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Nov 15—17, 2019
Institute 3: Algebraic Reasoning
Algebraic reasoning permeates all of mathematics and is about describing patterns of relationships among quantities – as opposed to arithmetic, which is carrying out calculations with known quantities. "The Standards in mathematics are built on progressions which describe the progression of a topic across a number of grade levels, informed both by research on children's cognitive development and by the logical structure of mathematics." This Institute explores the Expressions and Equations Domain of the AERO Mathematics Standards) and focuses on the development of algebraic reasoning using multiple representations such as words, tables, graphs, and equations to analyze and model mathematical relationships.
Participants will:
- Explore the progression for expressions and equations;
- Develop an understanding of the role of using multiple representations and contextual situations to support student algebraic reasoning
- Explore the concept of mathematical modeling and the implementation of rich tasks
- Critique classroom tasks for opportunities to engage in the mathematical practices.
- Examine student work to determine student engagement with the mathematical practices.
Jan 31—Feb 2, 2020
Institute 4: Functional Reasoning
Modeling bridges the gap between school mathematics and the mathematics in students’ lives. Modeling links classroom mathematics and statistics to everyday life, work, and decision-making. It is the process of choosing and using appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions. Incorporating tasks that are situated in real-life contexts and involve modeling help students see the purpose of the mathematics. The institute will explore the progression of the Functional Conceptual category of the Standards with a focus on the various ways students can represent their mathematical understanding, including visual, symbolic, and physical representations. Connections to the Modeling Conceptual Category and the modeling cycle will be examined.
Participants will
- Explore the connection between the conceptual category, functions, and the conceptual category of modeling in the AERO Standards.
- Identify authentic tasks which provide student opportunity to gain a deeper understanding of functional relationships and the various uses of a rate of change.
- Examine classroom tasks to determine student opportunity to demonstrate their understanding of functions
- Share formative assessment feedback strategies.
Apr 23—25, 2020
Institute 5: Geometric Reasoning
The process of articulating sound and precise reasoning is threaded throughout the Math Standards and requires reasoning and sense making to be a regular part of instruction. Integration of the Standards for Mathematical Practice is critical for student understanding of Geometry. Through “practicing” reasoning, students progress toward expressing grade-level appropriate geometric thinking by constructing viable arguments, critiquing the reasoning of others and attending to precision when making mathematical statements. This Institute will explore the Geometry Domain and Conceptual Category of the Standards for Mathematics in Grades 9-12, with a brief look-back to the standards from earlier grades to emphasize the overall K-12 coherence.
Participants will:
- Explore the progression of standards for geometry across Grades 9-12.
- Deepen understanding of the transformational approach to geometry advocated by the AERO Standards.
- Deepen their understanding of the ways in which students’ geometric understanding grows, and the implications for classroom instruction and assessment.
- Share strategies for posing questions and facilitating rich classroom discourse.
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