Course Philosophy:

 

Reconstructing Mathematics Understanding: Quality and depth of our learning depends on our ability to think about our own thinking and learning, to foster our own metacognitive reflection. Are you aware of some strategies that promote metacognition?

As teachers we want to be independent lifelong learners. That involves a collection of skills that are often named as self-regulated or autonomous learning skills. What might these skills be?

This class is about learning mathematics for understanding in an environment that nurtures development of autonomous learning skills and promotes metacognition.

Questioning: If you ask me "What is ..." I might answer with "Where are you in your thinking about it?" OR say, "Let's think about it together." My goal is to engage you in your own learning by providing a hint or sub-question that might take you a step closer to finding your answer.

Course Changes:We will go over the syllabus and due dates during the first class. Late work will not be accepted so please make sure you have these dates in your schedule. I try to improve this course every semester which often involves a number of changes. So, please check the things before accepting what you hear from students that took this course in earlier semesters.

During the semester, I usually do not make any changes, unless absolutely necessary, in which case I will definitely inform you about it and probably negotiate that with you in advance.

Input from my current and former students: I appreciate very much any input from my students. Please feel free to ask questions both in class and outside of the class.

What is your challenge/concern after reading this? What are possible misconceptions surfacing from this philosophy? Think about it. Talk with your colleagues about it. Email me. Let’s discuss it in class.

 

 

Faculty Member: Dr. Mara Alagic         

Office: 205 Corbin              

Office Hours:
        Monday: Skype or a Blackboard Chat: 9:00am – noon
        Tuesday: 10:00am – 1:00pm (when online week, 8:00 – 11:00)
        Other days by appointment; Appointment recommended.
        Skype contact name: maraalagic
        I do have open door policy. If I am in my office, please come in.

E-mail Address:  mara.alagic@wichita.edu (more efficient than phone)

Telephone:    978 6974

Department: Curriculum and Instruction

 

Note: Weather Cancellations – Call 978-6633 (select 2) to obtain information on weather related class cancellations.

 

Course Title: Mathematical Investigations (2 credit hours)

Catalog Description: This course is founded on National Council of Teachers of Mathematics (nctm.org) principles and standards for school mathematics. It will model an investigative problem-based approach to mathematics focusing on process standards: problem solving, reasoning and proof, communication, connections and multiple representations. Students should gain an active understanding of problem-posing and problem-solving in mathematics, as well as a familiarity with heuristics for problem-solving. Course will also utilize appropriate technology-based cognitive tools.

Prerequisites: MATH 501 Mathematics for Elementary teachers

 

Major Topics:

Mathematical Processes:

 

1. Problem Posing and Problem Solving: What do non-routine, ill-posed mathematics projects look like?

2. Reasoning and Proof: Inductive and deductive reasoning. What constitutes a mathematical proof at different levels of understanding?

3. Communications: Language of Mathematics

4. Connections: What might integration mean in the mathematics classroom? What is Zone of Proximal Development (ZPD) and how can that concept be useful in teaching? What is scaffolding?

5. Multiple Representations: Open-ended, rich problems; Conceptual understanding. 

 

Cognitive science: How people learn mathematics?

 

What is mathematical understanding? What’s THE right way to teach mathematics? Doesn’t every mathematics classroom look the same? How can I assess and evaluate my students’ learning? How can I effectively use technology within my mathematics program? How can I add breadth, depth, and dimension to my students’ mathematical learning?

 

Technology Expectations:  CORE 2 students will be able to

·        Use common media storage systems such as CD-ROM and Zip disks.

·        Create hyperlinks and graphics in word processing documents.

·        Use electronic resources ethically.

·        Manipulate data in a spreadsheet program.

·         Use presentation software to make class presentations.

·        Use word processing or desktop publishing to create instructional materials or newsletters.

·        Use video projectors, VCR, projection devices, digital cameras, CD/DVD, calculators, and other common instructional technologies.

·        Trouble-shoot basic computer problems.

·        Evaluate electronic materials for accuracy, appropriateness, and credibility.

·        Use concept mapping technologies for planning or instruction.

·        Apply technology and content area standards related to technology to planning and management.

·        Research and apply strategies that support digital equity for all students. (Including assistive technologies)

·        Use multimedia to support instruction.

 

 

Recommended Readings

National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics. National Council of Teachers of Mathematics. Reston, VA (also available online at http://standards.nctm.org/document/index.htm ) 

 

NOTE: I recommend becoming a member of National Council of Teachers of Mathematics (nctm.org). That will give you free access to the electronic textbook and many other things.

 

Math 501 textbook (any version)

National Research Council (2000). How people learn: Brain, mind, experience, and school. Washington, DC: National Academy Press. 

Daniels, H., & Bizar, M. (1998). Methods that matter: Six structures for best practice classrooms. York, ME: Stenhouse.

Carpenter, T. P., Fennema, E., Franke, M. L., Levi, L., & Empson, S. B. (1999). Children's mathematics: Cognitively guided instruction. Portsmouth, NH: Heinemen.

 

Helpful Links

National Council of Teachers of Mathematics http://www.nctm.org/

                NCTM standards  http://standards.nctm.org/

                Electronic Examples: http://standards.nctm.org/document/eexamples/

Illuminations http://illuminations.nctm.org/

Virtual Manipulatives http://nlvm.usu.edu/en/nav/vlibrary.html

Enrich www.nrich.maths.org

The Shodor Education Foundation, Inc. http://www.shodor.org/curriculum/

 

 

 

REFLECTIONS: ONLINE DISCUSSION GROUPS

 

You are a member of a Reflective Pod (online group on the Blackboard site for this class). Your weekly entry will consist of your reflective postings on (a) the topic assigned and (b) the readings of postings of other pod-members.

Every week one person, on a rotating basis, summarizes.

 

Procedure for Online Discussion:

Every week has one reflection/topic.

 1st entry is your first reflection.

2nd entry is your reflection after you read what everybody else submitted; commenting on what they did and relating it to your own contribution and thinking.

3rd entry - only if it is your turn to summarize.

 

You will be turning in your scores with a self-evaluation twice during the semester. I will periodically be checking the online conversations and match them with your self-evaluations.

 

Read rubric carefully to better understand requirements.

 

Online Discussion Rubric	Exemplary 15 pts	Competent 10 pts	Emerging 5 pts
Substantive Postings	Contributes more than one idea that is original to the discussion	Contributes one idea that is original to the discussion	Contributes to the discussion but offers no new ideas
Acknowledging Ideas of Others	Recognizes the contribution of another and expands on the idea with further examples OR  uses examples to explain reason for disagreement	Recognizes the contribution of another and provides some reason for agreement/disagreement	Recognizes the contribution of another with agree/disagree statement
Supporting Ideas	More than one idea supported with multiple examples from personal experiences and from other resources	More than one idea supported with an example from personal experiences or from other resources OR One idea is supported with multiple examples from personal experiences and/or other resources	One idea supported with an example from personal experience or from other resources
Timely Contributions	At least two substantive (competent level) postings completed on time and with separation of at least 24 hours	At least one substantive (competent level) posting completed on time	Posting done but not on schedule

The rubric above is constructed to guide you in self-evaluation of your contributions to your Online Discussion Group. I hope this will encourage creative, high quality discussions related to the learning of mathematics. I hope to build a community of learners engaged in joint knowledge building through discussion. In order to build such a community it is important to include discussions about the broader context of your lives as future teachers and life-long learners. Therefore, I encourage you to broaden your discussions outside of the required reflective discussions.

 

SELF-EVALUATION

 

DO NOT submit self-evaluation before submitting Problem Set One.

You may choose your own format but it has to include enough detail for me to understand how you are progressing in this class; at least one paragraph long report on each of the following questions. For the full number of points, question #1 will probably require more than one paragraph - select concepts that you find most significant, and go from there...:

1. What did I learn? Be very specific and give details. Think about this as being a test on what you have learned so far. Or, if you do not like tests, consider this a journal entry about the mathematics content knowledge and mathematics-specific pedagogical content knowledge (e.g. scaffolding) that you have acquired so far. Carefully select what you want to write about (2-3 concepts). Remember to support your statements clearly and thoughtfully. Do not write similar statements over and over; progress carefully from one thought to another.

2. What would I like to learn/change?  Be very specific.

3. The following two weeks I will focus on . . .  What can YOU do to enhance your learning related to this class? Include dispositions (both for yourself and me).

4. What is your point-average at this moment? How do you feel about it? (Attach a spreadsheet with your grades; include self-evaluation for online reflective journaling).

Clarifying self-evaluation requirements:

What do you mean when you say "select 2-3 concepts" to write about?

As you have been working on your Problem Set One and participated in online discussions, you used some mathematical and pedagogical concepts (open-ended problems, problem solving, volume, scaffolding, metacognition, zone of proximal development…). Select "2-3 concepts" and write in details what you learned and how you might apply that in your own future classroom.

What does it mean when you say to include dispositions for me and yourself? What is a disposition?

Define what dispositions are and reflect both on yours and mine (teacher’s) dispositions.

( If you did not have a chance to learn (yet) what dispositions are in your educational or other classes, try to find a good definition of disposition in the library, on the Internet or your own books.)

How do I know what my point average is if nothing has been graded?

Use the reflection rubric, grade your reflections as objectively as possible and include that into your self-evaluation. Provide argumentation that shows how you understand the reflection rubric and how you are meeting the requirements.

DO NOT submit self-evaluation before submitting Problem Set One.

 

PS1 – PS3: PROBLEM SETS

Your task is to design a collection of problems about a concept) that satisfy conditions listed below and the rubric.

 

Each problem set starts with ONE open-ended, real-life related challenging problem focusing on a big mathematical idea - volume for the first set-(grades 6-12).

 

The problem set continues with 7 additional problems scaffolding (every next problem easier than the first one) the main concept down to the elementary grades.

Ø  appropriate solutions  and justification

Ø  scaffolding for conceptual understanding (every next problem easier than the first one)   

Ø  concepts defined in clear and precise language

Ø  clear list of key concepts/vocabulary  

 

See the Problem sets grading rubric and the corresponding power point presentation for further details.

Each problem set utilizes technology tools in an essential way (e.g. multi-media, digital manipulatives, graphing calculators, spreadsheets, dynamic geometry).