Steve Dunbar/Raegan Higgins
Fall Semester 2006
Steve Dunbar 308 Avery Hall
Phone: (402-)472-7236 (with Voice Mail) email:
Raegan Higgins 336 Avery Hall
Phone: (402-)472-8176 email:
Math Department: (402-)472-3731 (M-F 8:00 AM - 5:00 PM)
Center for Science, Math & Computer Education: phone: (402-)472-8965, fax: (402-)472-9311
ECR Course Page:
EDU Web Page:
Blackboard Web Page:
my.unl.edu , then login, you should be
EXPR CONJECT&RESNING MATH804T SEC 700 FALL 2006
Prerequisites: Participation in the Math in the Middle Project
Required Text: The Heart of Mathematics, Second Edition, by E. Burger and M. Starbird, Key College Publishing, 2005 (ISBN 1-931914-41-9) and the corresponding kit.
Strategic Objectives for the Course:
The overall goal for this course is to bring you to the next level in the development of your mathematical habits of mind: A person who is an effective mathematical thinker has a toolbox of skills and knowledge to experiment, conjecture, reason, and ultimately solve problems. Habits of mind give both understanding of and experience using these tools. Habits of mind are marked by great flexibility of thinking and the strong belief that precise exposition of solutions are important. Flexibility of thinking includes the use of indirect arguments as well as making connections between knowledge the mathematical thinker possesses and the problem being considered. A person with well developed habits of mind, when presented with a problem to solve, will collect information, assess it, find multiple pathways to the answer, and explain that answer clearly to others.
Although a complete mathematical toolbox includes algorithms, a person with well developed habits of mind knows both why algorithms work and under what circumstances an algorithm will be most effective. Mathematical habits of mind are also marked by ease of calculation and estimation as well as persistence in pursuing solutions to problems. A person with well developed habits of mind has a disposition to analyze all situations as well as the self-efficacy to believe that he or she can make progress toward a solution. Such a person also engages in metacognition by monitoring and reflecting on the processes of reasoning, conjecturing, proving, and problem solving.
This is a condensed Math in the Middle statement consistent with the 5 strands from the National Academy of Sciences report Adding It Up:
From another view, that of the Principles and Standards for School Mathematics, the course strategic objectives focus on problem solving, reasoning and proof and the associated processes:
Two previous experiences teaching this course convince me that the content and approaches of this course are an effective way to meet these objectives.
To achieve the strategic goals of the course, I have divided the semester into four generally independent sessions. Each session will be 3-4 weeks in length, and will have two or three sub-sessions which will each take 1 to 2 weeks. In each sub-session you will have a pattern of activities to complete, which relate directly to the goals of the course:
Session Reflections: Choose one problem from each of Session A, B, C, and D to write a reflection about it. You should strive to select a problem that you had some mathematical insight on while you were working through the solution or describe a problem you worked that you shared with a colleague, friend, student, small group of students, or your entire class. Describe what happened in the interaction. Reflect on what mathematical ideas you learned from working on each problem.
Teaching and Learning Project:
This project explores learning and teaching from two perspectives. How can you embed the mathematics that you learn in your classroom? Does there exist a relationship between how well you understand the mathematics and how successful you can be as a teacher of that mathematics? For your Learning and Teaching Project this semester we would like everyone to use problems 6 (Baby Bunnies) on page 58 and 9 (Late Bloomers) on page 59 as the basis for your lesson. Last year, we found these topics were adaptable to a wide range of student ages and courses. You should make the judgment where you want to start with your students, what you expect from your students, and how far you can push your students. More details about what to do in the Teaching and Learning Project on the page titled ``Math 804T: Experimentation, Conjecture, and Reasoning, Math in the Middle, Learning and Teaching Project'' in your Portfolio. The materials you turn in for your Teaching and Learning Project will be assessed according to the rubric outlined on the pages labeled ``Assessment Rubric for Written Reflections on Learning and Teaching Project'' in your portfolio.
Learning Groups and Group Study Sessions:
Detailed Course Schedule:
|Beginning Workshop||Sep 15-16|
|Pythagorean Theorem||Read Chap 4.1||208-212||Sep 18|
|Habits of Mind||216||22|
|Homework received||RH||Sep 27|
|Homework returned||RH||Oct 2|
|Golden Rectangles||Read Chap 4.3||232-244||Sep 27|
|Habits of Mind||248||22|
|Homework received||RH||Oct 4|
|Homework returned||RH||Oct 9|
|Platonic Solids||Read Chap 4.5||269-284||Oct 5|
|Pre-Test||Solid Geom||Oct 5|
|Habits of Mind||286||22|
|Post-Test||Solid Geom||Oct 12|
|Homework received||SD||Oct 13|
|Homework returned||SD||Oct 20|
|Art Gallery Thm||Read Chap 4.2||218-228||Oct 17|
|Habits of Mind||230||21|
|Homework received||RH||Oct 25|
|Homework returned||RH||Oct 30|
|Symmetry and Shifts||Read Chap 4.6||249-263||Oct 25|
|Habits of Mind||268||21|
|Homework received||SD||Oct 31|
|Homework returned||SD||Nov 6|
|Fibonacci Numbers I||Read Chap 2.2||49-56||Nov 1|
|Habits of Mind||62||38|
|Homework received||RH||Nov 8|
|Homework returned||RH||Nov 13|
|Fibonacci Numbers II||Nov 8|
|Solidifying Ideas||57||9,10,11,12, 14|
|Habits of Mind||286||40|
|Homework received||SD||Nov 15|
|Homework returned||SD||Nov 20|
|Habits of Mind||569||37|
|Homework received||SD||Nov 22|
|Homework returned||SD||Nov 30|
|Probability||Read 7.2||523-534||Nov 27|
|Solidifying Ideas||563||10,12,14,18 19|
|Habits of Mind||286||38|
|Homework received||RH||Dec 4|
|Homework returned||RH||Dec 11|
|Conditional Prob||Read||Dec 4|
|Pre-Test||Data Dist||Dec 4|
|Solidifying Ideas||On Web page|
|New Ideas||On Web page|
|Habits of Mind||On Web page|
|Homework received||RH||Dec 11|
|Homework returned||RH||Dec 18|
|Bayes Theorem||Read 8.2||645-658||Dec 11|
|Habits of Mind||615||21|
|Homework received||SD||Dec 18|
|Homework returned||SD||Dec 22|
|End of Course||Problems||my.unl.edu||Dec 18|
|Homework received||SD||Dec 22|
|Homework returned||SD||Jan 3|
Grading: We ask that you have a well-defined sense of professionalism, that you always give assignments your best effort, and that you develop a sense of responsibility to your educational community (school, district, ESU). We ask that you give this course your best effort and that you exhibit a persistent desire to learn. It is our goal to provide you with significant support and we strongly encourage you to ask for our assistance when it is needed. We are confident in your success.
Grading will be based on the work submitted for the portfolio the approximately weekly 8 Solidifying Ideas, New Ideas, and Habits of Mind solutions, the Post-Tests, and the Essays on Proof from each section. Reading and writing will serve as the basis for some of your learning in this course. When you are asked to read or write something, the following is expected: Read in a manner that enables you to be an active participant in discussions of text. Write in a manner that represents a significant response to a posed question and illustrates attention to grammar and the mechanics of writing. The course instructional team will offer comments that will assist you in learning to solve each problem assessed. As you are all self-motivated, we recognize that you are all putting forth your best effort. Our goal is to offer comments on how your solution can be improved. Your 3-ring binder has a divide for your homework solutions for each section. The binder preserves your work and gives a sense of completeness. Feel free to include personal reflections on the mathematical skills and concepts that are clear to you and those which may still be confusing. You may consider keeping all your work on a problem or only your final solution of a problem.
Grading Scale: Each of the 10 sub-sessions has eight problems, and these problems will be graded on a scale of ``1'' for a good or satisfactory solution, ``2'' for a better or noteworthy solution, and ``3'' for an excellent or exemplary solution. Therefore each of the 10 subs-sessions will be worth up to 24 points total, and each of these homework sub-sessions will count about 5% of your grade for a total of 50%. The 10 Post-Tests, one from each subs-session will count about 2.5% each, making another 2.5% of the grade total. The Teaching and Learning Activity and the End of Course Problem set will count about 10% and your responses and critiques posted on the Blackboard discussion lists will count about 5% of your grade.
Late Homework, and Re-Do Policy Homework should be faxed to the Center Office on the due date noted in the schedule. Nevertheless, we understand that circumstances can arise in busy lives. However, we also need to complete our grading in a timely fashion, so contact us for special consideration if it is really necessary. Any problem on which you receive a grade of ``1'' can be re-done, and resubmitted up to 1 week after the homework is returned for a re-grade. We would rather that you learn to do the problems correctly and completely than to hand out ``punitive'' grades.
Part of our responsibility as the instructional staff is the assessment of each participant's achievement in each Math in the Middle course. We recognize that teacher-participants are drawn from different grade levels, have different certifications to teach mathematics, and have different educational backgrounds with respect to previous opportunities to learn mathematics. Thus, we believe it is appropriate to have an assessment system that values effort, teamwork, progress in learning mathematics and the development of knowledge, skills, and dispositions for teaching and inquiry.
Expectations and typical characteristics of achievement at each grade level: