# Assignments Schedule for EDU 432 -

Elementary and Middle School Math Methods

Spring 2014

## Overview

Review the assignments to see how they are related to each other and to the decisions professional educators make. Each box has descriptions for the ten major class assignments (shorter list with points) they are followed by the weekly schedule. Links to sources are provided for your convenience.

- When you get ready to read -
*never be in a hurry*. It takes time to think about the big ideas, what they mean, and how teachers use them so slow down achieve*flow*and enjoy the mathematical and the pedagogical thinking and learning. - The purpose of your reading should be to
*reflect*on what you know about teaching mathematics and how to improve on that understanding to become a better teacher. Therefore, as you read identify and record pedagogical ideas related to the mathematical ideas you believe will be useful for you as a professional educator. In practice pedagogy interacts with the mathematics and we often stop to think about one, at the exclusion of the other, which can be problematic. So try to deliberately include both in your thinking by asking how students learn and teachers teach the ideas of mathematics for mathematical literacy. If you have questions or comments about any of the information, bring them to class as the professor will start each class by asking, "What questions do you have?" - The first three chapters 0-2 provide background information for teaching and learning (pedagogy) and the processes or practices of mathematics (doing math or mathematizing). Some people tend to want to skip over this information, because it may not match their previous experiences in math and hence their ideas of what is mathematical. However, it includes the essence of what is mathematics and must be included if you are to become an outstanding teacher, who is able to facilitate student's use and value of mathematics. Accomplished when teachers make good decision about: what to teach, what tasks to use, what questions to ask, how to sequence tasks, how to assess, what to assess, and how to make all the thousands of decision a teacher makes everyday. Most importantly it includes the mathematical practice and processes mathematicians use. This information is classified in the standards as
*processes*for doing math. In the*Constructing Mathematics series*it is called mathematizing. In the*Common Core State Standards for Mathematics*(CCSSM) it is the eight mathematical practices. It relates to pedagogy (teaching and learning) because it describes how students must do mathematics. It is what teachers need to know when assessing students to attain information to provide tasks or problems and activities to help them learn mathematics. Therefore, these chapters discuss the what, how, when, and in what ways to facilitate students eight mathematical practices of the CCSSM: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics.5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning. Using the mathematical processes:*problem solving, reasoning and proof, representation, communication, connections*in a manner for students to acquire positive dispositions: values, attitudes, and habits of mind, for mathematics. - Chapters 4, 5, 6, 7, 8, 9, 12, 14, 15, focus on the content of mathematics along with how, when, and in what ways to interact with students to facilitate their learning. The content of mathematics (number value and operations, geometry and measurement, algebra, and data analysis and probability) which is necessary to be mathematically literate.
- Information in all the chapters will be used for all class assignments: chapter application notes; video analysis; mathematical educator position paper: outline and final paper; curriculum pieces; and instructional sequence plan. The activities and vocabulary for each chapter is to provide background information for these assignments as well as for making better pedagogical decisions.

*Reading Assignments for*Mathematics: A Good Beginning (15 * 20 = 300)

Chapter 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15

- Read each chapters and identify the big mathematical idea(s) (landmarks in the constructing mathematics series) identify them and how to communicate their meaning orally, in writing, visually, and concretely.
- Unpack the related information needed to construct their meaning. Identify these ideas and how they are related to each other and the big ideas.
- Create a sequence of how the ideas might be conceptualized. What ideas have to be made sense of to build upon and connect with other ideas to understand and create the bigger ideas.
- Identify activities to assess and facilitate the conceptualization for the ideas.
- Create and bring a copy of a concept map to hand in on the first day the chapters are listed in the schedule. Points will be assigned based on the evidence of an honest attempt to come to class prepared.
- Concepts and sequences are referenced Online and within each chapter for your use in completing this assignment. This information will be applied to diagnose and prescribe activities for students in the videos.

*Video analysis:*(12*20=240)

- Be familiar with the information in the textbook that relates to the content topic of the group of videos. The big ideas for the topic and an unpacked sequence of information that needs to be known for the content area.
- Use the matrix provided for the sets of videos or create your own outline for the areas described.
- View the video clips. find links to worksheets in schedule.
- Review the description of what the student did on the matrix.
- Describe what you can infer about what the student knows and describe what specifically the student did to validate your inferences.
- Identify where in your sequence the student's understanding is.
- Describe evidence to support that placement. (What the student did or couldn't do and what that suggests he or she knows.)
- Make recommendations of activities, from the book, to be used to build on their understanding and move toward mathematical literacy?

*Reflection for*Algebra book (100) ... Suggestions ...

- My notes on reasoning and proof should provide a concise review of information to accompany the book. Additionally related information is at the Algebra directory and the Reasoning and proof directory.
- Read the chapter and
*identify*four ideas (may be polka dotted items on the reference page), and describe the*value*of each for students. *Additionally*select one idea from the chapter and describe an activity that can be used with students: one you have viewed, or participated in. Describe with a specific example of its use and tell how it was or wasn't of value. If you have not experienced one, then select, find, or make one up you would like to see or try and describe it, a specific example, and its value.

*Reflection for Young Mathematicians reading activity*(50)

- Select one of the following three
*Young Mathematicians at Work*books:

*Young Mathematicians at Work Constructing - Number Sense, Addition and Subtraction*, suggested for those interested in grades K-2*Young Mathematicians at Work Constructing -**Multiplication and Division*suggested for those interested in grades 3-4+;*Young Mathematicians at Work Constructing**- Fractions, Decimals, and Percentages*suggested for those interested grades 5 and above

- Reference information, picture of book and table of contents.
- Read the book and identify at least
*ten ideas, from the book,*you believe are important for teachers to know and apply.*Describe*how you have seen each*applied*with students, your self, or imagine how you would apply it or it should be used and describe the*value*. - Evaluated on quality.

*Research question and suggested implementation from*TCM (

*Teaching Children Math*) or MTMS (

*Mathematics Teaching in the Middle School*) (30)

- Create and identify a question related to teaching and learning mathematics you would like to know more about to better facilitating mathematical literacy in your classroom.
- Research your question in
*one*of these two NCTM journals: Teaching Children Math. or Mathematics Teaching in the Middle School - Find and describe suggestions to answer your question found in the journal article and explain what gives you confidence it will achieve positive results with students.
- Evaluated on the quality.

*Research question and suggested implementation from*JRME (

*Journal for Research in Mathematics Education*) (30)

- Create and identify a question related to teaching and learning mathematics you would like to know more about to better facilitating mathematical literacy in your classroom.
- Research your question in the NCTM: JRME: Journal for Research in Mathematics Education.
- Find and describe suggestions to answer your question found in the journal article and explain what gives you confidence it will achieve positive results with students.
- Evaluated on the quality.

*Curriculum pieces*(250) ... Suggestions ...

A teacher needs to have a solid understanding of what: mathematics is, what mathematical literacy includes, and based on that what we want our students to know at various points of time.

Comprehensive mathematical curriculum documents include or are based on critical ideas related to mathematical literacy, learning, and facilitating mathematical literacy. A framework or outline of these and other important ideas can be made to guide curriculum decision making and its documentation.

While the curriculum pieces are subcategories for some of the processes and content areas of mathematics, the information used to make curricular decisions is common among all.

The selected subcategories required for the course are: Problem solving (50) Representing (50) Proof and Reasoning (50) Number value (50) and a Self selected area. (50)

Samples for curricular areas or dimensions are shown in a corresponding matrix. Each of the five subcategories has the same four areas to document. These areas are:

- Concepts or big ideas with supporting information of what the students need to know or learn.
- Outcomes - what the students will do to demonstrate their learning or what a person can observe to use to infer the extent students have conceptualized the big ideas and related facts and concepts.
- Activities and activity sequences to provide opportunities for students to learn or conceptualize the ideas and apply them in problem solving situations.
- Evaluation levels - the possible levels students might demonstrate an understanding for the information.

Additional resources to assist are:

Resources for process and content areas:

- Problem solving - chapter 2 resources, problem solving directory and sample matrices for processes linked above
- Representing - book chapters and representing directory
- Proof and reasoning chapters 1 and 2 and algebra book, - | reasoning and proof mini lecture | reasoning and proof directory | concept map for reasoning and proof |
- Number value - chapter 3 or place value chapter 4 (number value directory) or any of the other chapters for whole numbers rational, fractions, decimals ...
- Selected area for math content could be Patterns and algebra directory | or Geometry directory or | Measurement directory or | Data analysis and probability directory |

*Position paper and outline or map (10 + 100 = 110) ...*

*Suggested resources:*

- Chapters 0 - 2
- NCTM standards
- Principled procedures of mathematics
- Common Core State Standards for mathematics summary
- Suggestions for professional educator development. Including ideas for some of the categories

*Outline or map* (10)

- Outline or map words and maybe phrases that you want associated with categories related to how educators facilitate mathematical literacy: multidimensional math description, how people learn, how people become mathematically literate, how to help teach/facilitate/instruct/ mathematics literacy, and how to assess mathematical literacies' dimensions.

*Final paper* (100)

- Quality and comprehensiveness of the position taken as a professional math educator that is consistent with current research and wisdom of practice as it relates to mathematics as multidimensional, how people learn in general, how people become mathematically literate, how to help teach/facilitate/instruct/ mathematical literacy, and how to assess mathematical literacies' dimensions.

*Instructional sequence teaching plan (100)*

There are several ways to think about information to sequence experiences for students:

- Look at a big idea by imagining a mapping of ideas from simplest to complex (big idea), how one idea logically fits or is required by another in a hierarchy of complexity. (Doing this doesn’t imply that each idea must be taught in isolation or in sequence though).
- Look at how big ideas developed historically.
- Think how your understanding about a big idea was constructed over the years or talk to other people and ask them how they constructed their understanding over the years. This is limited to our more recent ideas since we don’t usually remember much about our own early understandings or misunderstandings as we developed or conceptualization for conservation, early number value, and such.
- Use experiences from working with students; observing their different levels of understanding and how they become more comprehensive over time.
- Read professional books, journals, and other publications on children's development of mathematical big ideas.

When you have identified three or more dimensions or categories (problem solving, representation, number value, ...) Then identify a topic that can be used to integrate parts of each into an investigation, study, or learning sequence.

Resources:

- Considerations for Planning to Facilitate Students' Construction of Big Ideas, Generalizations, Concepts, and Facts
- Review maps for unpacking big ideas | planning concept map categories with explanation | planning concept map for area | planning concept map for classification | planning concept map for reasoning and proof |
- Sample plans: from best to worst

| Counting |Shows depth of planning integration of mathematical dimensions, developmentally appropriate ...

Rounding numbers and body proportion | Includes integration of mathematical dimensions, good for proportion, could use editing for clarity and more depth for procedures

Card trick | Includes integration of mathematical dimensions, good for proof, could use some editing for clarity.

Reading and writing numbers with numeral and words | Good activity for skill building and necessary skill, doesn't include integration of mathematical dimensions,

Estimating chocolate chip | Has potential, but needs a lot more information for integration of mathematical dimensions and extended activities.

*Reflection (30) ... Suggestions ...*

- A good reflection includes discussion on how teachers make decision.
- How teachers interpret or make inferences as to what students know, how teachers make decisions based on this information, and how this process continues on the fly through learning sequences by collecting and analyzing assessment information to determine current levels of understanding for different students as they continually progress from one level to the next.
- For helpful questions to consider for comprehensive reflection, read hints for reflection.

*Final review*: (40)

*Total points* 1300

## Week 1 - January 13, 2014

- Select your choice of one of the following three books obtain a copy, begin to read and write a reflection: Constructing Mathematics books written by Fosnot/Dolk (1. ...number sense, +, -; 2. ... multiplication and division; 3. ... fractions, decimals, percent)
- Read Ch. 0 -
*Teaching in a Changing World: It's Complicated*Mathematics: A Good Beginning - Create a chapter map for the focus question - What do teachers need to know about
*children, society, and mathematics*to facilitate mathematics literacy?

Concepts and relationships to include in the map:

- The
**child, society, and mathematics** - Conceptual and procedural knowledge - card trick will do in class
- Behaviorism, reinforcement (extrinsic and intrinsic), motivation and self-efficacy
- Degree of child orientation - hands-on, minds-on, representation
- What is the information in the Standards and how can it be used by teachers to make curricular decisions? Example these two curricular documents: Principled procedures for a math educator and a curriculum framework or outline. NCTM and Common Core State Standards for mathematics?, NCTM standards,

- Take the math pedagogy survey, bring the print out of your results to class and be prepared to comment on your reactions to what the research suggests about the survey questions.
- Review information on why we have theories and reasons for education, you can skip the two motivational essays to change current educational systems. Then read the 7 questions related to an Educational Philosophy and read my answers. Among the key ideas to consider from a general educational philosophy is how to make what students are learning immediately valuable for them so they can apply it in their lives.
- Card tricks - The information demonstrates the difference between conceptual and procedural thinking and learning. How were they included on your chapter map?

## Week 2 - January 20, 2014

- Read Ch. 1
*- Designing Mathematics Instruction: Learning Trajectories and Emerging Technology* - Create a chapter map for the focus question - What information do you need to know to plan for teaching mathematics?

Concepts and relationships to include in the map:

- Your personal philosophy and research connections. Week 1.
- Communication as the pedagogical link between students, society, and students.
- Standards, and what's math. Week 1 ...
- Internal and external representations
- Problems, open ended and closed
- Learning theories - constructivism, rote learning, behavior, Vygotsky (ZPD), Piaget learning theory, child development: preoperational thinking, developing conservation, and concrete operational thinking , formal operational
- Technology (TDI, TEI, TMI. using the computer as a tool, tutor, and tutee
- Suggested planning map categories with explanations for each category.

- How flexible are your mathematical abilities? Here are some problems to challenge your math flexibility. Mental math quiz - Travel to the quiz, read the problem, solve it in your head, and write the answer on the paper beside the number of the problem. Remember to solve the problem in your head. ONLY write the answers. When you are done move to the URL that has some ways I thought of to solve the problems. How did your solutions compare? How do these problems relate to the ideas of - what the book will describe as a good math problem in the next chapter?

## Week 3 - January 27, 2014

- Class activity for Reasoning and proof, problem solving, representing, geometry... How many squares activity
- Use the sample concept map for learning proof and reasoning to create additional ideas for each category ... Suggested resources book and mini lecture on reasoning and proof | links in Algebra directory | concept map for reasoning and proof |
- Read and reflect on Algebra book chapter 10
- - Proof - sample three different developmental levels odd + odd = even | video student proving |
- Begin to work on your curriculum piece for Proof and reasoning - see more information in the Curriculum Pieces Suggestions box above.
- Ch 2 -
*Mathematical Practices, Pathways to Problem Solving* - Create a chapter map for the focus question - What information do you need to know to plan for teaching problem solving in mathematics?
- Discussion. How do the ideas associated with the words in the chapter and study guide relate to math education and how can each be used for positive effects? One suggestion might be to interview a teacher about the ideas and ask how they fit into her planning and the school's curriculum. Translation of ideas;

- Classification - properties or characteristics, similar, different; conditions - sufficient, necessary, equivalent, independent; reasoning and proof - inductive, deductive, counter example, faulty reasoning, needed information, extraneous information, generating cases, approximating, analogies; metacognition; & high order thinking...
- Bloom's levels of thinking.
- What makes a good problem and Guiding Questions to Prepare Mathematical Investigations, Tasks, or Powerful Problem, Ways to communicate problems or represent problems, open ended and closed questions or problems.
- Identify skills or categories of information you think needs to be taught and learned to solve math problems?
- Are the problems on the
*mental math review*good problems? Why or why not? - Begin to work on your curriculum piece for Proof and reasoning - Check out the resources at this link for Problem solving. Problem solving is one of the categories in the processes dimension. I would bet it is in every curriculum or standard categorization of mathematics and mathematical literacy. What does a person need to know about problem solving according to yours selected curriculum. Would your ideal curriculum be like the one you are using or different? If different, record the differences on the - Big Ideas for my grade level.

## Week 4 - February 3, 2014

- Read and reflect on Algebra book chapter 1 - Algebra: Structures or Structuring?
- Read and reflect on Algebra book chapter 2 - The Landscape of Learning
- What's mathematics anyway? Add a definition of mathematics and mathematical literacy to your notes for your position paper. Some sample definitions of mathematics. Not to be confused with the dimensions of mathematics.
- If there are any links you have not visited in the curriculum plans or position paper, then visit them this week.
- Select an activity, describe the activity very briefly and identify what was used as an external representations and what might have been students' internal representation.
- Use your math curriculum to identify which of the following are included and give a brief example if it is. If they are not, explain how they should or shouldn't be included. Numbers - counting, whole, finite, rationale infinite, zero, integers; sets - elements, union, intersection; classification, operations - +, -, *, /, inverse; symbols of inclusion; algebra; representations; variables, formulas, equality, inequality, patterns, and functions.
- Add ideas and words to your position paper outline or map.
- How will you plan for math lessons, lesson plan, activity sequence?
- Reasoning and proof curriculum piece
*due*

## Week 5 - February 10, 2014

- Finish reading your chosen
*Construction of Mathematics book*and turn in you book notes. - Curriculum piece problem solving
*due* - Chapter 3
*Getting Ready for a Good Beginning - Classification, Number sense, and Counting* - Create a concept map for learning number sense or number value. Suggested resources book and prenumber sense - number sense

- Videos | video worksheet |
- Read and reflect on Algebra book chapter 3 - Early Structuring of the number system

## Week 6 - February 17, 2014

- Chapter 4 -
*100s, 10s, 1s, The Best Yet! Our Base Ten System of Numeration* - Create a concept map for learning place value. Suggested resources book and Place value,
- Videos | video worksheet |
- How is your position paper coming? Write what you want to include for what is math, math literacy, how to learn and teach mathematics.
- Position paper outline
*due* - Curriculum piece representing
*due*

## Week 7 - February 24, 2014

- Chapter 5 -
*Addition and Subtraction of Whole Numbers: Constructing Meaning* - Create a concept map for learning addition and subtraction. Suggested resources book and Addition and Subtraction of Whole Numbers and basic operations (types of addition and subtraction), basic facts,
- Videos | video worksheet |
- Describe how to facilitate mathematical learning for the overview of the year plan.
- Chapter 6
*Addition and Subtraction Whole Number Algorithms: Understanding, Applying, and Estimating* - Bring a sequence for transition from addition and subtraction to using an algorithm. Suggested resources book and
- Videos | video worksheet |

- Mathematics research number one
*due*-*research question and suggested implementation from TCM or TMMS*.

## Week 8 - March 3, 2014

- Chapter 7
*Multiplication and Division of Whole Numbers: Constructing Meaning* - Create a concept map for learning multiplication and division. Suggested resources book and - Multiplication and Division of Whole Number, basic facts, properties, (unpacking) | multiplication represented as rectangles | second example | third as - work sheet |
- Videos | video worksheet |
- Read and reflect on Algebra book chapter 4 - Continuing the Journey: The role of contexts and models

## March 10, 2014... mid term break

## Week 9 - March 17, 2014 Assessment retreat Friday 21 no class

- Chapter 8
*Multiplication and Division Algorithms: Understanding, Applying, and Estimating* - Create a concept map for transitioning to a multiplication and division algorithm. Suggested resources book and Multiplication and Division of Whole Numbers Algorithm
- Videos | video worksheet |
- Multiplication of multi-digit numbers | multiplication related to algebra |
- Curriculum Pieces for number value

## Week 10 - March 24, 2014

- Chapter 9
*Some Theory about Numbers: Factors, Multiples, Primes, and Composites* - Read and reflect on Algebra book chapter 6 - Variation versus variables
- Create a concept map for topics in the chapter.
- There are no videos for this chapter. Complete the worksheet
- Self-selected curriculum piece

## Week 11 - March 31, 2014

- Chapter 10
*Not All Numbers Are Whole Numbers: Representing, Adding, and Subtracting Rational Number* - Create a concept map for rationale numbers. Suggested resources book and - Rational numbers - fractions,
- Videos | video worksheet | mixed fractions |
- Algebra chapter 5 - Equivalence on the Horizon

## Week 12 - April 7, 2014

- Chapter 11
*Security it Knowing why: Multiplying and Dividing Rational Numbers* - Read and reflect on Algebra book chapter 7 - Integers and equivalence
- Create a concept map for learning the rest of the rationals. Suggested resources book and - fractions decimals, percents - decimal concepts
- Videos | video worksheet |
- Constructing Mathematics research
*research question and suggested implementation from JRME*

## Week 13 - April 14 2014

*Sequence plan due*. Evaluation criteria- Chapter 12
*Seeing is Believing: Constructing Geometry Ideas* - Videos | video worksheet |
- Create a concept map for learning geometry. Suggested resources book and - concepts - developmental sequence - another way to view geometric development Van Hiele

## Week 14 - April 21, 2014 Monday spring break no class

- Chapter 14
*Sizing it Up: The Attributes of Measurement: The Measurement of Attributes* - Support - concepts - curriculum
- Videos | video worksheet |
- Read and reflect on Algebra book 8 - Comparing quantities and relations
- Read and reflect on Algebra book 9 - Algebraic strategies
- Position paper
*due*

## Week 15 - April 28, 2014

- Chapter 15
*Making Numbers Count: Collect and Represent, Interpret and Predict (Analyzing Data and Using Probability)* - Create a concept map for data analysis and probability
- Concepts -K-4, 5-8, 9-12 - graphs - statistics
- Videos | video worksheet |
- Done teaching
*Instructional Sequence plan* *Reflect due and share the reflection from teaching a mathematics activity.*Evaluation criteria -- All assignments
*due*for any exception allowed. Except final review

## Week 16 - May 5, 2014

- A bit more chapter 15 related ...

## Week 17 - May 6-9, 2014

- Final class meeting - Wednesday May 7, 01 - 1:00-3:00; 02 - 3:30-5:30

## Graduation May 10, 2013