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Please complete the initial discussion board and reply to 2 classmates- APA format

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EDUC 530

QUESTIONUsing George Polya’s four-step problem solving strategy (Johnson et al., 2018, pp. 114-115) explain

how you might model problem solving steps while integrating some of the “Twelve strategies: Tools for

Problem Solving” found on page 115 of our text. Finally how might a problem based classroom differ

from a traditional mathematics classroom?

Threads must be 300 words, and replies must be at least 150 words. You should include at least 1 citation in

your initial post and one citation in at least 1 reply. Remember to include a reference list in current APA

style.

DISCUSSION GRADING RUBRIC

Content 70%

Advanced

Thread

18 points

Content

All key components of the

Discussion prompt are

answered in the thread. The

thread has a clear, logical flow.

Major points are stated clearly.

Major points are supported by

good examples or thoughtful

analysis.

Proficient

16 to 17 points

Most of the components of the

Discussion prompt are answered in

the thread. The thread has a logical

flow. Major points are stated

reasonably well. Major points are

supported by good examples or

thoughtful analysis.

Developing

1 to 15 points

The Discussion prompt is

addressed minimally. The thread

lacks flow or content. Major

points are unclear or confusing.

Major points are not supported

by examples or thoughtful

analysis.

Not Present

0 points

Not present

Page 1 of 2

EDUC 530

Replies

10 points

Each reply focuses on a

meaningful point made in

another student’s thread. Each

reply provides substantive

additional thoughts regarding

the thread and an explanation

of why the student agrees or

disagrees with the idea

presented in the thread. Each

reply is clear and coherent.

Structure 30%

Advanced

Post

5 to 6 points

Grammar,

Spelling and grammar are

Spelling, & correct. Sentences are

Current APA complete, clear, and concise.

Paragraphs contain

appropriately varied sentence

structures. Where applicable,

references are cited in current

APA format

Post Word

4 points

Count

Minimum word count of 300

words met, but not exceeded

by more than 100 words

Replies

4 points

Word Count At least 2 replies are present

and a minimum word count of

150 words is met but not

exceeded by more than 100

words

9 points

Replies generally focus on a

meaningful point made in another

student’s thread. Replies generally

provide substantive additional

thoughts regarding the thread and

an explanation of why the student

likes or dislikes the idea presented

in the thread. Replies are generally

clear and coherent.

1 to 8 points

Replies somewhat focus on a

point made in another student’s

thread. Replies could be more

substantive regarding the thread.

Replies lack clarity and

coherence.

0 points

Not present

Proficient

4 points

Some spelling and grammar errors.

Sentences are presented well.

Paragraphs contain some varied

sentence structures. Where

applicable, references are cited

with some current APA

formatting.

Developing

1 to 3 points

Spelling and grammar errors

distract. Sentences are

incomplete or unclear.

Paragraphs are poorly formed.

Where applicable, references are

minimally or not cited in current

APA format.

Not Present

0 points

Not present

3 points

Word count of 250 words met

1 to 2 points

Word count of 200 words met

0 points

Not present

3 points

At least 2 replies are present, or a

minimum word count of 100

words is met

1 to 2 points

At least 1 reply is present, or a

minimum word count of 1 – 99

words is met

0 points

Not present

Page 2 of 2

Classmate #1“Teachers find problems based in children’s experiences that require mathematical

skills and concepts. Students encounter problems through realistic situations,

imagined stories, puzzles, games, and manipulative activities” (Johnson et al., 2018,

p.112). George Polya developed a four-step problem solving organizer, like the

scientific method, that children can use to solve any math problem. The steps include:

Identify the problem or question, propose a solution, carry out the plan, look back and

evaluate the solution.

The text identifies twelve strategies for solving math problems for elementary

mathematics. Using these strategies, students can expand upon the methods of

George Polya’s four steps. For example, to understand a simple math problem

pertaining to patterns a student would identify a pattern, build a model of the pattern,

or draw a picture of the pattern. If the student were asked to extend the pattern, he

would use trial and error, and work backwards to check his work. These two strategies

would be proposing the solution, carrying out the plan, and evaluating the solution.

A problem-based classroom differs from a traditional mathematics classroom in

multiple ways. The first way the classrooms differ is the layout of the classroom. In a

traditional classroom desks are arranged individually, and forward facing, and the

teacher is the central focus. In a problem based, or project based, classroom, the desks

are aligned in groups for centers, a rug for group discussion, and tables in the room for

instructional support activities. A traditional classroom relies heavily on directinstruction, while a problem-based classroom utilizes a variety of methods and

supports student-led projects. According to Johnson et al., “although curriculum goals

are established by standards, problem-based investigations provide a way that

students can push the curriculum. Providing time and support for project-based

learning stimulates students to be independent learners” (Johnson et al., 2018, 5-3e).

Johnson, A., Tipps, S. & Kennedy, L. (2018). Guiding Children’s Learning of

Mathematics (13th ed.). Cengage.

Classmate #2When a student is presented with a problem and neither the answer nor the procedure

is known, they need to be aware of the steps they can use to address and answer a

problem. Students could use a four-step strategy suggested by George Polya. His

strategy can be applied to all types of problem solving and it resembles the scientific

method. In elementary mathematics, Polya’s steps may be called understand, plan, do,

and check back (Johnson et al., 2018, p. 115). Basically, a student must determine the

problem, suggest a resolution, follow through with their strategy, and assess their

results.

In our text there are “Twelve strategies: Tools for Problem Solving”, which are tools

students can use to solve problems (Johnson et al., 2018, p. 115). These tools are

highly effective for solving mathematical problems, especially with elementary school

students. Students can also incorporate George Polya’s four-step strategy into any of

these twelve strategies. For instance, If I were to model using the finding a pattern

strategy, along with incorporating Polya’s four-steps for my students, it would look

something like this; I would decide what pattern that is to be found, which would be the

understand step. Next, I would determine the process of how I will find the pattern,

which would fall under the planning step. Then I will look for the pattern, which would

be incorporating the do step of Polya’s strategy. Lastly, I would apply the pattern to

solve the problem, which would be the check back step. For another example, building

a model is another one of the twelve strategies I could model for my students. For the

understand step, I would model determining what situation or problem needs to be

solved. Next, to plan, I would decide how I could build a model that will be relevant to

the situation or problem at hand. Next, for the do step, I would build the model. Lastly, I

would check back and evaluate my model and incorporate it into answering the

problem. The four-step strategy of Polya can be used with any of the Twelve strategies

for problem solving, the others being act it out, draw a picture, make a table or graph,

write a mathematical sentence, guess and check, account for all possibilities, solve a

simpler problem, work backward, dimensional analysis, and break set (Johnson et al.,

2018, p. 115).

Problem solving classrooms would be encouraging and motivating environments that

encourage children to think through problems, while providing them with the tools and

strategies to solve them. I believe there would be more challenges, struggles, and math

anxiety in a traditional classroom that does not focus on problem solving strategies.

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Explanation & Answer:

300 Words

2 Posts

Tags:

mathematical skills

George Polya

Four Step Problem

solving strategy

model problem

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