SD COUNTS

Strands of Math Proficiency – Adding It Up

Mini-Foundations Agenda

NOTES:

Items in this color are available in the Adding It Up section of the Foundations binder from Spearfish ’06.

Items in this color relate to copies of the text, Adding It Up- the PDF for chapter 4 was emailed to you on May 9th. The pages from chapter 1 will have to be copied.

Agendapower point are available in your email. Johny is putting together a meaningful practice packet that will be coming soon.

Brenda’s Blocks Task—this problem was from one of our earlier trainings—we used this in place of the water task!

 / Welcome and Introduction
  • Introduce Me?
  • Share Objective for today’s session:
  • Participants will have an increased understanding of the five strands of mathematical proficiency
  • Participants will have an introduction to classroom applications for the five strands of mathematical proficiency
  • Participants will have an increased understanding of the research supporting inquiry-based mathematics in teaching and learning.
  • Today we will be using a key chapter fromAdding It Up
  • Goals of AddingIt Up
  • Represents a synthesis of the research on mathematics learning
  • Provides research-based recommendations for teaching, teacher education, and curriculum for improving student learning.
  • Provides advice and guidance for educators, researchers, policy makers, and parents.
  • Today will focus on Chapter Four
  • Explain the variety of tasks
  • Some tasks are more challenging because I want you to experience mathematics from a student’s perspective; all are designed to model one or more of the strands of mathematical proficiency.
  • Roles and Rules
  • Group Work: Choose: Time Czar; Recorder, Reporter.
  • Rules: (student helper scribe and post)
  • Take care of yourself….bathroom location
  • Respect and value everyone’s thinking…today we are all learners.
  • Anyone want to add to the way we will work together today?????
Comment: Say something like, “If this were a math class, I’d have more people share…(rushed because of the time constraints)” / Materials:
  1. Markers
  2. Buy Treats 
  3. Agenda & POWER POINT
  4. PDF of chpt. 4
  5. ProjectorScreen –for showing video &/or power point

10 min.

45 min. / Strands of Mathematical Proficiency – Developing Background
  • Divide group into five groups by counting off.
  • Assign Reading
  • Every one Reads Pgs. 115- middle of 118
  • Each group also reads the information on their strand.
  • Conceptual Understanding – pgs. 118-120
  • Procedural Fluency – pgs. 121-124
  • Strategic competence – pgs. 124 – 129
  • Adaptive Reasoning – pgs. 129 - 131
  • Productive Disposition – pgs. 131 – 133
  • Directions:
  • Read assigned parts individually (10 minutes)
For the sake of time, groups may divide their pages
  • GROUP WORK (20 minutes)
  • Within your group, select a recorder, reporter, and a time czar.
  • Locate worksheet in packet – explain sections—use this as your group discussion guide:
  • Strand name in the middle oval
  • Working Definition—this is the definition written in your own words…not copied out of the text
  • Examples: May be problems or scenarios….whatever will convey to the large group the essence of this strand.
  • Work with your group to create a Frayer Model(on chart paper) that will describe your strand to the large group.
THINK ABOUT:
-What do you see your students doing? How would you know that this strand is being developed? Evidence?
  • Report Out: Groups share and answer questions (10 minutes) USE: Understanding Strands of Mathematical Proficiency Handout
  • REFLECTION: (if time) Using your journal (or reflection guide) write any questions you still have about the 5 strands of mathematical proficiency? How will you increase your understanding?
/ Materials:
  1. Adding It UPchpt. 4
  2. Highlighters- if giving individual copies of chpt.
  3. Pencils
  4. Frayer Model Handout
  5. Chart paper & markers
  6. Understanding Strands of Mathematical Proficiency Handout

 / Scale Problem: Brenda’s Blocks
  • Group into ___ groups depending on number in group
  • Provide with Handout: Brenda’s Blocks Task
  • Task:
  • Give participants 10 (15?) minutes of private think time to work the problem.
  • Get into groups and discuss strategies/answers
  • Using chart paper, have each group illustrate the strategies that they used to solve
  • Each group shares strategies
  • Further Discussion if time:
Discuss or journal what strands of mathematical proficiency were represented with this problem? What evidence would you give to support your thinking? Ask for individuals to share reflections. / Materials:
  1. Chart Paper
  2. Pencils & markers
  3. Individual problem worksheet from earlier training

30 min

30 min.
*This will be rushed! / Making the Case
  1. Introduction: Why all the discussion around inquiry – based mathematics? Why should we consider thinking in a different way about how we teach mathematics and how students learn mathematics? (Brief whole group discussion) 5 minutes
  1. There is compelling evidence in your text that speaks about the need for changes. Let’s take a minute to read what the “experts” say about that.
  1. Individually, please read from Chapter 1 in Adding It Up. Please read individually, pgs. 15 – 21. You will be talking with a partner about these two questions?
  2. What implications for teaching and learning were alluded to in the text?
  3. What questions did this reading raise for you?
  1. You will have 10 minutes to complete the reading.
  1. Explain Pyramid Partners Process – Pass out worksheet (explain process) 5 minutes
*Round One: 5 minutes
*Round Two 5 minutes
  1. Large Group Discussion: (5 minutes) What kinds of questions did this raise for you? Keep track of the questions and address those that come up over and over again.
  1. If there is any time, this would be a great place to share videos or testimonials from teacher leaders!
/ Materials:
  1. Adding It Upchapter 1(pgs. 15-21) *make copies
  2. Pyramid Partners Process Handout
  3. Pencils
  4. Stop Watch
  5. Bell

 / Acrobats, Grandmas, and Ivan (procedural fluency)
Lots of different ways to solve the problem.
*Goal- shows procedural fluency.
  1. Introduce problem.
  2. How many grandmas/grandpas in the audience?
  3. In this problem, you will know who won the first two round of the tug-of-war and you will need to figure out who won the final round. The first two rounds give you the information you need to decide who won the final round. (Pass out worksheet and give directions for working.
  1. Work the problem individually? Share your solution with group?
  2. Record all solutions on chart paper.
  3. Share with the large group and explain your thinking.
Large Group Discussion
1. How many strategies did we have to solve this problem? (Book…Method of substitution, Given points, fractions (two ways) and a reasoning paragraph) What strands of mathematical proficiency are represented. Explain your thinking. / Materials:
  1. Problem worksheet
  2. Chart paper
  3. Markers

30 min.

25 min. / BASIC SKILLS & final math activity: How Many Rows and How Many in Each Row. (Optional – Depending on Time)
  1. Open with an Article about Basic Facts in Conceptual Understanding Concept. – if time allows, jigsaw each section or highlight key points in order to answer questions raised on power point.
  1. Meaningful Practice- How Many Rows? How Many in Each Row.
  2. Pass Out Handouts and Review Directions
  3. Ask participants to partner with someone at their table.
  4. Pass out Die
  5. Play!
  6. Discuss meaningful practice
/ Materials:
  1. Hand out a copy and useQuestions About Basic Skillshandoutto answer QUESTIONS on power point slides.
  2. Game Handouts – Directions and Game BoardDice
  3. Johny is putting together a meaningful practice packet

 / Closure
  1. Summarize the day
  2. Questions, Comments

5 min.

SD Counts Summer Institute

Strands of Mathematical Proficiency1