# Course Information for Mathematical Reasoning EDU 614

(3 Credit hours)

July 2014

The intention of this page it to explain and provide resources for each activity.

- Syllabus
- General suggestions
- Required readings
- Activity sheet
- Math pedagogy survey
- Mental math quiz
- Conceptual / procedural - card trick
- Forum
- Position paper
- Reflections
- Activities
- Reflective listening
- Videos

## Syllabus

If you haven't read the syllabus, please do. It is available from the Menu on the left and there is also a copy in Resources.

## General Suggestions

Never be in a hurry. It takes time to think about the big ideas, what they mean, and how teachers use them so relax slow down and achieve *flow* while you enjoy the mathematical and the pedagogical thinking and learning. Particularly if you are reading on the internet. Seems we all have a hankering to want to move on or click that next button. If you are unsure about an assignment or have a question, contact me.

Your purpose should be to reflect on what you know about teaching mathematics and how to improve on that understanding to become a better teacher. Therefore, identify and note pedagogical ideas that can be related to and used with the mathematical ideas you believe will be useful.

Remember the goal of the course is to analyze, sythesize, and evaluate new ideas you can apply as a professional educator to faciliate students' learning by making good decisions based on and congruent with Principled procedures for mathematics educators and curriculum decision makers. You should find these procedures, also referenced in the syllabus, helpful in making good decision. I encourage you to revisit them periodically. The information is powerful and hopefully will be more so as you read your selected readings or participate in other activities and revisit them.

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?

## Professional readings

Readings - at least 444 pages from books or journal articles are required. You may select from this list of recommended books for math educators, or you may also select journal articles from the National Council of Teachers of Mathematics. You can search the database at NCTM or Ebsco online at the Conn Library. Most of the articles are available in full text online. If they are not you can Message me the reference information for articles and I will put a .pdf in the Resources for you.

*National Council of Teachers of Mathematics (NCTM) has good resources for teachers*

Journals:

If there are other readings you would like to include, ask me and I will approve them if I believe they are appropriate for the intent of the class.

While I am on the subject of research materials there is a *Distance Library brochure* in the Resources on how you can optain references through the Conn Library. If there are any materials you would like to see, I encourage you to contact

You are encouraged to read the books as soon as possible, even though the due dates are across four weeks.

## Activities

### Activity Sheet

Course activity sheet: Select activities and complete the course activity sheet listing the activities you plan on doing for the class, include a short description of what you intend to do, and the number of points. The total number of points should be 1 000 if your goal is for a grade of A.

### Sample Activity sheet:

Required short activities

(20 points) Mathematical Pedagogy Misconceptions Survey

(20 points) Mental Math quiz

(20 points) Conceptual and procedural thinking - card trick

Required readings

1. (100 points) Powerful Problem Solving: Activities for Sense Making with Mathematical Practices. 2013: 111 pages

2. (100 points) Powerful Problem Solving: Activities for Sense Making with Mathematical Practices. 2013: 81 pages

Mathematics a Good Beginning. chapter 0 and 1 = 33 pages

3. (100 points) Mathematics a Good Beginning. chapter 3 - 7. 125 pages

4. (100 points) Mathematics a Good Beginning. chapter 8 - 11. 111 pages

(50 points) Professional Teaching Reflections

(50 points) Professional Teaching Reflections

(50 points) Curriculum or big idea mapping or outline to use with teaching reflection and activity plan

(50 points) Curriculum or big idea mapping or outline to use with teaching reflection and activity plan

(30 points) Activity plan to use with teaching reflection

(30 points) Activity plan to use with teaching reflection

(100 points) Professional writings short position paper, 2-3 pages, on What needs to be know to be mathematical literate, how students learn mathematics, how it should be taught and assessed.

(100 points) Lesson sequence or unit

(80 points) Student performance analysis from videos

1000 points

## Required short activities

### Mathematical Pedagogy misconceptions survey.

Take the quiz, read about what the research suggests, and comment in the Forum. Question are welcomed.

### Mental Math quiz

There are 21 math problems for you to solve in your head. Yes, mentally. Oh, you don't have to transmit the answer to me mentally, you can write the answer for each problem. It is a timed test and should be completed in under ten minutes. Take the Mental Math Quiz and when you are done, review some possible solutions. After reviewing the information comment on the experience in the Forum. Question are welcomed.

### Conceptual and Procedural thinking and learning - Card trick

The information demonstrates the difference between conceptual and procedural thinking and learning. Review the information and post how yo will apply it in the Forum.

## Professional writing:

Could be a research paper, a position paper, or white paper for the role of mathematics in education that could be shared with parents, other educators, or for your personal use or any other writing related to math education.

Some sample topics:

- What is mathematical literacy?
- How do students learn mathematics?
- How should mathematics be taught?
- How should mathematics be assessed.

Information about the topics above see this URL and of course the Principled procedures for mathematics educators.

- What does research say about ________ (fill in the blank with any math idea: content, practice, pedagogy...)

Writing suggestions:

Chose your words carefully and be sure that any ambiguous words are defined or explained in context so its meaning is communicated. Words and phrases like "hands on", "concrete", "abstract", "basics", and "problem solving" among others have been defined by different people sometimes in direct opposition to each other. If you aren't sure about a word or phrase, try it out on the discussion board or ask a question of the professor. Believe it or not I enjoy that kind of discussion and look forward to it.

If you are not sure what you might write about or project to create you might find these Planning Steps and Sample process helpful. Completing this work sheet is ** not required**. Even though it is kind of corny, it isn't time consuming, if you don't have a good idea of what you want to do, then that is an excellent reason to maybe work through this process.

## Professional Teaching Reflections

Select any math activity, plan on how to use to instruct another person, teach it, and reflect on the process. The student can be anyone of any age, as long as there can be a true facilitation of learning mathematical ideas with the activity. Therefore, the other person or student should not have experienced the activity and they are not fully proficient with the ideas required for them to complete the activity and conceptualize the concepts. Suggestion on activities may come from your readings and ideas on quality reflections are available at this URL.

## Student performance analysis from videos

Select and watch videos of students performing an activity, analyze what the student knows, any difficulty he or she may be encountering and make a recommendation of where instruction might start. There are summary sheets for each group of videos, but you do not need to use them. Your choice. Nor do you need to do all videos in a set.

Videos are available at this link along with summary sheets,

## Curriculum or big idea mapping or outline

Select a topic or big idea and create a map or outline to include information which is considered by teachers when facilitating learning of the big idea. Research suggests ideas high quality teachers consider ideas included in these categories: perceptual ideas or misconceptions, facts and properties, concepts and big ideas, observations on which to build understanding, bridges or transformations from facts and observations to concepts or big ideas, activities, levels of understanding or performance, and real world understanding.

Concept mapping or outlining instructional considerations

- Category Explanations for Planning to Teach Big Ideas, Concepts or Generalizations
- Blank Concept Map
- Concept Map for Classification
- Concept Map for Mathematics Topic of Area
- Concept Map for Proof and reasoning

## Lesson sequence or unit

Lesson sequences string several activities or lessons together for a topic or theme over a period of time usually longer than a week or two. Four significant conditions are usually apparent in a good comprehensive sequence. The mathematical information for at least one topic is presented in a conceptually comprehensive manner as to allow students to conceptualize the big ideas in a comprehensive manner as it relates to the mathematical topic and is appropriate for their developmental levels. Second, the mathematical information included in the sequence includes ideas from multiple dimensions, and includes in the planning how those different ideas will be discussed and used by the students as they relate to big ideas for the different dimensions and topic. Third, the topic and ideas are selected and presented in a manner that motivates students by relating to world experiences and applications for which students experience in their everyday lives. Fourth, the information needed to facilitate students learning is included so a reader could use the sequence to teach.

Sample parts and pieces of sequence plans

- Sequence plan with activities to build to cardinality. Good start with multiple concepts, sequence of concepts, and very good lists of activities for concepts. Need more integration of mathematical dimensions for practice of mathemtics and scoring guides with levels.
- Sequence plan for measurement, data analysis, and proportion Includes beginning ideas for integration of mathematical dimensions and some for mathematical practices, good for proportion, could use editing for clarity and more depth of procedures.

## Activity plan

An activity plan explains how to do one activity with students. It may be used within a sequence or it could be used on its own. It can have all four of the significant conditions as a sequence, except the comprehensiveness of developing a big idea and topic.

Activity plans

- 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.

## Curriculum outline or guide parts

This is not a complete curriculum guide. The scope of this activity would develop for a specific grade level an outline of the categories for students to learn to become mathematically literate. For each of these categories big ideas or concepts would be included, possible outcome or indicators, assessment levels in scoring guides or a rubric, and some sample activities to show how the sample activities would provide students with opportunities to learn in the multiple categories (threading across the curriculum).

## Other student created activities

Create your own and Message me.

## Focus Questions for the Course and possible writing topics.

When ever I think about a subject I think of a few questions to focus on the big ideas that outstanding teachers of the subject, in this case mathematics, need to know. These are what I think as

* Focus Questions for the course:*

- What is mathematics?
- What needs to be know for mathematical literacy?
- How is mathematical literacy assessed?
- How do children, adolescents, and adults learn and attain mathematical literacy?
- How do teachers facilitate mathematical literacy?

Next I asked how would outstanding teachers answer these questions and what would they do to demonstrate their outstanding abilities. That of course is the content of the class and what all of us are in the process of seeking. As we do we are constantly thinking about our answers to these questions to guide our thinking.

I look forward to this class and hope you enjoy it and get as much from it as I know I will.

Thanks,