Strategies for Solving Math Problems Grades 9-12: Course Description, Outline & Web Resources [Best viewed using MS Internet Explorer for Mac or for PC ]

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1st Quarter Reading List/ Reading Assignments

2nd Quarter Reading List/ Reading Assignments

2000-2001 Parent Letter

GENERAL REQUIREMENTS. Students shall be awarded 5 credits for successful completion of this year long course. This course is recommended for students in grades 9 through 12.

INTRODUCTION. Problem solving has been defined by some as what a person does when they don't know what to do. Problems are more complicated then the 15-30 "problems" that are normally handed out each evening by the a math instructor. This type of an assignment is really an "exercise" that is asking the student to repeat a method that they were introduced to in class. In this course, when a student receives a problem or problem set to solve, they will normally not have a preconceived method by which to find the solution(s). They will, however, be equipped with general, wide-ranging strategies for solving those problems. With that said, the Strategies for Solving Math Problems course provides students with many opportunities to experience the application of different strategies that help provide a mean to attack difficult problems. The book that we will be using,

Problem Solving Strategies,

CROSSING THE RIVER WITH DOGS

and Other Mathematical Adventures,

by Ken Johnson and Ted Herr,

published by Key Curriculum Press

(2nd Edition) 2001

is an excellent text for providing students with the opportunities to read about, learn, practice and improve their ability to use Strategies for Solving Math Problems.

PHILOSOPHY OF THE COURSE. The class is based on the idea a person's problem solving ability can be improved by learning and practicing general strategies that are employed by individuals that deal with "Real Life" problems on a daily basis. The goal of this course is that when a participant finishes, he or she will be able to understand the mathematics that is being used to solve a given problem and to be able to explain their reasoning in writing and to other participants in the immediate problem solving community. Below is a brief overview of how the class wil be run to promote critical thinking:

1. The course coverage is designed so that students grasp more. The weekly instructional plan is laid out in such a manner to let students attain the organizing concepts that enable them to retain more of what is taught.

2. Lecture will not be commonly employed so that students have more time think, ask questions, and discuss between them selves what they need to acquire to understand for thoroughly the concept being presented.

3. When lecture is used...

• It will not be delivered like a mother robin-chewing up the text for the students and putting it into their beaks.
• It will be used to prepare them to be more active and analytical when they read the text for themselves.
• Focus, in other words, on how to read the text not on "reading the text for them".
• Focus on fundamental and powerful concepts with high generalizability.

4. More time will be spent applying and analyzing basic problem solving strategies while engaged in problem-solving and reasoned application then will spent introducing more new strategies.

5. Problem solving strategies, as far as possible, will be presented in the context of their use as functional tools for the solution of real problems and the analysis of significant issues.

6. Specific strategies will be developed for cultivating critical reading, writing, speaking, and listening skills. It will be assumed that most students start the course - as indeed they often do - with limited skills in these essential learning modalities.

7. The instructor will often “think aloud” in front of the class. This allows them hear what he/she is thinking, better, puzzling through as they proceed slowly through the problem solving process. (The instructor will try to think aloud at the level of a good student, not as a speedy professional, allowing students a better opportunity to internalize the process being acted out/ verbalized.

8. Students will be regularly questioned Socratically: probing various dimensions of their thinking: their purpose, their evidence, reasons, data, their claims, beliefs, interpretations, deductions, conclusions, the implications and consequences of their thought, their response to alternative thinking from contrasting points of view, and so on.

9. Students will frequently be called on who don't have their hands up. Next, other students to will be called on to summarize in their own words what the first student said (so that they actively listen to each other).

• Concrete examples will be used whenever they can be to illustrate abstract concepts and thinking. The instructor will often cite experiences that he/she believes are more or less common in the lives of their students (relevant to what is being taught).
• Problem solving assignments that require rigorous written express will be a regular requirement for the class.

12. The intellectual standards that will be used in the grading policy will be spelled out explicitly, with explanation. Students will be taught, as well as possible, how to assess their own work using those standards.

13. When possible, the class will be frequently broken down into small groups (of twos, threes, fours, etc.), giving the groups specific tasks and specific time limits. Afterwards, particular groups will be called on to report back on what part of their task they completed, what problems occurred, how they tackled those problems, etc.

14. All activities and assignments will be designed to including readings so that students must think their way through them. Discussions will be lead on the kind of thinking that is required.

15. The logic of the most basic concepts will be kept in the foreground, continually re-weaving new concepts into the basic ones. The whole will commonly be related back to the parts and the parts in relation to the whole.

16. From the first day of class, students will be aware of what they are in for. They will be made aware of the instructor's philosophy of education is, how they are going to structure the class and why, why the students will be required to think their way through it, why standard methods of rote memorization will not work, what strategies you have in store for them to combat the strategies they use for passing classes without much thinking, etc.

Adapted from < http://www.criticalthinking.org/k12/k12class/tsrecom.nclk > .

CRITICAL ELEMENTS OF ACTIVITIES involving Strategies for Solving Math Problems. Although there will be a great diversity in the kinds of problems and strategies employed in the Strategies for Solving Math Problems course, each problem solving foray will include the following elements:

• Activities that reinforce one or more strategies found in the course outline.
• Activities that allow students to have direct experience with attempting to solve and solving real world problems involving math.
• Activities that involve observation of phenomena or systems, the collection and analysis of data and/or other information, and the communication of observations and/or results.

The relative magnitudes of these elements may vary from activity/problem to activity/problem. As a whole, however, each of the problem-based components will attempt to encompass all of these elements.

CHALLENGING STUDENT ABILITIES. Each activity/problem used in the Strategies for Solving Math Problems course will attempt to challenge every student's ability to:

• critically analyze a math-based problem in context to the real-world situation
• develop and conduct well-designed and communicated solutions
• utilize appropriate mathematical skill, techniques and problem solving strategies
• analyze and interpret data, including appropriate statistical and graphical presentations
• think analytically and apply concepts to describe physical and mathematical phenomenon
• make conclusions and evaluate their quality and validity
• propose further questions for study
• communicate accurately and meaningfully about observations and solutions/conclusions
  

SUGGESTED SUPPLIES.

EXPECTATIONS.

Attendance: It is important that students maintain good attendance. Two or more unexcused absences will be cause for student to be recommended for academic review. Attendance is also important to academic success as many of the class meetings will be lab investigation, discussions, or demonstrations. which cannot be easily duplicated in the home and they will also count toward the academic grade. Missed class meetings, discussions, and problem solving sessions due to excused absences may be made up at the scheduled make-up times.

The tardy policy for this class is reflected in the AAE student handbook. A student is considered tardy to a Strategies for Solving Math Problems class meeting if they are not in their seats with their daily materials (such as books, Interactive Student Notebook, pencil, 3 ring binder with paper etc.) out and ready to use.

Class Meetings: Generally each class session will begin with students in their seats, their books and assignments out ready to go. If it is a day to do a spot check of work completed at home, that will be done the first few minutes of class. This is generally followed by a brief overview of topics covered in the proceeding days. This is time that students can ask question about work that was completed at home. Next, there may be an introduction to the topic to be discussed in class that day. On most days, there will be some sort of discussion, problem solving session, or question & answer time that supports the topics /concepts covered during the rest of the week. The work done during a class meeting will be included/written into/attached to the pages of each student's Interactive Student Notebook and will count towards the students academic grade. The class will end with reminders about what is in store for upcoming class meetings.

HOME SESSION ASSIGNMENTS/ACTIVITIES: All daily course work which is taught/assigned by the instructor and finished at home will be graded by the teacher unless the student an/or parent is requested to do so at home. The work completed at home will count towards the student's academic grade. This work will need to be kept in the STUDENT SUCCESS binder or INTERACTIVE STUDENT NOTEBOOK [ISN] depending on the instructions given during Class Meetings. The way in which this work will be given academic credit is through a weekly "spot check" of that work.
Spot checks work as follows:

• On the designated day, at the very beginning of class, each student will have the work, from the previous weeks home activities, displayed on their desk so that each page/ assignment is clearly visible.
• The instructor will then quickly go around the room and check off students who have completed the work. Students who have completed the work will receive full credit. If no work has been completed, then the student will not earn any credit. Partial credit will not be given. (extenuating circumstances aside).
• It is very important that students keep up on their daily Home Session Assignments/Activities, not only for the effect it will have on their grade but also for the effect it will have on their understanding of work done in class.
• The point value of the weekly work completed during Home Sessions will approximately equal the value of the work done in class for the week.
  

If a student is absent from class : The student is still responsible for the work missed while absent. In the event of a missed lab investigation, the student should plan to make up the investigation during one of the scheduled open lab times. If this is an impossibility, the student should speak with the instructor. It is up to the student to make up any class notes that were missed. For other types of missed assignments, the student needs to see the instructor or, when possible, consult the appropriate weekly Parent-Student guide handed out in class or on-line @
<http://www.avstc.org/SciMat/Pro_Sol_agenda.html > to complete assignments at home.

Grades 9-12 California Math Academic Content Standards: This course has been designed with alignment to the state standards in mind. Each week, during class meetings, activities and assignments have been chosen which address the overarching standard that covers problem solving strategies.

Parent Information Section In Binder: In the student three ring binder, you should make sure you set aside a special place that you use for parent information. In this section, instructors will ask students to place any special notes or memos that are directed to parents. This will provide a place for parents to check for updates and improve home/school communications you should consider using this section for all AAE classes. Mr. Huffine can also be reached by e-mail @ mhuffine@avstc.org or current information can be found on-line @<http://www.avstc.org/SciMat/Pro_Sol_agenda.html> .

Exams: At the present time, I do not foresee the use of exams. The nature of "problem solving" does not lend itself to such a form of assessment.

Interactive Student Notebooks & Cornell Notes: Students will receive instructions for developing an Interactive Student Notebook using an 8.5 x 11, 200+ page spiral notebook. Once this notebook has been setup, student will be expected to write all of their class notes (Cornell fashion), attach all class handouts (with glue stick, tape, or rubber cement) and record all of their data collected during class meeting investigation. Each class meeting, students will be required to take Cornell Notes, The process for this type of note-taking will be discussed at the start of the first semester. These notes will prove especially helpful in studying for the final exam.