Chapter 01

Mathematical Literacy: Acquiring the Big Ideas While Doing Mathematics 2

Conversation in Mathematics Discuss how this student is mathematically literate. 3

Process Standards Pedagogy Mathematics is both Knowing and Doing 4

Balance Mathematical Literacy Thinking Mathematically Content Process Discuss the relationship between the notion of literacy in mathematics and the vital importance of learning to think mathematically. Then discuss that a truly literate person knows the content of mathematics as well as the processes that characterize meaningful mathematical thinking. 5

Standards Content Standards Process Standards Number & Operation Algebra Geometry Measurement Data Analysis & Probability Process Standards Problem solving Communication Reasoning & Proof Representing Connections The NCTM has produced a document that defines both the content that students should acquire as well as the specific mental processes that characterize good mathematical work, or “mathematizing.” Discuss the instructional relationships between content and process. 6

Definitions to Live By Problem Solving - Solving real-life problems in multiple ways Communication - Explaining problem solving strategies Reasoning & Proof - Justifying those strategies Representing - Showing (modeling) mathematical thinking in multiple ways Connections - Making mental links between representations and/or between strategies Discuss the interrelationships between the five processes – how they are similar and how they are different. Then invite students to develop working definitions of the processes. 7

Multiple Representations This figures shows the five different ways that problems can be represented. We want to make sure that we are encouraging children to use as many of these as possible in each math lesson. Suggested Activity: Pose a problem, such as 45 + 23, and ask the students to represent this problem using each of the representations listed above. 8

Curriculum Focal Points Content The “Big Ideas” Movement 9

Key Ideas Discussion National Curricula Checklists “A mile wide and an inch deep” Big Ideas Focal Points Developmentally-appropriate Use these main points to discuss the history of the “Big Ideas” movement in math education. 10

Big Ideas vs. Skills Definition: A big idea is a statement of an idea that is central to the learning of mathematics, one that links numerous mathematical understandings into a coherent whole. Some districts and states write their standards using skill language, where as others may incorporate the language of big ideas. Suggested Activity: Using the Big Idea sort worksheet found on the website, have students cut out the different cells and sort whether the description is a big idea or a skill. Discuss the sorts. The above Essential Learnings comes from San Diego Unified School District, grade 3 multiplication of concepts and facts. www.sandi.net/depts/math/03.html. The above objective comes from the Utah State Math Core. www.uen.org/core.do?courseNum=5030 11

Focal Points Discuss the structure of this Focal Points chart found in the chapter. Invite students in small groups to discuss how grade level expectations increase in curricular complexity across the grades. Be sure also to highlight the relationships between this chart, the complete Focal Points document, and the Content Standards. Suggested Activity: Using the 5 content strands, brainstorm some big ideas that would go for that strand. Split class up into 5 groups and assign each group one strand. Determine if what they suggest is a skill or big idea. Compare it to definition 12