In this course, we will work to see the connections between mathematical ideas, the strands of mathematical proficiency, and the Common Core content and practice standards. The purpose of the portfolio assignments (due Weeks 2, 6, and 10) is to provide structured opportunities for you to reflect on your developing understanding of these ideas, proficiencies, practices, and standards, as well as receive frequent comments and feedback.
Your first reflection should address:
Your growing understanding of the strands of mathematical proficiency discussed thus far.
Descriptions of each strands key ideas and why they are important to developing mathematical proficiency, based on the overview section of Adding It Up, with emphasis on the productive disposition strand. For example, Productive disposition means a person is able to ____ as well as ____.
Connections between productive disposition and other ideas discussed in class (e.g. mathematics identity, smartness, or exploration and flourishing).
Examples of how you saw yourself or others developing/demonstrating productive disposition during class or through course activities. For example, I saw myself demonstrating ____ during ____ because I did ____.
Your current questions about the strands, and conjectures about possible answers to those questions.
Your growing understanding of the Common Core State Standards for Mathematics (CCSSM), including the standards for mathematical practice (SMPs) and the content standards, with respect to:
Descriptions of the SMPs and CCSSM and why they are important to learning and doing mathematics. For example, Knowing how the CCSSM structure the spiraling of ____, across grade levels means that secondary students build on ____ from elementary grades. This is important because a key part of doing mathematics is ____.
Your current understandings of the differences and similarities between the SMPs and CCSSM.
Connections between math practices and other ideas discussed (i.e. mathematics identity, multiple representations).
Your current wonderings about the practices, and conjectures about possible answers to those wonderings. For example, How is SMP ____ different from SMP ____ when they both talk about ____?
Your understanding of the interconnectedness of these two frameworks (CCSSM/SMPs and the strands of mathematical proficiency), including:
Similarities and differences between what these two frameworks describe and attend to in terms of doing mathematics.
Your current wonderings about these frameworks, and conjectures about possible answers to those wonderings.
Connections between the strands of proficiency discussed thus far and the SMPs, such as how developing a particular strand can support engagement in an SMP. For example, Productive supports procedural fluency because _______. However, procedural fluency also supports conceptual understanding because _______.
This assignment should meet the following requirements:
No less than two pages, single-spaced, in length total
No more than four pages, single-spaced, in length total
Please identify each part (A, B, C) of your response clearly. Your narrative for each section should include topic sentences and elaboration that clearly connect to the prompts from the section. You may use headers in your writing to show when you transition from one prompt to the next. to structure your reflective writing (i.e. Paragraph 1 addresses strands of mathematical proficiency, Paragraph 2 addresses the Common Core State Standards/mathematical practice, Paragraph 3 addresses the interconnectedness of the frameworks)
Pages 115-118 & 131-133, Mathematics Learning Study Committee, Division of Behavioral Social Sciences Education, National Research Council, & Center for Education. (2001). The Strands of Mathematical ProficiencyLinks to an external site.. In Adding It Up (pp. 115-156). National Academies Press.