Problem Solving
Math Reasoning Inventory From Marilyn Burns
Dan Meyer video on reshaping the math curriculum to make it more relevant and problem orientated.
http://www.ted.com/talks/dan_meyer_math_curriculum_makeover.html Upside down teaching GREAT Dan Meyer, math needs a make over.
http://www.ted.com/speakers/dan_meyer.html more info on Dan
http://blog.mrmeyer.com/ Dan’s blog
Teaching Secrets, How to Make Math Meaningful for All by Cossondra George

Definition—How would you define problem solving? Problem solving is not how many answers you know but how you proceed when you don’t know the answer. Or put another way problem solving is what you do next when you don’t know what to do next.

For a definition and funny look at problem solving take a look at my favorite book “The Math Curse” by by Jon Scieszka and Lane Smith.

Problems
Dan Meyer--What is best problem that you could tweet.
Carpet for a room. Start from the beginning.

Problem Solving Strategies

Marilyn Burns 10 big ideas.doc 10 big ideas from Marilyn Burns. This is also found at http://www2.scholastic.com/browse/article.jsp?id=3596
Problem Solving Argument.doc Answers to five potential arguments against a focus on problem solving
Seven stages of Problem Solving.pdf This table comes from "Becoming a Problem Solver" Teaching Children Mathematics p 98-103. A description is given as students move from concrete, readiness, copying, mechanical, novice problem-solver, apprentice problem-solver, and problem-solver.
Problem solving quotes.ppt This power point contains quotes that are used in the problem solving presentation.

Problem Solving Plans

AEIOU—A method to provide students specific instructions and expectations when solving and writing explanations of problems.
  • AEIOU and Always Y, A Simple Technique for Improving Communication and Assessment in the Mathematics Classroom, Mathematics Teacher August 2008, p 16-23
  • AEIOU explain.doc Summary of article in Mathematics Teacher
  • AEIOU rubric.pdf Rubric for AEIOU from article
  • aeiou from Ed.doc Organizer for AEIOU from Ed Ankrom
4 Corner and Diamond Graphic Organizer
  • Mathematical Graphic Organizer, November 2009 Teaching Children Mathematics, p 222-230
  • 4 corner and diamond template.doc word document that can be used with students. This can be created by folding a blank paper in half and half again. Fold the inside corner down to make the diamond and unfold.
IDEALIdentify the problem, Develop plan, Explore Possible Strategies/Estimate or predict reasonable solution, Act, Look Back reflect, evaluate.
Other Problem Solving plans to consider. UPAL, UPAC, UC3, Polya, UC4 (adds communication to UC3)
BUGS
  • Bracket the question, Underline the information, Garbage X out extra information, Solve the problem.

Making Problem Solving Like Kool-Aid
SIP goal Improving Problem Solving.doc Steps to make problem solving school wide.

Student Working Strategies

I do, We do, We share or Me, We, We share
  • Try the problem individually
  • Work with a team which helps students develop confidence and get started
  • Share/present to whole class. This promotes a variety of solutions, peer to peer explaining is good for both and more detailed work and explanations are shown
Sharing student work
Students can complete work on overheads
A document camera or elmo can be used to project images.
  • Information for document camera I used CDW-G, Item #: 1403129, Avermedia CP300 Document Camera, $609.57 (ESU #6 cost), contact Chad Lane, chadlan@cdwg.com
  • The Logitech Quick Cam Pro 9000 web cam has been modified by adding a flexible desktop base to the unit to turn it into a document camera. This setup for less than $90 provides for a great document camera. Information is found in the document document Camera Logitech sheet.doc
Enhanced Think-Pair-Share
An article from Teaching Children Mathematics April 2010 pages 451-455. "The goal is to develop a community of mathematicians who share their thinking, listen to one another, and carefully consider the math presented." The five stages are Orientation, Play-investigate, Share-reorient, Pair play-pair listening, Whole-group share. More details of the phases are provided in the following power point. enhance think pair share.ppt
Chalk Talk
Several problems are placed around the room on chart paper or the board. Students are placed in groups. Each group reads the problem and writes comments on the problem on the chart paper. Students do not work the problem but talk about possible strategies, information provided, more information needed. Works well with 4 corners and diamond.

Sources of Problems

www.nctm.org National Council of Teachers of Mathematics For sources of problems and much. $78 for membership which includes 9 issues of one journal
Teaching Children Mathematics (PreK-6)
  • Problem solvers: problem—a problem of the month is presented
  • Problem solvers: solution—a problem presented a year ago is shown with student demonstrations
  • “Math by the month” presents several problems by grade band
Mathematics Teaching in the Middle School (5-9)
  • “Cartoon Corner” presents several problems related to a selected cartoon.
  • Palette of Problems presents several problems with their solutions
Mathematics Teacher (8-14)
  • Monthly Calendar presents a problem for each day of the month.
Wealth of resources for problems K-5
Math Counts Resources download 2013-14 Math Counts Handbook
Brain Boosters http://school.discoveryeducation.com/brainboosters/
NATM has a Facebook page that post a problem of the day.
NCTM Problems to Ponder: http://www.nctm.org/about/content.aspx?id=26070
SAT problem of the day will frequently have math problems http://sat.collegeboard.com/practice/sat-question-of-the-day
ACT question of the day will frequently have math problems http://www.actstudent.org/qotd/
Problem of the Week http://www.colstate.edu/mathcontest/
Marilyn Savant from Parade newspaper http://www.parade.com/askmarilyn
Problems created during the NMPDS 2009-10 Problems for NMPDS.doc
American Mathematics Competitions for grades 8, 10 and 12 http://www.unl.edu/amc/ register to participate in the competition or download sample test and solutions.
Math Counts is a competition for middle level students https://mathcounts.org/ contains this websites contains problem of the week as well as sample problems.
The Math Forum is an excellent site for math resources. http://mathforum.org/ They do have a problem of the week but it cost $25 per year to participate.
Problem Based Learning Curriculum Maps
Grade 8 Problem Based Learning
Somewhat of a surprise source but I have found some good articles here. http://www.cartalk.com/content/puzzlers
Brilliant provides a weekly problem for students 11-18.
Problem Solving program
Superstars Math III problems for grades K-2, 3-5, 6-8 (2)

K-2 Problem Solving Resources

  • John Van De Walle's books and Kathy Richardson's books are great for developing problem solving skills with the lower grades. I used both with kindergarten and first grade when I was a math specialist and had great results. Carrie Persing CPAM Virginia
  • Cognitively Guided Instruction is also a great resource for teachers in understanding how students approach problems to solve and the developmental paths they take toward THEIR understanding. Becky Holden CPAM Tennessee
  • We have been seeing a tremendous amount of success with Cognitively Guided Instruction in Arkansas, and I agree that Children's Mathematics is a great place to start. CGI focuses on Numbers and Operations and Algebra, though having a deep conceptual understanding of these strands does of course affect children's ability to solve problems in others.
  • Additional resources for teachers are “Children’s Mathematics Cognitively Guided Instruction by Carpenter, Fennema, Franke, L:evi and Empson and published by Heinemann. Also, Angela Adnrews and Paul Trafton’s book, “Little Kids-Powerful Problem Solvers, Math Stories from a Kindergarten Classroom. That also is published by Heinemann.
  • Other titles you may want to look at are “Developing Number Concepts” by Kathy Richardson (Didax) and the “Math Process Standards Series, Grades K-2” by Susan O’Connell (available through NCTM/Heinemann Publishing).

Assessing Problem Solving

Rubric types.ppt Power point with descriptions of the types of rubrics shown below.
Rubrics can be classified by the following
Holistic—looks at the total process
Analytic—looks at the parts or steps of the process
Specific—is used with single problem.
General—can be used to assess many types of problems.
Which means that rubric can be Holistic/Specific, Analytic/Specific, Holistic/General, Analytic/General
CREATING
http://rubistar.4teachers.org/ is a website that facilitates creation of rubrics. Samples of rubrics from other teachers as well as a template to create a rubric with suggested headings and indicators. A free registration will allow for created rubrics to be saved and modified at later times.
SAMPLES
Science Framework PS Rubric.pdf Analytic general from the Nebraska Mathematics/Science Framework
Student Problem Solving Rubric.doc Analytic general
SCORING GUIDE Double the Carpet.doc Analytic specific for double carpet problem.

Problem Solving Articles

“Becoming a Problem Solver”, Teaching Children Mathematics, October 2002 Contains the “seven stages of becoming a problem solver.”
"Children Who Enjoy Problem Solving" Teaching Children Mathematics May 2003 p 539-544