SPRING 2008

Remember, Attitude is a small thing that makes a big difference :)

 

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."

Course Changes: I try to make my courses better every semester which always 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.

 

CI 319 Mathematics Investigations

Instructor: Dr. Mara Alagic

Associate Professor

 

Spring 2008

 

Faculty Member: Dr. Mara Alagic         

Office: 205 Corbin              

Office Hours:
        Monday and Thursday: Skype or a Blackboard Chat: 10:00pm – 11:00pm
        Tuesday: 10:00am – 11:00am
        Wednesday: 10:30am – 11:00am
        Skype contact name is my email: maraalagic
        I do have open door policy. If I am in my office, which is whenever I do not teach, please come in.
        Other times by appointment. Appointment recommended.

Telephone:    

E-mail Address:  mara.alagic@wichita.edu

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:

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

 

Learner Outcomes

 

Related Assessment

KSDE Elementary Education Standards

National Council of Teachers of Mathematics (NCTM) standards

Conceptual Framework Connections

(Guiding Principles)

 

 

 

 

 

The student demonstrates the ability to use effective, developmentally appropriate instructional strategies to help all k-6 students learn and use their mathematical skills in many different situations and applications to solve real life problems.

Digital file/resource

S2-P3

Teaching Principle;

Technology Principle

HDD

The student knows a variety of developmentally appropriate assessment tools that align with curriculum and instruction.

Digital file/resource

S2-K4

Assessment Principle

HDD
CTA

The student uses diverse and developmentally appropriate assessments that align with curriculum and instruction.

Digital file/resource

S2-P4

Equity Principle

HDD
CTA

The student knows and understands the mathematical concepts of number sense, number systems and their properties, computation, geometric figures and their properties, transformational geometry, measurement, data analysis, data representations, probability, patterns, functions, and representations of algebraic and geometric situations/solutions.

Digital file/resource

S2-K1

Content standards: Number sense and operations, Algebra, Geometry, Measurement, Data analysis and probability

CKS

T

The student understands the five process standards (problem solving, reasoning and proof, communication, connections and representations).

Digital file/resource

S2-K2

Process standards

CKS

T

Appropriate to k-6 students' age and development, the student can use and apply, demonstrate, and teach the concepts of number sense, number systems and their properties, computation, geometric figures and their properties, transformational geometry, measurement, data analysis, data representations, probability, patterns, functions, representations of algebraic and geometric situations/solutions.

Digital file/resource

S2-P3

Curriculum Principle

HDD

CKS

T

The student integrates the five process standards (problem solving, reasoning and proof, communication, connections and representations) into math instruction.

Digital file/resource

S2-P4

Curriculum Principle

HDD
CKS
T

 Required Readings

  1. 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.

Recommended Readings

  1. Math 501 textbook (any version)

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

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

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

 

CI 319 ASSESSMENTS

NOTE: Late work will NOT be accepted. Plan your personal due dates accordingly.

Assignments

Assessment tool & points

Due dates

Points
       

Class participation  (active involvement in class work, whether it is face-to-face or online) 

check list;
15 days x 10 

Ongoing
For online sec

150
Dispositions self-assessment and epistemology survey

100 points

Beginning and end of the semester
 Available online - see Blackboard Course Documents

  

Reflections
(Bb - reflective pods)

check list;
15 weeks x 15

weekly - due by Sunday midnight (each Pod has to decide how much time they will provide for a person summarizing; my suggestion - 1st entry by Wednesday; 2nd entry by Friday; summary by Sunday midnight; as a group you can negotiate different plan )

225

Self Evaluations (include your grades - spreadsheet)

check list;
1 entry -  50pt

Due 03/02

100

Problem sets

rubric;
3 entries x100

PS-ONE (Volume) - DUE 02/24
PS-TWO is DUE 03/31
PS-THREE is DUE 04/27

400

Final Exam - presentations

rubric;
1 entry x 100


Drop-box and email final presentation (ppt) by MAY 4

100

Total possible (tentative)

1000

NOTE: Late work will NOT be accepted. Plan your personal due dates accordingly.

READINGS DISCUSSIONS

are part of REFLECTIONS

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.

Read rubric carefully to better understand requirements.

Online Discussions

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.

You will be turning in your scores with self-evaluation. I will periodically check the scores with reference to your actual online contributions.

HINTS:

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.

 

 

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 enough 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 (scaffolding) that you have acquired so far. Carefully select what you want to write about (2-3 concepts). Remember to support your statements.

  2. What would I like to learn/change?  Be very specific. Include dispositions (both for yourself and me).

  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).

Answering students' questions:

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

As you are working on your volume set and reflections, you used some mathematical and pedagogical concepts (open-ended problems, problem solvig, volume, scaffolding, metacognition, zone of proximal development,…). Select "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?

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. Define it and after that reflect both on yours and mine (teacher’s) dispositions.

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.

 

Four 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.

·       appropriate solutions  and justification

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

·       concepts defined in clear and precise language

·       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).

Problem sets: Grading rubric

 CI 319

Problem Designation:

Excellent

Mediocre

Acceptable

Non-acceptable

Challenge problem selection and quality of its solution
20pt

The following attributes met:  open-ended, real-life related, significant mathematical idea/concept addressed;  Each step of the solution identified and justified; metric system used.

At least 3 attributes met

At least 2 attributes met

Less than  2 attributes met

Scaffolding - representations leading to the main concept
20pt

Rich collection of simpler word problems leading step-by-step to the challenge (at least 7 in addition to the challenge problem).

A collection of a couple of simpler problems leading to the challenge

Development of representations incomplete

None of the attributes met

Quality of the solutions
20pt

All solution steps and corresponding justification details included; two-column solution format; metric system used

 Some solution steps OR corresponding justification details missing; OR solution format not followed OR metric system not used 2 or more attributes missing

None of the attributes met

Vocabulary
10pt

Precise connections; Concepts clearly introduced after an experience provided with a challenge problem (or other).

Connections not precisely introduced; OR Concepts introduced before activities/experiences

Connections not precisely introduced; AND Concepts introduced before activities/experiences 

None of the attributes met

ICT tools/virtual manipulatives
10pt

ICT (Information and Communication Technology) representation appropriate for the task, part of a problem; interactivity clearly described

Not interactive (electronic work sheet) OR not described OR problem not included

Insignificant value of the ICT integration and one of the previous three requirements not in

None of the attributes met

References
5pt

Detailed references (APA style)

Basic references

Incomplete

Not included

Metacognitive Reflection
15pt

Justification: What is the main quality of this set?  Describe your own thinking during the design of the set. What did you learn in terms of (a) content (b) yourself? How are problems connected?

Justification incomplete;
Unclear possible resolutions

Justification incomplete or unclear; Obstacles not recognized; No ideas for resolutions

Not included

Essential recommendation: Support each of the statements you make with a very specific detail.

Due Dates: September 21; October 20;

 Criteria: Each student will demonstrate an acceptable or better rating on each of the entries.

 

Presentation (Final Exam)

Power Point Presentation (part of the final exam) has to include:

  1. A selected challenging problem  (from one of your problem sets; feel free to improve it)
    • include most significant point of your justification for this challenge problem! (ppt)
  2. Interactive ICT integration problem from any of your problem sets
  3. Reflection on strategies that promote metacognition (ppt) - What did you learn from your metacognitive reflections and how are you going to use that in the future?
  4. Artifact (k-6) that you ‘made’/designed to support your ppt presentation (poster, manipulatives, game, ...) put a picture of your artifact or a similar clipart into your ppt - include short explanation - show your creativity

See the Presentation grading rubric (below) for further details.

 

Presentation: Grading Rubric
  Emerging Competent Exemplary
Challenging problem
30 pts		 Have a problem and a point from the solution Clearly stated challenging problem and a point from the solution Creative, attractive presentation of a clearly stated problem and a well-selected point from the solution
Interactivity (ICT)
30 pts		 PowerPoint or just a description Interactivity only described, not well illustrated The class could be engaged in changing some elements to observe resulting changes
Artifact
35 pts		 Mentioned Well illustrated, elements of interactivity Engaging. hands on, connected to a rich mathematical concept
Metacognitive reflection (all problem sets)
30 pts		 Reflective statement - not clear metacognitive connection One well supported metacognitive reflective statement A couple of well supported metacognitive reflective statements

Academic Honesty: A standard of honesty, fairly applied to all students, is essential to a learning environment.  Students abridging a standard of honesty must accept the consequences; penalties are assessed by appropriate classroom instructors or other designated people.  Serious cases may result in discipline at the college or University level and may result in suspension or dismissal.  Dismissal from a college for academic dishonesty, constitutes dismissal from the University. (WSU Student Code of Conduct)

Special Needs: ADA:  If you have a physical, perceptual, psychiatric/emotional, medical, or learning disability that may impact your ability to carry out assigned course work, contact the Office of Disability Services (ODS), Grace Wilkie Annex, room 173.  (Voice/TDD 978-3309).  ODS will review your concerns, confirm your disability, and determine, with you, what accommodations are necessary.  All information and documentation of your disability is confidential and will not be released by ODS without your written permission.

 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/

 

 

 

 

  CALENDAR *

TENTATIVE CALENDAR – SPRING 2008

 I teach 3 sections of CI 319; two sections are combination of face-to-face (hybrid) instruction and one section is completely online. All the work, rubrics, assignments and calendar are the same, except that online section gets class-work in a different format – both through the Blackboard and my website (http://www.education.wichita.edu/alagic/). Please email me (mara.alagic@wichita.edu) or call () at any time if any of the information, calendar or syllabus is confusing. Be very specific with your questions so I can help you better.

 NOTE: The only email that I will be using for you is your wichita.edu email address. Make sure that if you use other email address, your wichita.edu is merged in, or you check it regularly. In the subject line  please always include what class you are in - CI319 Tuesday, CI319 Wednesday or CI319 online. If your email is urgent, please add that word "urgent" in the subject line.

 

Weekly-work

 Reflection

 

Week 1: 01/22 

Dear CI 319 students,

I am very sorry that I have to cancel our first face-to-face class. I am in Europe for a very sad family event; my father passed away. Therefore, I will replace this first class with an online assignment for you.

  1. Please reply to this message IMMEDIATELY so that I know whether you know that you don’t need to go to class Tuesday morning. I can check my email as I travel: mara.alagic@wichita.edu

  2. DUE FRIDAY: Please study very carefully my CI 319 syllabus (WEB PAGES) that I used in the Fall 2007; it will be very similar to one for this semester. Here is the URL: http://www.education.wichita.edu/alagic/319fall2007/319fall2007.htm Formulate at least three questions about this material and email them to me. I will compile them and answer when I see you next week

  3. DUE SUNDAY: There is PPT presentation “CI319 Philosophy” available at the same URL. You just need to double-click (download) on the highlighted words ‘Course Philosophy’. Please study it carefully and prepare a reflection to share with the rest of the class about the way you will apply information from that PPT in this class. Email it by Sunday as an attachment.

Thank you for your understanding and willingness to attend to these assignments. Looking forward to meet you all!

Best regards,

Mara Alagico

To access discussion board for your group, go to Blackboard place for this class, click on the class. When in, click on Communication (on your left) and Group Pages after that. Click next on your group and after that to group discussion board. Click on Reflection that you need to do. Either  start a New Thread (top left) or, if someone already posted something, you can just hit “reply” to get your reflection in.

Email (mara.alagic@wichita.edu) or call me (978 6974) if you have any questions or suggestions.

NOTE: I use Blackberry for emails and I can answer short urgent questions almost immediately, most of the time (unless I am in class teaching or in the middle of a meeting).

REFLECTION #1

Please study Course Philosophy carefully and prepare a reflection to share with the rest of the class about the way you will apply information from that PPT in this class. Email it by Sunday as an attachment.
Week 2: 01/29

HUGE APPOLOGY IF MY FIRST ANNOUNCEMENT CONFUSED YOU.

Let me try to explain why that happened and what that means for each of you.

I am teaching two sections of Mathematics Investigations, one section is online and the other meets on campus every other week.

ONLINE means online, unless you arrange an appointment with me because you want to meet me in person and talk to me; so, please ignore what I mentioned as ‘in class’. ON CAMPUS section will meet on campus approximately every other week; rest of the work will be accomplished online.

Last week assignment was to send me questions and write a reflection on the PPT Course Philosophy. This week assignments are:

#1 Study reflection rubric

#2 Go to Blackboard>communication>group pages>click on your group>Group discussion Board>Reflection 1 - work on this reflection keeping in mind the grading rubric for reflections.

#3 Fill the attached form and dropbox it (unless you already got a hard copy and filled it up). The form is available in Course Documents.

NOTE: Semester calendar and work for the next week will be posted by the end of this week.

THANK YOU very much, both for your understanding and for sending me emails to keep me on track with things. This is very difficult time in my life and I appreciate very much your understanding.

Continue to email whenever you have questions.

 

REFLECTION #2. NOTE: Study carefully rubric for reflections before working on your contribution.

(a)     Share with your group members one positive experience about mathematics (it can be any grade and it can be outside of school).

(b)     Decide on a group name. The first person from the group list should email me that name (mara.alagic@wichita.edu)

NETiquette

Please identify yourself in your messages: Tuesday class or Online class.

Please sign your messages with your full, first and last, name.

I appreciate your questions. Help me out by being specific as much as possible. For example, ‘What are problem sets?’ is a very general question. You need to read what syllabus says about it and formulate some specific questions. Asking more than one question is perfectly fine.

If you don't get an answer from me within 24 hours, assume that I did not get your email. So, please email again.

If it is really urgent, put URGENT in the subject line of your message.
Week 3: 02/05 1. Volume Problem (warm-up): Which one holds more?

Fold a piece of paper horizontally into a cylinder (“hamburger” fold) so that edges perfectly touch (you can tape it).  Fold another piece of paper of the exactly same size into a cylinder, but now vertically (“hotdog” fold). You have two cylinders. Which one can hold more (rice, water …)? Make a prediction, write it down and write why you think that. Than TEST your answer. Was your prediction correct? Can you provide better explanation? (no need to submit your answers; you can include them in your reflection for this week)

2. Explore Virtual manipulatives website: http://nlvm.usu.edu/en/nav/vlibrary.html 
and solve a couple of problems related to volume: http://nlvm.usu.edu/en/nav/frames_asid_273_g_2_t_4.html (Include in your weekly reflection how challenging this was and what you learned from that)

3. Study carefully power point explaining problem sets rubric (see Course Documents).

4. Prepare draft of your problem set on Volume. Have it ready by February 11. If you are in on campus class - bring hard copy with you. If you are in online class - you will get instructions next Monday how to submit it for peer evaluation from your colleagues.

5. Email me if you have any questions. Be very specific.

REFLECTION #3

Describe what you learned from the volume experiments (see announcement),

(a) Which one holds more, &

(b) Fill and Pour (virtual manipulative).

 

First Entry due Wednesday (02/06/2008) midnight; Second Entry Due Friday (02/08/2008) midnight & Summary Due Sunday (02/10/2008) midnight.

IMPORTANCE OF REFLECTIONS
Reflections are very important part of this course, not just a busy work.

In addition to being part of your reflective practice, they are also part of your weekly participation. So, maximum points that you can get for weekly reflections is going to be 30 points starting today. Here are the findings so far:

  • Some Groups haven’t posted their reflections yet!
  • Groups which have done those are not providing the complete views or ideas to fetch the full points.
  • Regarding Sub