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Test your basic knowledge |
Teaching Though Problem Solving
Start Test
Study First
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. 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
Open ended problems
After phase
Tiered Lesson
Value of teaching through problem solving
2. 5. Builds students confidence..Math power. 6. Fun for students 7. Allows for extensions and elaborations
practice
Why the 'teaching for problem-solving' approach is not successful in supporting student learning and retention of math concepts
Value of teaching through problem solving (2)
What it means to teach mathematics through problem solving
3. 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
Accommodation
Barriers and solutions to learning for students with disabilities
Multiple Entry Points
Value of teaching through problem solving
4. 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
Conceptual Mathematics
When selecting appropriate tasks consider...
formative assessment
Why writing is important
5. 1. Conceptual Mathematics - 2. Algorithms and Processes
Diversity in today's classroom includes..
Why writing is important
practice
Examples of Problem-Based Tasks
6. Repetitive - Non-problem based exercises designed to improve skills in an area (multiplication facts - + --)
drill
formative assessment
Modification
Conceptual Mathematics
7. Before phase - During phase - After phase
The importance of talk time
During phase
Examples of Problem-Based Tasks
Three phase Lesson Plan
8. Cumulative evaluations that generate a single score. Eg. End of unit test - occurs at end of an instructional unit & document student learning
Summative assessment
practice
What it means to teach mathematics through problem solving
After phase
9. 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.
Three phase Lesson Plan
What it means to teach mathematics through problem solving
Value of teaching through problem solving (2)
The importance of talk time
10. 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.
Problem-Solving Strategies
4 step problem solving process
Multiple Entry Points
10 steps to planning a problem based lesson plan
11. 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
Before phase
Open ended problems
Problem-Solving Strategies
During phase
12. 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
Tiered Lesson
Accommodation
Three phase Lesson Plan
After phase (steps)
13. 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
How a problem is defined for learning mathematics
Open ended problems
The importance of talk time
10 steps to planning a problem based lesson plan
14. Math needs to be conceptional - not procedural Math understanding the student brings to the problem
When selecting appropriate tasks consider...
How a problem is defined for learning mathematics
Value of teaching through problem solving
What it means to teach mathematics through problem solving
15. Allow for maximum student interpretation. Answers will vary. Eg. Planning a party and have X amount of money to spend.
1. Teaching for Problem Solving 2. Teaching About Problem Solving 3. Teaching Through Problem Solving
Summative assessment
Open ended problems
drill
16. 1. Understanding the problem 2. Devising a plan 3. Carrying out the plan 4. Looking back
Multiple Entry Points
4 step problem solving process
Why writing is important
Problem-Solving Strategies
17. A change to the problem or task itself. Eg. simplifying the wording
Modification
drill
4 step problem solving process
The importance of talk time
18. 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
What it means to teach mathematics through problem solving
Multiple Entry Points
After phase (steps)
Problems with multiple solutions
19. Teacher chooses problem - based on 'just right fit'. Teacher does problem herself - gives proper support to student - making sure problem is challenging.
1. Teaching for Problem Solving 2. Teaching About Problem Solving 3. Teaching Through Problem Solving
drill
Value of teaching through problem solving (2)
Planning a problem based lesson..eg.
20. 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
Problems with multiple solutions
After phase (steps)
Value of teaching through problem solving
practice
21. 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
Why the 'teaching for problem-solving' approach is not successful in supporting student learning and retention of math concepts
During phase
Problems with multiple solutions
Before phase
22. 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
Examples of Problem-Based Tasks
Conceptual Mathematics
Open ended problems
Problem-Solving Strategies
23. 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.
When selecting appropriate tasks consider...
Why writing is important
Value of teaching through problem solving (2)
During phase
24. 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!
Accommodation
After phase (steps)
Summative assessment
After phase
25. Different problem based tasks or experiences spread over numerous class periods - each addressing the SAME ideas
Problems with multiple solutions
Three phase Lesson Plan
practice
Tiered Lesson
26. 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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27. 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)
The importance of talk time
Multiple Entry Points
Why writing is important
How a problem is defined for learning mathematics
28. Providing a different environment or circumstance made with a particular student in mind. EG. changing lighting in a room - allow to work alone
10 steps to planning a problem based lesson plan
Accommodation
1. Teaching for Problem Solving 2. Teaching About Problem Solving 3. Teaching Through Problem Solving
Tiered Lesson
29. Assessment used throughout teaching of a lesson and/or unit to gauge students' understanding and inform and guide teaching
Justify
formative assessment
Problem-Solving Strategies
Summative assessment
30. 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
drill
Flexible grouping
Justify
Problem-Solving Strategies
31. Research identifies 3 ways that problem solving might be incorporated into mathematics instruction. What are they?
Flexible grouping
What it means to teach mathematics through problem solving
Why the 'teaching for problem-solving' approach is not successful in supporting student learning and retention of math concepts
1. Teaching for Problem Solving 2. Teaching About Problem Solving 3. Teaching Through Problem Solving
32. Think IK topped out of math in elementary school - and went to middle school for more intense training
How a problem is defined for learning mathematics
drill
Flexible grouping
practice
33. 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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34. 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
Summative assessment
Open ended problems
10 steps to planning a problem based lesson plan
When selecting appropriate tasks consider...