# Mathematical notes

The purpose of these pages is to document a knowledge base of information for educators to teach mathematics. Information is organized in three broad areas:

- Mathematical literacy knowledge base
- Knowledge on the development of math literacy and activities to develop it, and
- Knowledge to develop professionally and create learning experiences to facilitate mathematical literacy and teacher tools to assist.

*Knowledge base* for mathematical literacy:

Definitions, concepts, outcomes, & vocabulary by levels

- Definitions of mathematics and focus questions to analyze them
- Mathematical concepts / outcomes includes content, processes, and attitudinal (values & dispositions)
- Algebra & patterns
- Attitudinal (disposition & value statements)
- Classification
- Communication
- Connections & perspectives
- Data Analysis & Probability
- Geometry
- Measurement & measurement estimation
- Number value
- Operations & computation estimation
- Problem solving
- Reasoning & proof
- Relative Position and Motion
- Variable

- Mathematical vocabulary lists by dimensions & levels

## Knowledge on the *development* of math literacy & *activities* to develop it.

### Process dimensions

### Content dimensions

## Knowledge base for professional mathematical development

- Books for professional educators
- Books for professional math educators
- Conceptual and procedural knowledge - Illustrated with card trick magic ...
- Considerations for Planning to Teach: Big ideas, concepts, and generalizations
- General information for professional educators
- Hands on: What is it really?
- History of mathematics in North America
- Independent study: planning guide to help select and refine topics
- Misunderstood mind on PBS
- Principled procedures for Math Educators
- Reflecting on mathematical instructional practice suggestions
- Sample outline with suggestions for creating a professional portfolio
- Survey your current mathematical practices and research, then compare your thoughts with what current research suggests.
- Solve some arithmetic problems and compared your solutions to other solutions. When you complete it, see how your solutions compare to these solutions.
- Mathematical vocabulary lists to review for planning
- Visual & Spatial Representations, Modes of visual learning, Literacy, Research, Activities

## Math teacher's planning tool box

### General planning

How to map or outline content to prepare for instruction.

- Framework with explanations of mapping categories for planning to teach big ideas, concepts or generalizations
- Blank planning map
- Classification sample planning map
- Geometry, Area sample planning map
- Proof and reasoning sample planning map

Planning information

- General steps in planning to facilitate generalization
- Overview for planning and creating curriculum documents
- Outline for a year plan and suggestions
- Outline for a sequence or unit plan with suggestions
- Thoughts about math games, competitions, and simulations
- Use of literature to teach math

Suggestions for selecting problems and investigations

- Problems by categories
- Selecting problems --->> > sample problems with different formats , characteristics of a good problem , guiding questions to prepare mathematical investigations, tasks, or powerful problem

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 plans

- Card trick | Includes integration of mathematical dimensions, good for proof, could use some editing for clarity card trick demonstration with different instructional strategies [conceptual & procedural].
- 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.

Assorted tools

- Characteristic of mathematically talented & development of talent
- Mathematics & Logic adapted Frayer Model
- Manipulative materials list
- Parent letter for using manipulatives and representation with multiplication & division
- Eight different uses of literature for teaching mathematics
- Annotated list of literature and classroom uses in NCTM Journals
- Mathematical terms and their representations with Cuisenaire Rods
- Investigations with Cuisenaire rods & student work sheets
- Comparison or English - Spanish wording in math. Translations of some mathematical ideas. Notice how some are the similar and others are very different. Demonstrates that direct translation is generally not as simple as one thinks unless one is bilingual.
- Math Their Way notes

## Assessment

- Assessment introduction and review: [Suggestion for creating criteria referenced assessments] [Norm-referenced test information]
- Letter to parents for student lead conferences and authentic assessment
- Questions from standardized achievement tests. SAT, FAA, MCAT, ...
- PISA 2012 Problem-Solving sample questions
- Curriculm Documents with concepts, outcomes, and assessment levels

*Sample assessments*

- Student survey - open ended about student's math practice - one page
- Student survey - rating sheet (always, mostly, some, not) - about two page

## Curriculum

- Comparison of dimensions and categories of NCTM and CCSS of math
- Concepts, suggested sequences, plans, rubrics, and other stuff may be found linked at the top of the page in mathematics content.
- Standards
- Curriculm Documents with concepts, outcomes, and assessment levels
- Rubrics click the desired mathematics dimensions at the top of the page to locate concepts... assessment... evaluation ...
- Notes on exemplary and promising math programs

## Workshops, courses, tutorials

- ESU #1 Algebra Workshop information
- Information for graduate Class or professional development
- Information for preservice Class or professional development
- Videos for professional development
- Technology Help Pages - ILife and Windows Media tutorials and help pages for using/ making: photos, audio, and video --->>> directions and tutorials...
- NATM fall conference presentation 2006
- NATM spring conference presentation 2005
- NCTM regional presentation fall 2004

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*Problems & challenges*:

Activities by dimensions:

*Process*:

*Content*:

- Algebra, Patterns, Ratio, & Proportion
- Geometry & Visual spatial reasoning & representation
- Data Analysis & Probability
- Measurement
- Number value & Operations (addition, subtraction, multiplication, & division)

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There are *10* kinds of people in the world. Those who understand *binary* and those who don't.

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Jeffery Weld asks:

*Why is it whenever* students don't do well on a national test the news agencies report one or a few particular items that were on the test by stating the test questions, then they believe it is necessary to provide the answers. *If their listeners need the answers, why should we expect students to be able to answer it correctly? *

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The Jibaro Indians of the Amazon rain forest express the number five by the phrase

"wehe amukei,"

"I have finished one hand," and the number ten by

"mai wehe amukei,"

"I have finished both hands."

*Frank J. Swetz*

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"These landmarks must not be treated as objectives to be marked off. The goal is to mathematize not pass landmarks. Enjoy the journey create systems to do mathematics with the knowledge that students have. One should recognize the fallacy of thinking there can be one activity or sequence of activities for all students."

*Catherine Twomey Fosnot & Maarten Dolk* in Young Mathematicians at Work: Constructing Number Sense, Addition, and Subtraction

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One of the universal customs that man has successfully established on earth is the

*Hindu - Arabic numerals*

to record numbers.

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Math is meditation for thinking about the world.

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Geometry is the science of correct reasoning on incorrect figures.

* George Polya *

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*Galileo* was put under house arrest and allowed visitors, but no *mathematicians*.

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*Directory links*:

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*U.S. Students*

Score in the top tier on

the PISA 2012 Math Creative Problem SolvingAssessment

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Read*... Cell phone mathematics.

*The story of how Brad Parkinson*used creativity and mathematics to enable the use of cell phones.

--------- *Free* --------

---* Coding software* ---

*Mozilla*:

*Google*:

Made with code - projects, mentors, resources ...

---*--Free & for sale* ---

--- Graphing software ---

Read: *The Graphing Calculator Story* by Ron Avitzur, then below the article are links to download the software.