students can participate actively in mathematical discussions. It is the goal of the curriculum to foster a shared comprehension of the underlying structure of routines through their systematic introduction at various points.

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Community Building

The first few weeks of school are crucial for instructors to create norms and form a mathematical community in order to encourage students in developing a positive attitude toward mathematics and to help them engage in mathematical practices. Everyone in a mathematical community is free to share their mathematical thoughts and opinions with others, which fosters an atmosphere conducive to group development and understanding.