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. 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 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 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.
Week 3: 02/05	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 Substantive Postings, many students in the groups haven’t given more than one idea to get 15 points. Many have stopped with only one idea relevant to the original discussion. Regarding Acknowledging Ideas of Others, many are just agreeing to others reflection, but not expanding by providing examples. Regarding Supporting Ideas, not more than one example is provided. Timely Contributions are good leaving 24 hours. FROM TODAY (February 7) POINTS FOR REFLECTIONS WILL BE DOUBLED TO REFLECT THEIR SIGNIFICANCE AS PART OF YOUR PARTICIPATION IN THIS CLASS.
Week 4: 02/12	Remember that I am still not grading your Problem Set on Volume. It is just a draft that you should attach to your reflection #4 so that other group members can learn from it and you can get some input from your peers, your group members. When you are done with that, look at what other group members submitted. Use problem set rubric (I am sending an email with the rubric) to provide input to everyone’s paper from your group: mark on the rubric what you think is missing and what can be done to improve this first problem set. When you do that for every group member, reply to their postings and attach the rubric with your comments. Remember to put in the rubric both your name and the name of the person whose work you are looking at. Be patient. This is somewhat tedious work, but you will learn a lot from this. This process of providing input to each other should be finalized by Sunday, February 17^th. After that you have one more week to work on your problem set about volume. Therefore, Problem Set on Volume is due Sunday midnight, FEBRUARY 24^th. Your first self-evaluation should be written AFTER February 24^th (after you submit your Problem Set ONE). It is due March 2^nd. Problem Set TWO (topic will be announced on February 25^th) is due March 31. Problem Set THREE (topic will be announced on February 25^th) is due April 27^th. Final Presentation is due May 4^th.	REFLECTION FOUR: Can frustration be productive? Most of us get frustrated in a challenging situation, especially if we do not recognize a purpose of the challenge. What are some constructive learning strategies to move us from an ineffective frustration stage to a productive zone of proximal development? (NOTE: If you are not familiar with the term “zone of proximal development” please find out; get into agreement with your group about this concept, before proceeding to discuss the reflective question.) First entry due Wednesday midnight (02/13); 2^nd entry due Saturday (02/16), noon; summary due Sunday(02/17) midnight. REFLECTION FOUR: Problem Solving Stan
Week 4: 02/12	SUMMARY OF WHAT YOU NEED TO DO FOR THE PROBLEM SET ON VOLUME 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).
Week 5: 02/19	MORE HINTS - THINGS YOU SHOULD BE THINKING ABOUT: 1. Which one holds more? Are we all clear that shorter one holds more because the difference in the base between the two cylinders is significant (you need more paper for the top and bottom of the short one than the tall one; or, you figured out that the radius in the formula of the volume V=πr²h, since it is squared, is much larger for the short one). 2. Virtual Manipulatives - We all agree that Fill and Pour activity can be frustrating; patience is required to always carry the process in one direction (either left => right or right =>left) 3. Developing formula for volume of a box, Volume=BaseHeight* has to be part of your problem set. Problems can incorporate the following ideas: a. A box and enough cubes to fill it to the top b. A box and enough cubes to cover the bottom, a little bit more (enough to count the height with cubes) but not enough to fill the box c. A box and enough cubes to count number of cubes at the longest side Please try this hands on if it is not visually obvious what the purpose is. Let me know if you have any questions. 4. Open-ended problems have more than one solution. You need to show only one possible solution.	Reflection 5 Problem Solving Standard for grades k-12 can be summarized in the four bullets that you see below. Work with your group members to provide an elaboration on each of the four bullets, using what you learned while designing your problem set 1. Ø Build new mathematical knowledge through problem solving. Ø Solve problems that arise in mathematics and in other contexts. Ø Apply and adapt a variety of appropriate strategies to solve problems. Ø Monitor and reflect on the process of mathematical problem solving. What does this mean to you? For your first entry (DUE Thursday), try to elaborate on each of these bullets, thinking about your first problem set. Provide examples if appropriate. For the second entry (DUE Saturday), as usual, reflect on what your group members wrote.
Week 6: 02/26	Exponential growth (Problem Set 2) PS2 Introductory STORY: King's chess board Wiseman did not want any award from the King Finally he said: Give me one grain of rice on the first square on the chess board; 2 the second day (doubled), double the next day, so it is going to be 4, …doubling goes on PROBLEM: How much rice is the Wiseman getting? Does King have that much rice in his Kingdom? Make a T-chart Use rice to demonstrate what is going on for the first couple of days. Answer the following questions: How many grains of rice king gave on the third day? How many grains of rice Wiseman had on the third day? After 5 days? After 7 days? After 10 days? 4047grains of rice? How many grams is that (4047 grains of rice) if we know that a small cube (1cm³) corresponds to one gram of volume? What do you need to do first? Estimate how many grams of rice you can fit in that small cube? If you put grains of rice on the top of a cube – how many is that? How many such layers do you have? What next? SPREADSHEETS PROBLEM 2: Design multiplication table using spreadsheets: Do 12 by 12 table (instead of 10 by 10 which you usually do); Search and color some patterns PROBLEM 3: Use spreadsheets to solve King's chessboard problem (Problem 1 above). Graph it. NOTE: Spreadsheets are required technology tool to be used for ICT integration in the problem set 2. Your questions are welcome! They help me provide more details for you in case you need them.	Reflection #6: Spreadsheet Tutorial http://www.k12.hi.us/~tethree/01-02/tutorials/ss/home3.html ENTRY ONE: Use this website to learn something new about spreadsheets and share with your group members. ENTRY TWO: Design one problem that can be solved using spreadsheets and share with others in your group.
Week 7: 03/04	This week you should be working on your Problem set 2 and reflection #7. . By the end of this week you should have three (3) problems ready about exponential growth (PS2). You will need them for the next week reflection. I will put more details on Monday, with reflection #8. Kings’s chess board problem and multiplication table spreadsheet	Reasoning and Proof Standard for grades k-12 can be summarized in the four bullets that you see below. Work with your group members to provide an elaboration on each of the four bullets, using what you learned while designing your problem set 1. Recognize reasoning and proof as fundamental aspects of mathematics Make and investigate mathematical conjectures Develop and evaluate mathematical arguments and proofs Select and use various types of reasoning and methods of proof What does this mean to you? For your first entry (DUE Thursday), do some research, and try to elaborate on each of these bullets, thinking about your first and second problem sets. Provide examples if appropriate. For the second entry (DUE Saturday), as usual, reflect on what your group members wrote.
8: 03/11
9: 03/25	*Tips:* Exponential growth resource is available within the Course Documents on the Blackboard. If you have trouble downloading it, please email to my graduate assistant Sandeep (sxsevakula@wichita.edu). He will be happy to forward it to you as an attachment. NOTE that this resource is just to get more ideas in case you need them! Think critically about this compiled resource and make your own judgment when using materials from here. About interest rate & exponential growth: You can use interest formula. But, it is not easy to develop that formula while you are scaffolding your problems. So, all I am saying is: If you are very familiar with interest formula and you know how to develop it, feel free to use it. Otherwise, it might be easier to say within the ideas shared with the "rice" example. ICT=Using spreadsheets for this assignment	Reflection #9: Exponential Growth and Self-Regulated Learning For this week reflection, please reflect on challenges and opportunities that you had while learning about exponential growth: (a) What worked well for you and what did not? (b) Reflect also on your learning habits: Are you a self-regulated learner or not? Why or why not?
10: 04/01	Geometry: Where should you as a teacher be: From the basic concepts to the big picture OR looking at the big picture first and ‘projecting down’ ? Brainstorm on these ideas and if you are in the online class, use your discussion group to share your thinking. You can use your Math 501 book as a basis for the discussion. Both approaches are ok! What are transformations and how we can carry on a transformation? Consider: reflection, translation and rotation. What are relationships? Consider: Congruence, similarity, ... ICT integration for the PS3 Geometer Sketchpad: http://www.ettc.net/techfellow/sketch.htm; I suggest reading through this tutorial and then going to our tech lab to try it out, OR To try at home how Geometer Sketchpad works you can download free demo from http://www.chartwellyorke.com/sketchpad/gspdemos.html Introduction to Geometer Sketchpad Draw a triangle and find its perimeter Measure angles of a triangle Show that the sum of angles in ANY triangle is 180 Construct all angle bisectors in a triangle; what property do they have ...inscribed circle Construct perpendicular bisectors of all sides in a triangle; what property do they have... circumscribed circle Problem Set 3. ?? Pick your favorite geometry concept and develop your problem set around it. Use Geometer Sketch Pad for technology integration. If you are using Lab software, you can copy and paste your pictures into the Word. If you are using free download version, you will not be able to copy and paste but you can capture the whole computer screen (Fn and PrntScrn buttons on your keyboard) and you can use ‘crop tool’ to cut out the extra stuff.	Communication Standard for grades k-12 can be summarized in the four bullets that you see below. Work with your group members to provide an elaboration on each of the four bullets, using what you learned while designing your problem set 1 & 2. · Organize and consolidate their mathematical thinking through communication · Communicate their mathematical thinking coherently and clearly to peers, teachers, and others. · Analyze and evaluate the mathematical thinking and strategies of others · Use the language of mathematics to express mathematical ideas precisely What does this mean to you? For your first entry (DUE Thursday), try to elaborate on each of these bullets, thinking about your first problem set. Provide examples if appropriate. For the second entry (DUE Saturday), as usual, reflect on what your group members wrote.
11: 04/08	ASK YOURSELF: What geometry CONCEPT is MY problem set going to be about?
12: 04/15	PS3 TIPS: to help yourself in developing PS3, ask yourself the following questions Which geometry concept did I select? What is the theory about this concept that I need to know? – first, look up the theory behind the concept – 501 book, internet, … Am I ready to start? Do I understand this concept well? Where shall I start? From simplest to challenge From challenge to simplest Any place that I can --from that go both directions - to simpler - to more complex, until I have 8 problems Check scaffolding Remember ICT Metacognitive reflection Look at the rubric - do I have everything? Power Point File (Final Exam) - Create a power point presentation 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) interactive ICT integration problem from any of your problem sets 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? artifact (k-6) that you ‘made’/designed to support your ppt presentation (poster, manipulatives, game, ...) - include explanation into your ppt - show your creativity
13: 04/22	Van Hiele's levels of understanding geometry	REFLECTION #13. What does geometry mean to you? Recall what you like(d) or did not like about geometry. Get familiar with the PPT: Van Hiele's levels (available from the calendar or in the Course Documents). ENTRY 1. Select any geometry concept and write a paragraph (250- 300words) about that concept: (a) Describe/define the concept; (b) Give examples of real-life applications of that concept; (c) Relate/connect that concept to other parts of mathematics. ENTRY 2. How is your concept relates to the concepts that your group members wrote about; Design a problem or an example relating all the concepts mentioned in this week discussions.
14: 04/29
15: 04/06
04/13

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

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.

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

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;

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

August 2007
	These pages are always under construction: I am trying to keep them up-to-date with my activities :) Questions and/or comments are welcome!	Maintained by: Mara Alagic Mathematics Education Curriculum & Instruction Department Wichita State University Wichita, Kansas 67260-0028

Learner Outcomes