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Teaching Though Problem Solving

Subject : teaching
Instructions:
  • Answer 34 questions in 15 minutes.
  • If you are not ready to take this test, you can study here.
  • Match each statement with the correct term.
  • Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.
1. Promoting mathematics as a conceptual tool - not limited to procedural thinking - also promoting the educational reform necessary to help students see math as a creative way of thinking






2. 1.Teacher activates Students prior knowledge. Think the estimate Raisins problem. 2. Make sure student understands the problem (KWL) 3. Establish clear expectations on how they will work (together - or alone) what the end product needs to be. Eg. Thi






3. Teacher determines the learning goals for all students - but the level of difficulty of the task is adapted up or down to meet the range of the learners. Is not just about content - but can include the amount of assistance provided - structure of les






4. Math needs to be conceptional - not procedural Math understanding the student brings to the problem






5. 1. Determine the mathematics and goals (state/county) 2. Consider your students' needs 3. Select - design - or adapt a task (task has to accomplish the content goals (step 1) 4. Design lesson assessments. What you want students to know and how they w






6. Students get to hear how others solved the problem - and hear diverse solutions to the problem. This also develops their social skills (socialization is important in learning)






7. Before phase - During phase - After phase






8. Think IK topped out of math in elementary school - and went to middle school for more intense training






9. Teacher chooses problem - based on 'just right fit'. Teacher does problem herself - gives proper support to student - making sure problem is challenging.






10. 5. Builds students confidence..Math power. 6. Fun for students 7. Allows for extensions and elaborations






11. A change to the problem or task itself. Eg. simplifying the wording






12. 1. Draw a picture or create a model 2. Look for a pattern 3. Guess and check 4. Make a table of a chart 5. Try a simpler form of the problem 6. Make an organized list 7. Write an equation 8. Working backwards






13. 1. S role is more demanding. They get to use various methods to solve problems in diverse ways 2. Allows an entry point for a WIDE range of S - so all S can be successful. Teacher gives problem and S decides how to solve it 3. S must be able to apply






14. Research identifies 3 ways that problem solving might be incorporated into mathematics instruction. What are they?






15. 1. Rehearsal time for the shy student 2. Prepares student to actually talk about his solution when the time comes 3. Used for assessment by teachers of the students work 4. Helps students to solidify their thoughts






16. 1. Conceptual Mathematics - 2. Algorithms and Processes






17. Different problem based tasks or experiences spread over numerous class periods - each addressing the SAME ideas






18. Students can approach from different angles - and can determine the simplest way to do the problem. Eg. Read a story and write a problem about the story.






19. Toughest phase for the Teacher. Think Vogisty (ZPD). 1. Teacher has to let go and let the S do the work! Math write time! 2. Listen actively as this is the assessment piece...walk around 3. Provide appropriate hints to funnel towards right answer 4.






20. Students should be encouraged to solve in multiple ways - as this provides multiply entry points for students. This provides rich learning opportunities for math talk. Provides an easy way to tier assignments. Eg. A or B or C or D






21. Repetitive - Non-problem based exercises designed to improve skills in an area (multiplication facts - + --)






22. Assessment used throughout teaching of a lesson and/or unit to gauge students' understanding and inform and guide teaching






23. Student gives rationale for the way they solved the problem. Using pictures - numbers or words. Draw - solve - write it down. Think of the students explanation of how many buses needed for the school trip ;-) This helps teacher to understand students






24. It must begin where the students are -The problematic or engaging aspect of the problem must be due to the mathematics that the students are to learn (students are Doing the activity) -It must require justifications and explanations for answers and m






25. Cumulative evaluations that generate a single score. Eg. End of unit test - occurs at end of an instructional unit & document student learning






26. Allow for maximum student interpretation. Answers will vary. Eg. Planning a party and have X amount of money to spend.






27. 1. Teacher facilitates discussion only. Students do most of the talking. Talk time! 2. Include students at ALL levels 3. Call on shy ones - after giving them a chance to prepare to foster a community of learners 4. Encourage students to ask questions






28. 1. Understanding the problem 2. Devising a plan 3. Carrying out the plan 4. Looking back






29. 1. STAR (Search problem for information -Translate into words or pictures - Answer the problem - Review your solution) 2. Reinforce key words/vocabulary. Create a word or symbol wall 3. Use friendly numbers. Round up from $6.13 to $6.00 4. Vary the t






30. It assumes that all students have the necessary prior knowledge to understand the explanations;presents only one way to do the problem - while communicating that there is only one way to solve the problem;puts students into a passive learner role;pro

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31. ELL - Special Needs - Gifted - Learning Disabilities - Cultural background. These are all things teachers must be aware of when presenting problems to students.

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32. Most overlooked phase due to time - and some teachers don't see the value - but don't miss this phase as it is the phase that brings things back around allowing S to get meaning out of the 1st two phases!






33. Providing a different environment or circumstance made with a particular student in mind. EG. changing lighting in a room - allow to work alone






34. Problem-based tasks or activities are the vehicle by which the desired curriculum is developed. The learning is an outcome of the problem-solving process.