Family+F+Strategies

**__Family F Strategies__ (Strategies for Consideration Link) - Strategy Details **
Problem solving strategies from Ontario Curriculum Grade 9-10 (Pg 13) Problem solving strategies using Heuristic approach (Exemplary practices Pg 133-134) Leading math success: Mathematical literacy, Grades 7- 12 strategies for improving literacy skills... Strategies for Supporting different ways of learning and demonstrating understanding (Leading Math success Pg 52) Strategies to improve the Mathematical processes (Developping mathematics literacy TIPS4RM page 3) Collaborate with students, asking questions or thinking aloud when a student or a group it is not making progress. Scaffold based on the knowledge and skills of individual students Provide resources and time for the students to gather data, detect patterns Ask probing questions Guide students as they apply the chosen strategy Direct students to use multiple strategies to solve the same problem, when appropriate Validate the same approaches to the same problem Support and encourage risk taking, and apploud creative approaches Encourage independance and interdependance Facilitate sharing the student finding Model alternative and procedures and strateies such as using manipulative and technology
 * guessing and checking; looking for a pattern; making assumptions; making a model, picture or diagram; making an organized list; making a table or chart; making a simpler problem; working backward; using logical reasoning;
 * read the problem (understand the problem)
 * Select a strategy (devise a plan)
 * Solve a problem (carry out the plan)
 * look back(check the solution)
 * Introduce most of the skills and concepts through problem solving (Leading Math success Pg 47)
 * Develop vocabulary skills (e.g word walls)
 * Read problems aloud and highlight the key word
 * help the students understand the features of the textbooks and graphics
 * Organize the information by using concept maps and other graphic organizers
 * Select an important mathematical idea; identify various ways of aproaching the idea; pull together the tools that the students needs to engage in the various approaches (e.g technologies and manipulatives); organize the students in groups to work in different approaches; have students share their strategies
 * Problem Solving

Selected TRIBES activities for building problem-solving skills
 * 300, Tribe Graffitti, 329, Tribal Peer Coaching, 330, Jigsaw, 356, Flies on the Ceiling, 372, Student-Developed Lesson, 380, Group Inquiry
 * Backward Design Planning (Talk About Assessment chapt. 13)
 * Developing and using rich learning tasks (Rich Learning Tasks, by: Gary Flewelling, William Higginson, 2003)
 * 3 Part Lesson Design
 * Co-Teaching
 * Lesson Study
 * Bansho
 * Teacher Moderation (process of coming to consensus when evaluating students' work)

Instructional method should be a hybrid of the procedure based approach and discovery lesson (Teaching and Learning Mathematics – expert panel grades 4-6, page 10) · The teacher chooses a problem that offers a range of entry points for students at different levels · The teacher poses the problem of sets the investigation without giving the steps for the solution · Students work in pairs or in small groups to solve the problem · Students work to make sense of the problem in their own way. They look for patterns and for connections with other problems · The teacher asks careful questions that will help students to deepen and clarify their thinking · Students communicate their mathematical thinking to one another, explain their ideas, listen to their peers, and talk with the teacher · Students learn to persevere · The teacher takes the necessary time, focusing on key ideas in some depth, rather than on a broad coverage of concepts. At least one hour a day should be allotted to mathematics instruction at the junior level. · Students and the teacher examine errors together as important opportunities for learning. · Students share, explain, and examine a range of solutions with the whole class, discussing the common elements, looking for patterns, and making sense. · The teacher facilitates the sharing of ideas and discoveries in a community of learners · The teacher organizes the discussion by choosing particular samples of students ‘ strategies to build understanding of specific mathematical concepts and to support students’ movement towards efficient methods.

Chapter 6: Research to Practice - What Works for Both Literacy and Numeracy Chapter 7: Effective Instructional Approaches and Teaching Strategies for Numeracy Chapter 9: Organization and Management Four Process of Problem Solving - Pg 2 Mathematics as Language - Pg 7 Strategic Reading - Pg 15 Other Reading Strategies (graphic organizers) - Pg 18 Guided Reading (teachers should ask questions such as the following ...) - Pg 21 Written Response to Mathematics Problems - Pg 27 Discourse in the Mathematics Classroom - Pg 74-81 In this strategy students use a worksheet (chart form) similar to K-W-L to analyze and plan how to approach solving a word problem. Using the word problem, students answer what facts they **K**NOW, what information is **N**OT relevant, **W**HAT the problem asks them to find, and what **S**TRATEGY they can use to solve the problem. Using a teacher-constructed graphic organizer, student must evaluate facts, concepts, rules, mathematics ideas, and approaches to solving particular word problems. This strategy can help students focus on the important facts in a word problem. It allows students to check the usefulness of a number of approaches, questions, or computations in solving a problem. This strategy gives students a chance to collaborate on solving a problem and then to communicate their thought process and solution in writing, and when used in a group problem solving activity, they can benefit from communicating their own thinking and hearing other students’ thinking.
 * Education for All**, The Report of the Expert Panel on Literacy and Numeracy Instruction for Students With Special Education Needs, Kindergarden to Grade 6
 * Differentiation of Instruction (teacher, student, strategies) - Pg 15
 * Specific Instructional Strategies (scaffolding, modelling, instructional language, guided practice, strategy instruction, teaching techniques) - Pg 62 - 66
 * Focus on "Big Ideas" - Pg 73
 * Link Procedural Knowledge and Conceptual Understanding - Pg 74
 * Use of Concrete Materials (Manipulatives) - Pg 74
 * Elements of an Effective Mathematics Learning Environment - Pg 75-76
 * Teaching Through Problem Solving - Pg 77-80*
 * Table 8. Teaching Strategies that Promote Communication - Pg 76-90*
 * Accommodations and/or Modifications - Pg 117-122
 * Literacy Strategies for Improving Mathematics Instruction** by Kenney, Joan M.
 * Modelling and formulating; Transforming and manipulating; Infering; Communicating
 * Confusing Terms, Format, and Symbols in Mathematics
 * Frayer Model (4 quadrants --> define term in own words; list facts; list examples; and list non-examples of the term)
 * Semantic Feature Analysis Grid (use to compare features of mathematical objects in same category)
 * **SQRQCQ** Problem Solving Process
 * 1) **Survey** - Read the problem quickly to get a general understanding of it.
 * 2) **Question** - Ask what information the problem requires.
 * 3) **Read** - Reread the problem to identify relevant information, facts and details needed to solve it.
 * 4) **Question** - Ask what operations must be performed, and in what order, to solve the problem.
 * 5) **Compute/Construct** - Do the computations, or construct the solution.
 * 6) **Question** - Ask whether the solution process seems correct and the answer reasonable.
 * What would you be doing in that situation?
 * Does this make sense?
 * What does the picture/graph/chart tell you?
 * How does the title connect to what we're reading?
 * Why are these words in capital letters? highlighted? underlined? etc ...
 * Why is there extra white space here?
 * What does the word mean in this context?
 * journal, create problems similar to the one being solved (if students begin the problem on their own, they are starting from their own mathematical way of thinking)
 * Involve students in engaging and challenging problems.
 * Ask open questions to stimulate student thinking. (Eg. "What does this make you wonder about?" "Are there patterns?" "Is this logical?" "Can we estimate a solution?" ...)
 * Listen carefully to student responses. Ask for clarification so that you and others really understand.
 * Train students to listen to their classmates' observation by asking questions that engage: "Does this work?" "What do others suggest?" "More?" ...)
 * Honour ideas even if they're incorrect. Do not quickly agree or disagree ... give time to think and justify.
 * Encourage mathematical arguments between students.
 * Take time to let students share different problem solving methods. Even when a correct solution has been shown, ask if there are other ways to do the problem. This helps to deepen understanding and makes students more willing to work with their own strategies, rather than think there is only one correct method.
 * Tangents are good. If an idea emerges from class discourse and captures the group's imagination, go with it. Keep the big ideas in mind, and don't forget to return to the concepts you plan to teach, but capture those teachable moments.
 * Teaching Reading in Mathematics 2nd Edition** by Mary Lee Barton & Clare Heidema
 * SQRR Strategy** – Pg 31
 * **S**urvey the problem. Read the question sentence first.
 * **Q**uestion yourself. “What is this asking me to find?” (This provides a purpose for reading the problem word by word.)
 * **R**ead the problem aloud in its entirety, and explain how you determine which information is key and which information is extraneous. If appropriate, draw a sketch and label it using the key information.
 * Ask, “What is the correct process to solve this problem?”
 * Work the problem.
 * Check your **R**easoning. Ask, “What process did I use? Why did I choose that process? Was my reasoning correct?”
 * Polya’s Four Step Process** – Pg 32
 * 1) Understand the problem.
 * 2) Devise a plan.
 * 3) Carry out the plan, checking (or proving) that each step is correct.
 * 4) Examine the solution obtained.
 * Five Step Problem Solving** – Pg 98
 * 1) Restate the problem/question;
 * 2) Determine what information is needed to solve the problem;
 * 3) Plan the steps (calculations) to be performed;
 * 4) Carry out the plan (perform the calculations); and
 * 5) Evaluate the reasonableness of the solution.
 * K-N-W-S** (K-W-L “What I Know, What I Want to Find Out, What I Learn” for Word Problems) – Pg 110
 * Three Level Guide** – Pg 128 to 129
 * 1) The first level should include a set of facts suggested by the data given in the problem. The students’ goal is to analyze each fact to determine if it is true and if it will help them solve the problem.
 * 2) The second level should contain mathematical ideas, rules, or concepts that students can examine to determine which might apply to the problem-solving task.
 * 3) The third level should include a list of possible ways to get the answer. Students will analyze these to see which ones might help them solve the problem.
 * Word Problem Roulette** – Pg 130-131
 * 1) Divide class into collaborative groups, and provide each group with a word problem.
 * 2) Explain to students that they are to solve this problem verbally. No writing or drawing may be done at any time during this step.
 * 3) After the groups have discussed the problem and agree how to solve it, members should take turns writing the steps to the solution in words rather than in mathematical symbols. **Each group must write one sentence and then pass the solution sheet to the next group member so s/he can add the next sentence**.
 * 4) After the groups have finished writing down all of the steps, ask each group to select one member to read the solution steps to the class while another writes the symbolic representation of this solution on the board.
 * 5) Solicit volunteers from the other groups to write there version of this mathematics sentence on the board for the class to review.