Assignments Schedule for EDU 432 -
Elementary and Middle School Math Methods

Spring 2014 May 28, 2015

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.

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
  1. 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.
  2. Unpack the related information needed to construct their meaning. Identify these ideas and how they are related to each other and the big ideas.
  3. 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.
  4. Identify activities to assess and facilitate the conceptualization for the ideas.
  5. 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.
  6. 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)
  1. 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.
  2. Use the matrix provided for the sets of videos or create your own outline for the areas described.
  3. View the video clips. find links to worksheets in schedule.
  4. Review the description of what the student did on the matrix.
  5. Describe what you can infer about what the student knows and describe what specifically the student did to validate your inferences.
  6. Identify where in your sequence the student's understanding is.
  7. Describe evidence to support that placement. (What the student did or couldn't do and what that suggests he or she knows.)
  8. 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:
  1. Young Mathematicians at Work Constructing - Number Sense, Addition and Subtraction, suggested for those interested in grades K-2
  2. Young Mathematicians at Work Constructing - Multiplication and Division suggested for those interested in grades 3-4+;
  3. 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:

  1. Concepts or big ideas with supporting information of what the students need to know or learn.
  2. 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.
  3. Activities and activity sequences to provide opportunities for students to learn or conceptualize the ideas and apply them in problem solving situations.
  4. Evaluation levels - the possible levels students might demonstrate an understanding for the information.

Additional resources to assist are:

Resources for process and content areas:

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

Suggested resources:

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:

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

  1. The child, society, and mathematics
  2. Conceptual and procedural knowledge - card trick will do in class
  3. Behaviorism, reinforcement (extrinsic and intrinsic), motivation and self-efficacy
  4. Degree of child orientation - hands-on, minds-on, representation
  5. 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,

Week 2 - January 20, 2014

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

Week 3 - January 27, 2014

  1. 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...
  2. Bloom's levels of thinking.
  3. 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.
  4. Identify skills or categories of information you think needs to be taught and learned to solve math problems?
  5. Are the problems on the mental math review good problems? Why or why not?
  6. 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

Week 5 - February 10, 2014

Week 6 - February 17, 2014

Week 7 - February 24, 2014

Week 8 - March 3, 2014

March 10, 2014... mid term break

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

Week 10 - March 24, 2014

Week 11 - March 31, 2014

Week 12 - April 7, 2014

Week 13 - April 14 2014

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

Week 15 - April 28, 2014

Week 16 - May 5, 2014

Week 17 - May 6-9, 2014

Graduation May 10, 2013

 

Dr. Robert Sweetland's notes