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Programs and Presentations

2014 Summer Institute Banner Algebra 6-8 

Program & Presentations

The goal of this institute is to provide an interactive professional learning experience that enables participants to understand the growth of algebraic thinking and reasoning across the grades to enable teachers to prepare students for algebra.


Program Overview

Focus on Your Grade 

Who Should Attend 

What You'll Accomplish  

Schedule Overview 

General Information 

Keynote Sessions 

Breakout Workshops 

Register Now 


Focus on Your Grade—Pick a Strand

The experience will be suited to your interests—you’ll take part in sessions and be grouped with educators according to the grade level you select for your strand of focus. Each strand will experience a progression of activities to address mathematics content related to algebra readiness.

Strands 

  • Grade 6
  • Grade 7
  • Grade 8 
  • PD Strand—If you are a professional development leader, this strand is for you. PD Strand participants will attend sessions according to their grade band, and will participate in an additional three-hour session on Day 1. They will also attend a debriefing session at the end of each day. (Note: There is an additional cost for this strand.)

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Who Should Attend

  • Grades 6–8 classroom teachers
  • Preservice teachers
  • High school teachers of struggling learners

Expanded audience for PD Strand:

  • Math specialists and coaches
  • Math supervisors
  • Lead teachers
  • Curriculum coordinators

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What You'll Accomplish—The Institute's Defined Outcomes

Activities are designed for you and your peers to achieve defined outcomes together. Participants will—

  • gain strategies to build the foundation of knowledge and skills that lead to students' future success in algebra; 
  • explore tasks and instructional techniques, including posing purposeful questions, that support students’ development of conjectures and generalizations;
  • learn instructional strategies, such as implementing tasks that promote reasoning and problem solving, that provide all students opportunities to develop strong algebraic reasoning skills.
  • determine the role of the Standards for Mathematical Practice in instructional strategies and assessments.
  • understand how concepts within multiple domains of the Common Core State Standards support algebraic reasoning.

PD Strand Additional Outcome: Participants will—

  • examine models of professional development that support teachers as learners, teachers as teachers, and teachers as reflective practitioners.

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Keynote Sessions

 Margaret Peg Smith  Opening Keynote: Promoting Algebraic Reasoning: The Role of Mathematical Tasks
Margaret (Peg) Smith, University of Pittsburgh, Pittsburgh, PA

This session will focus on the features of mathematical tasks that support students learning of mathematical content and practices. Specifically, during the session participants will consider: 1) the differences between high- and low-level tasks and their impact on student learning; 2) the characteristics of tasks that have the potential to engage students in algebraic reasoning; and 3) what teachers can learn from student responses to high-level tasks.
    
Jon Star 137px  Keynote Session: Understanding the “What” and “Why” of Algebra
Jon Star, Harvard University, Cambridge, MA

Fundamental to our efforts in preparing students for success in algebra is understanding what algebra is: What is algebra? What are the big ideas of algebra? Why do we teach algebra? Answers to these questions can begin to inform our conversations about readiness for algebra. 
   
Johnny Lott 131px  Keynote Session: Functioning with a Coordinated Plan
Johnny Lott, Retired, University of Montana, Missoula, MT

The term functioning implies doing an activity or working on related things. In another sense, it implies mathematical relationships and interactions between variables. This session’s aim is to consider functioning, with all meanings intended. We will start with a pattern from early grades, and show how that pattern can morph and be revisited at different levels, with students progressing from simple recognition in early experiences to writing a linear function with a graph at middle school level. A coordinated curricular plan provides all teachers a method of working toward these common end goals while realizing that we are dependent on one another for overall student learning. 
   
Diane Briars 135px  Closing Keynote: The Power of Teacher Collaboration to Support Students’ Learning of the Common Core State Standards for Mathematics
Diane Briars, President, National Council of Teachers of Mathematics (NCTM)

The Common Core State Standards represent a significant shift in what mathematics is currently taught in most classrooms and how it is taught.  Making these shifts successfully is a collaborative, rather than an individual, teacher effort.  Learn the value of establishing a professional learning community culture within your school.  Examine effective grade-level and course-based collaborative team actions that will both increase your understanding of CCSSM and support your enactment of the mathematical practices so that all of your students develop proficiency in CCSSM. Obtain resources to support the work of collaborative teams in your school.

PD Strand 

Through the professional development strand, middle grades mathematics teacher leaders (those interested in designing and delivering professional development) will explore student work, engage in non-routine problems, discuss evidence of student engagement in mathematical practices, and anticipate student and teacher misconceptions. These experiences will be linked to effective professional development models and their design and implementation components.

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Breakout Workshops

Lead Facilitators/Advisors 

Barbara Dougherty
University of Missouri, Columbia
Columbia, Missouri

Jessica Ivy
Mississippi State University
Starkville, Mississippi

Arlene Mitchell
RMC Research Corporation
Denver, Colorado

Facilitators 

Carla Kirkland
Bailey Kirkland Education Group
Madison, Mississippi

Matt Switzer
Andrews Institute of Mathematics & Science Education
Fort Worth, Texas

Temple Walkowiak
North Carolina State University
Raleigh, North Carolina

Zandra deAraujo
University of Missouri
Columbia, Missouri

Shawn Towle
Falmouth Middle School
Falmouth, Maine

Sarah Bush
Bellarmine University
Louisville, Kentucky

Grade Level Mathematics Content Workshops

Participants will attend a series of three workshops within their grade-band groups. Workshop leaders will engage participants in hands-on activities focused on developing algebraic reasoning:

Grade 6 

Key mathematical content: ratio and rate; expressions and equations (writing, interpreting); points on the coordinate plane; variable; using expressions and formulas; understanding equality; using equations to model relationships between two quantities; equivalent expressions; comparing ratios

Key instructional practices: Creating and critiquing arguments; developing generalizations and conjectures; promoting student discourse; using small groups in multiple ways; creating questions to elicit critical thinking; adapting tasks; using writing in mathematics classes

The sessions for grades 6 will focus on concepts related to ratio, rate, and variable as fundamental concepts in the development of an understanding of expressions and equations. The three components of algebraic reasoning are forming, reasoning with, and applying generalizations. Participants in these sessions will—

  • discuss the challenges of implementing, and teaching strategies for facilitating, a classroom environment conducive to student learning;
  • investigate the connections between ratios and algebraic reasoning with expressions and equations;
  • explore characteristics of tasks that develop generalizations about relationships between dependent and independent variables;
  • connect concepts, multiple representations, and skills with algebraic expressions to number concepts and skills;
  • examine and generalize multiple solution processes for equations and inequalities through student discourse; and
  • model relationships between and among quantities with equations, inequalities, graphs, tables, diagrams, and natural language.

Grade 7 

Key mathematical content: applying proportional relationships; expressions and linear equations; scale; slope; distinguishing proportional relationships; equivalent expressions; solving problems by using algebraic expressions and equations (real world and mathematical); unit rate, including graphs on the coordinate plane; using inequalities and equations to solve problems

Key instructional practices: Creating and critiquing arguments; developing generalizations and conjectures; promoting student discourse; using small groups in multiple ways; creating questions to elicit and build critical thinking; adapting tasks; using writing in mathematics classes

The sessions for grade 7 will focus on expressions and equations as fundamental concepts in the development of an understanding of functions. The three components of algebraic reasoning are forming, reasoning with, and applying generalizations. Participants in these sessions will—

  • discuss the challenges of implementing, and teaching strategies for facilitating, a classroom environment conducive to student learning;
  • investigate relationships between proportional reasoning and algebraic concepts such as slope;
  • explore the characteristics of tasks that develop generalizations about proportional and nonproportional relationships;
  • connect concepts and multiple representations of inequalities and equations to problem-solving strategies;
  • examine the importance and relevance of developing a relational understanding of equality through student discussions; and
  • model unit rate through multiple representations, using student discourse to develop connections with the concept of function.

Grade 8 

Key mathematical content: linear equations and systems to solve problems; special linear equations; slope as rate of change; linear functions; radicals and integer exponents; defining, comparing, and evaluating functions; using functions to model relationships between quantities; graphing proportional relationships

Key instructional practices: Creating and critiquing arguments; developing generalizations and conjectures; promoting student discourse; using small groups in multiple ways; creating questions to elicit and build critical thinking; adapting tasks; using writing in mathematics classes

The sessions for grade 8 will focus on concepts related to functions that lead to an understanding of relationships among quantities represented in multiple ways. The three components of algebraic reasoning are forming, reasoning, and applying generalizations. Participants in these sessions will—

  • discuss the challenges of implementing, and teaching strategies for facilitating,  a classroom environment conducive to student learning;
  • investigate multiple representations of functions and their connections with other domains.
  • explore explanations and understandings related to the development of the concept of function;
  • connect proportional reasoning and slope to representations of linear relationships, applying this reasoning to solve simultaneous equations.
  • examine the construction of functions, with a focus on using these constructions to determine and analyze rates of change; and
  • model multiple representations of proportional, linear, and nonlinear relationships.  

Mathematics Teaching Practices (Integrated) Workshops

Participants will attend a series of three workshops that focus on productive teaching practices that promote mathematical thinking in the classroom.

Facilitating Effective Mathematical Discourse 

Mathematical discourse is central to meaningful learning of mathematics. Purposefully facilitated mathematical discourse builds on student thinking and leads student learning in a productive direction, supporting the Standards for Mathematical Practice with students actively engaged in explaining their reasoning and considering the mathematical explanations and strategies of their classmates. In this session, we apply the processes of selecting, sequencing, and connecting using student work from a task completed in a content session.

Building Student Responsibility within the Community
  

There are several essential elements to establishing a classroom community that fosters student learning.  In this session, we will consider group organization and dynamics, productive learning environments, student expectations, and student accountability.  Through consideration of a video exemplar and classroom experiences, we will discuss how these elements support the Standards for Mathematical Practice and build student responsibility within the classroom community.

Posing Purposeful Questions

Different types of questions can be asked in a mathematics class, each with a  very particular purpose. In this session, we focus on six different types of questions, providing a structure to help participants generate other questions of this type. We explore three ways to extend and deepen students’ understandings using skill problems as the foundation.  We then look to class discussions and opportunities to enhance student discourse. These six question types support the Standards for Mathematical Practice and help to create a classroom environment that promotes high student engagement and critical thinking.

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