MT 445 Final Reflection

8/3/2019 MT 445 Final Reflection

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Rozga, Molly

MT 445 Advanced Topics

Final Reflection

1. Describe how you challenged yourself regularly with solving unfamiliar problems.Give some examples of problems you found challenging.

This class provided a lot of problems that were challenging and unfamiliar. I would keep

reminding myself that these problems were designed to show the different ways to

approach them. There are a lot of math facts that I just simply did not remember

enough at first to put to good use. The tethered goat question was one that I needed to

draw, to scale, the information that was given so that I would be able to see what I

needed to figure out. Another approach that helped me to solve some of the problems

was organizing the data into a table, like theCatch Up problem. As for challenging

problems, I thought most of the Algebra and Geometry questions were challenging. It

was almost like waiting for my brain to remember that I have seen problems like this

and what strategies did I have.

2. Did you find working on unfamiliar problems interesting? Give some specificexamples.

I thought that working with these unfamiliar problems was very interesting. It

challenged me to think of things outside of the way day-to-day math tasks are done. I

dont have a goat at home tethered to a barn. If I had a pocketful of coins, I would

simply count them. Using alternate approaches, because these things arent common

place, makes problem solving fascinating. Once we got into the algebra and geometryproblems, those required more thought and persistence.

3. Did you have emotional reactions to solving unfamiliar problems? Frequently,problem solvers experience frustration in the face of being stuck.Did you have this

experience? How were you able to move past it?

I am someone who will not let something get the best of me. I will keep working and

keep working until there is light at the end of the tunnel. Despite my yearning for a final

answer, there were times that I thought these problems would never some to an end

(equilateral triangle with a triangle inside). I sat for two hours after class to put

together my answer for the area of the smaller triangle. Rather than sulking in the

being stuck feeling, I knew that if I just let the process happen, I would come to an

answer that I was satisfied with.


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Rozga, Molly


Final Reflection

4. How do you think you expanded or extended your ability and willingness to work onunfamiliar mathematics problems?

Something I learned about myself in this class, is that I have the determination to work

through these problems and come to a conclusion. Please note that a conclusion is not

always an answer, but sometimes it is what I need to get in order to get to a solution.

The most important thing to remember is that there are a number of ways to work with

a problem that is unfamiliar. The best advice is something that I heard a professor say

When you are stuck, take a break, clear your mind and then try again. Patience and

perseverance is needed when life presents you with an unfamiliar problem.

5. How do you think you might apply what you learned to your future work as ateacher?

As a teacher, I would like to offer my students challenge or puzzle problems on a

somewhat regular basis. To get students to be comfortable and confident in their

mathematic abilities, they need to be presented with situations that offer several

different ways to arrive at a solution and get them talking about their strategies. One of

the NCTMs process standards is Communication. These challenge or puzzle questions

would enable the students to communicate their approach to

their peers, and compare and contrast the different approaches to find an efficient one.

This would also incorporate a higher level cognitive demand, as these puzzle or

challenges would not necessarily have an algorithmic approach.

This would also benefit my students by helping them learn patience, persistence, and

the value of a short break from their homework time.

6. One goal was to build your persistence in solving unfamiliar mathematics problems.How well do you think you achieved this goal?

I think that I have achieved this goal. I believe that it is most clearly demonstrated in

the geometry problem with the equilateral triangle with a smaller triangle drawn inside.

I thought of how I might be able to solve the problem over a lunch break. During my

afternoon class, we were given some work time, and I spent that time working through

the triangle problem. By the end of the afternoon class, I came to a solution that I was

confident in presenting to our group.


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Rozga, Molly


Final Reflection

7. Examine the Student Learning Goals for this class from the syllabus. Choose at leastone of these goals and reflect in writing on your progress in this course related to

this goal in two paragraphs (for each goal) responding to:

a. Describe your personal progress; give examples as evidence.b. Describe aspects of the work in this course that you found interesting, helpful,

or challenging, in terms of your progress.

Students will employ multi-step reasoning to solve complex problems and explain

results.

At the beginning of the summer term, I was quite content to solve problems using

the format we had gone through in a class and be done with the work. This class helped

me to see the fun that lies within mathematical problem solving. We started the term

with the Pocketful of Coins problem, which caused me much grief. I thought for sure

that I would be able to solve this problem in an algebraic form, starting with a table of

information. Once I saw that I wouldnt be able to eliminate all of my variables, I almost

gave upon the problem. By the time we got to the algebra and geometry problems, I

was ready to tackle any challenge that this problem presented. I ended up working

away for two to three hours on this problem. In class, I was able to present the many

steps that I had found t o solve this problem. I used several technological tools to

demonstrate my understanding of this problem.

In knowing that there would be more than one way to approach each problem, I

really tried to clearly explain my thought process so that I would be able to connect my

solution to the solutions that were presented by my classmates. This was remarkable!

No matter what the problem was, there was always a way to connect the approaches

together to arrive at the same solution. In the beginning, before we were thinking about

writing briefs while the problems were presented, it was difficult to see why making

connections was important. Perhaps, this became the most clear when we were looking

at the juice question with student solutions. It was demonstrated very well there that

even though there were 12 different explanations of the solution, they all came to the

same results.


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Rozga, Molly


Final Reflection

8. What mathematical learning goals will you set for yourself as you move towardteaching?

Is there an email subscription service that will send you problems like the ones we were

working on? If there is, I would love to receive more questions on a weekly basis or so.

To take a break from homework to work on a challenging question may help my brain

think in a way that will help with homework. First goal, continue looking for challenging

problems and puzzles.

In finding these math puzzles and challenging problems, I would like to keep them

organized so that I have some ready extra activities for my students as they complete

their required work. Organization of papers is not necessarily my strong suit, so this will

challenge me to keep things ready for the future. Second Goal, keep it organized.

Part of the organization of the problems, will be a listing of solutions, so that I can

continually add to my collection with alternate ways to solve some of these problems.

Third goal, add additional approaches to organized problems.

I dont think there is a point where I will feel like I have learned it all. I want to include

in my professional development plan (during licensure) that I will continue to develop

my mathematical abilities.

MT 445 Final Reflection

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