Ok - we will have a test on October 14.

Here is a heads up and a head start! You will get this as a handout Tuesday.

TEN QUESTIONS OR GUIDES FOR A TEST.
Your test will come from these questions or questions very similar to these.
1. We used Geoboard grid paper to explore the area of squares. Now think about parallelograms and trapezoids. Develop an activity to help a student come up with the formula or method of finding the area of a non-rectangular parallelogram and the area of a trapezoid.
2. We did the Mathe Teakst Buk activity. How does this activity as a “math unit” contrast with the vision of the mathematics in the NCTM Standards?
3. The Standards for 6-8 say students should “Understand meanings of operations and how they relate to one another”. What does this mean in terms of fractions, particularly in terms of how we traditionally teach “fractions” and how we might teach them.
4. The Standards have been criticized for de-emphasis of computational skills. What do the Standards really say about the role of computational skills?
5. In the Consecutive Numbers activity, the overall goal was for students to develop a systematic way of developing the complete list of sums. What was that method and why didn’t the teacher just describe it to start the “lesson”? To answer this, Google Constructivism or Constructivist Teaching Methods, and see the Wikipedia entries.
6. You have 1000 feet of fence to surround a rectangular field for badgers. All the fence must be used, with no overlap. What are the dimensions and area of the fields with the smallest area and the greatest areas that can be enclosed with this fence? At first assume you can only have dimensions that are integers, then allow any real values for the dimensions. Explain your solution as you would want an 8th or 9th grader grade to do. Use no calculus.
7. When you double each dimension of a rectangle, the area increases by a factor of 4. Triple them, and the area is nine times as big. Does this same growth pattern apply to sides of a triangle? Justify your answer as you would want a mathematically empowered 8th or 9th grader to do. Visual models are always neat.
8. Super Chocolates are arranged in boxes so that a caramel is placed in the center of each array of four chocolates, as shown below. The dimensions of the box tell you how many columns and how many rows of chocolates come in the box. Develop a method to find the number of caramels in any box if you know its dimensions. Explain and justify your method using words, diagrams, and expressions as you would want a (beginning) Algebra student to do. (see the image in teh Algebra Standards and the handout you will get.




9. Ratio and proportion are Big Ideas in middle grades math and beyond. The poems below is taken form the Standards. How does it help address, teach, and/or reinforce these ideas? Answer as if you were developing a lesson around the poem.
One Inch Tall

If you were only one inch tall, you'd ride a worm to school.
The teardrop of a crying ant would be your swimming pool.
A crumb of cake would be a feast
And last you seven days at least,
A flea would be a frightening beast
If you were one inch tall.

If you were only one inch tall, you'd walk beneath the door,
And it would take about a month to get down to the store.
A bit of fluff would be your bed,
You'd swing upon a spider's thread,
And wear a thimble on your head
If you were one inch tall.

You'd surf across the kitchen sink upon a stick of gum.
You couldn't hug your mama, you'd just have to hug her thumb.
You'd run from people's feet in fright,
To move a pen would take all night,
(This poem took fourteen years to write—
'Cause I'm just one inch tall).

—Shel Silverstein

10. Look over the problems in the Probability and the EDA handouts.

Sorry I missed you

Sorry I got tied up last night - our hearing went long. I will try to email you somae materials, including assignments. Or I will fix a link to the documents you will need. Check back later today.
Thanks
Peter

Slowing down - a class announcement -no response needed

So here is the deal - less is more. You had a reading assignment that was fairly extensive. To avoid too much trauma, and to really get some focus, this week we are going to focus on the Principles and Standards Chapters 1 and 2 in a quick overview, then in Chapter 6 (the 6 -8 Standards} really focus on Number and Operations and Algebra Standards. We will actually use some of their examples. You will see these in the column to the left. You should also take a look at the Process Standards in this column, as well. So do this, and the write ups due this week and you are good to go.

Learning with understandaing and autonomy

From the Principles and Standards (The Learning Principle)

"A major goal of school mathematics programs is to create autonomous learners, and learning with understanding supports this goal. Students learn more and learn better when they can take control of their learning by defining their goals and monitoring their progress. When challenged with appropriately chosen tasks, students become confident in their ability to tackle difficult problems, eager to figure things out on their own, flexible in exploring mathematical ideas and trying alternative solution paths, and willing to persevere. Effective learners recognize the importance of reflecting on their thinking and learning from their mistakes. Students should view the difficulty of complex mathematical investigations as a worthwhile challenge rather than as an excuse to give up. Even when a mathematical task is difficult, it can be engaging and rewarding. When students work hard to solve a difficult problem or to understand a complex idea, they experience a very special feeling of accomplishment, which in turn leads to a willingness to continue and extend their engagement with mathematics."

Please reflect on the above and your experience - perhaps within mathematics, more likely in your other life, of something you have learned or some problem you have solved. Place that learning in the context of the statements above.

For example, I personally might reflect on how I learned how ro sail.

Two sort of important questions:

My colleague suggested that this course sounded like " A Conversation with Smyth". I like that idea - but maybe as a conversation among all of us. To start it off think about this:
We are math teachers. Consider these questions:

What is mathematics?
What does it mean to know mathematics?

Please respond to this post with a tentative answer to these questions - not as a mathematician, but as a math teacher. We will revisit these responses at the end of the course.