Problem+Solving

Problem Solving Math Reasoning Inventory From Marilyn Burns Dan Meyer video on reshaping the math curriculum to make it more relevant and problem orientated.toc [] Upside down teaching GREAT Dan Meyer, math needs a make over. [] more info on Dan [] 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**= 10 big ideas from Marilyn Burns. This is also found at http://www2.scholastic.com/browse/article.jsp?id=3596 Answers to five potential arguments against a focus on problem solving 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. This power point contains quotes that are used in the problem solving presentation.
 * [[file:lvermaas/Lotus Chart problem solving.doc|Lotus Chart problem solving.doc]]
 * [[file:lvermaas/Lotus Chart blank.doc|Lotus Chart blank.doc]] Lotus Chart word document than can be used as a template.
 * [[file:lvermaas/Problem solving strategies.doc|Problem solving strategies.doc]] Table of problem solving strategies
 * [[file:lvermaas/0.Math Problem solving bookmark2.pdf|0.Math Problem solving bookmark2.pdf]] Problem solving strategies bookmark--3 to a page
 * [[file:lvermaas/bookmark UC4 plan.doc|bookmark UC4 plan.doc]] UC4 plan to be copied on the back side of the strategies to make a bookmark
 * [[file:lvermaas/bookmark strategies.doc|bookmark strategies.doc]] UC3 plan to be copied on the back side of the strategies to make the bookmark
 * [[file:lvermaas/Guess and Check.ppt|Guess and Check.ppt]] Guess and check is as much about developing mathematical reasoning and problem sovling as it is about finding a correct answer. This power point comes from the article The Value of Guess and Check, Mathematics Teaching in the Middle School March 2010 p 392-398

= 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
 * [[file:lvermaas/AEIOU explain.doc|AEIOU explain.doc]] Summary of article in Mathematics Teacher
 * [[file:lvermaas/AEIOU rubric.pdf|AEIOU rubric.pdf]] Rubric for AEIOU from article
 * [[file:lvermaas/aeiou from Ed.doc|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
 * [[file:lvermaas/4 corner and diamond template.doc|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.
 * IDEAL **—** I **dentify the problem, ** D **evelop plan, ** E **xplore Possible Strategies/** E **stimate or predict reasonable solution, ** A **ct, ** L **ook Back reflect, evaluate.
 * [[file:lvermaas/IDEAL steps.doc|IDEAL steps.doc]] IDEAL chart
 * Other Problem Solving plans to consider. UPAL, UPAC, UC3, Polya, UC4 (adds communication to UC3)**
 * [[file:lvermaas/UPAL UPAC Polya UC3 UC4 plan.doc|UPAL UPAC Polya UC3 UC4 plan.doc]] Chart for these plans
 * [[file:lvermaas/UC3 Polya Broken Bow.doc|UC3 Polya Broken Bow.doc]] Plan from Broken Bow
 * BUGS**
 * Bracket the question, Underline the information, Garbage X out extra information, Solve the problem.

Steps to make problem solving school wide.
 * Making Problem Solving Like Kool-Aid**

= Student Working Strategies = Students can complete work on overheads **A document camera or elmo can be used to project images.** 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. 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 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 [] 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 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 =
 * 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**
 * 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 [[file:lvermaas/document Camera Logitech sheet.doc|document Camera Logitech sheet.doc]]
 * Enhanced Think-Pair-Share**
 * Chalk Talk**
 * 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.
 * 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 = 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 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. Analytic general from the Nebraska Mathematics/Science Framework Analytic general 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
 * CREATING**
 * SAMPLES**