He first mentioned two facts he learned during his years of teaching.

1) Students are impatient with their problem solving

2) Students aren’t engaged by math applications

Then he went on to make some analogies regarding math and real life.

One of which described perplexity as what keeps the the Math river flowing

He then tried to lay out a model to follow in order to create these perplexing lessons.

-begins with simple multimedia

-encourages a certain question

-encourages a guess

-offer lots of information or none at all

-encourages a certain skill

He then modeled a more specific problem that would perplex the students using these steps.

-hook

-what Information do you need?

-What skills are needed

-Answer

-Extension

Finally he walked us through how a lesson would work with one of these questions.

-Perplexing pedagogy

-Students form the question

-Exercise their number sense with a guess

-Decide what information they need

-Decide what skills they need

-Observe an answer

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I would have to say that the highlight of this course for me has been the interaction with the mathematical community at large. I was able to see that there are people out there that love math just as much ( if not more than ) I do. I also learned that I do not have nearly enough hours in the day to become as involved as I would like to in this community. I barely have enough time to feed myself and get a shower during the day I have so much going on already. I look forward to the challenge of finding time in my schedule to continue learning through the live events.

Thank you Maria for opening my eyes to a whole new world in which to explore mathematics.

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I thought Mr. Kirchoff’s presentation was excellent. He was by far the most prepared and well versed speaker I have seen at a live event this summer. His ideas were made very clearly and I truly wished he had cut the question/ discussion sections shorter and gotten to more of the prepared content.

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I would like to take your points one at a time,

1) Apparently you have either not seen the textbooks used in NY or PA for teaching algebra 1, or you have a different definition of rote instruction than I do. the text books I have been using for the last 7 years in those two states offer very little other than rote instruction. to the point that the practice questions actually refer back to the “instruction” given a few pages earlier. Usually, the instruction only consists of an example and how it is to be solved.

2)I disagree with your contention that he is implying that math teachers do not know math. He is simply stating that when a person has learned a topic one way it takes a lot of creativity and intelligence to try to teach it in a different way. When we, as teachers, are concocting our lessons it is only natural to fall back on the methods used to impart that same knowledge to us. Since most of us were taught in “traditional” settings it would only make sense that we would harken back to those same tools and methods when we are trying to duplicate the process for our students.

3) The question here is not whether traditional teaching methods work for a select few students. But rather, what will work for the greater majority. Working in low SES, underperforming schools for seven years has shown me that these students do not respond well to the way we are currently teaching math in this country. By the time my students get to me (9th grade algebra) they are already disillusioned with the study of math. I can not tell you haw many times I have had a student ask me, “When will I ever use this in real life?” In order to combat this disheartening attitude I have tried to enrich my teaching with problem based, real life scenarios. While I have not been completely successful in reaching a majority of my students, I have seen great strides in some of them.

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Assessment – Rubric

2) Using Geogebra, geometer’s sketchpad, or graphs (MacBook), create an applet that others can use to discover the relationship between the slope of a line and it’s equation.

Assessment – Peer assessment. Students will “trade” applets and work through them. Students will then grade each others assignments on a 1-5 scale based on ease of use and informative qualities. ( I will then go through each one and assess the student grades)

3) Students will search the Web for at least 5 definitions of slope and y- intercept. They will then rank these definitions in order from best to worst, creating a poster for each term.

Assessment – Rubric

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Assessment- #1) Check for completion #2) Journal entry having the students write an explanation of WHY they listed what they listed.

Understanding and analyzing- compare the two lists, answer the following questions about the lists. 1) Why is the second list so much longer than the first if we only added one more die? 2) What does this say about the possibility of getting a total of 3 in each case? What about getting a 6?

Assessment – #1) Have students compare and contrast the two sample spaces. #2) have the students create a powerpoint or keynote presentation outlining the differences between the two sample spaces.

Evaluating – perform an experiment. Roll a single die 50 times and record your results. then roll a pair of dice 50 times and record your results. Check your experimental probabilities against your theoretical ones. what did you find? What do you think would happen if you did each experiment 100 times? 1000 times? 1,000,000 times?

Assessment – #1) Peer assessment. students will compare their thoughts with a classmate’s and come together on a consensus. #2) Formative. students will use whiteboards to answer questions by the teacher that reflect the task at hand. As students hold up their answers the teacher can see where students thinking might need some redirection.

Creating – design another experiment involving probability using things you see in your everyday life. Find the theoretical probabilities and then carry out an experiment using the materials you describe. compare your results with your hypothesis (theoretical probabilities).

Assessment – #1) A rubric that clearly delineates the objectives for this assignment. This way the students can self assess as they work through the experiment. #2) Peer assessment. have students “trade” experiments. Students will then evaluate their classmates work and give it a grade from 1 – 10.

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This lesson shows the wonders we can do with graphs to make them show what we want people to see. It is a pretty elementary lesson that explains the importance of scales on a graph. I like the way the lesson gives examples of good scales and bad scales to show why the creators choice makes such a big difference in how the graph is read by others. As a student works his way through the assignment it becomes very clear how it is possible to manipulate data. For what it is worth, this lesson gets the job done.

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Don Cohen “The Mathman” guides students along a path to deeper understanding of patterns that lead to infinite series. during the Live event, we got to see the true joy that Don still gets from seeing his students succeed. Don has put together, with the help of one of his former students a wonderful “map” of calculus. The map has all sorts of examples of the work his students have done through the years. Some of the more notable work has been done by 2nd – 4th graders wherein they discovered infinite series while working on problems such as ” how can you divide 6 cookies among 7 people?” While he does not introduce any formal calculus terminology into his teaching of young children he is able to bring out the important concepts that they will need later in their schooling, all while helping to take away the “fear” of math.

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This lesson definitely falls on the low end of all of the spectrums we have been discussing in class. If we compare this with Bloom’s taxonomy it would have to be at the low (knowledge) end. Same with the Van Hiele Model, we are simply asking students to identify a property visually, so that would be a level 0 task. In terms of Problem solving and problem posing, their is very little depth to this lesson.

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