Week 4 - True Blue Color Tiles Probability Lesson Plan

True Blue Color Tiles Probability Lesson Plan and Supporting Documents

This lesson requires the use of Color Tiles.

I tried this lesson with four of my eighth grade students at lunch. It is very interesting to note that their predicted probabilities did not match up with either their experimental probabilities or the theoretical probabilities. Based on the discussion that the students and I had, it became apparent that they had trouble understanding the concept of not replacing a Color Tile. In essence, if there are six tiles for the first draw then there are only five tiles for the second draw. Obviously, this caused many of the students to come up with predicted probabilities that were not close to what one would expect them to be.

On the other hand, students developed a deep understanding of the idea that as the number of trials increases the experimental probability becomes closer to the theoretical probability. This is a very important concept for students to learn because it is something that can be applied to the real world quite often. In addition, students must use this concept quite often in the scientific laboratory setting.

Week 4 - Reaction to Private Universe Workshop 4 – Thinking Like a Mathematician

One very important suggestion that was made in the video with regard to the Tower of Hanoi Problem was to try a simpler problem. This is a very important strategy to teach students because often problems in mathematics look very difficult. Trying to solve what appears to be a very difficult problem can quickly become frustrating. However, if students can simplify a problem, learn something new from the simpler problem, and then apply what they learned to the original more difficult problem then the problem becomes easier to solve. The nice thing about having students use a strategy like this is that it forces them to look for patterns in simplified problems that can be applied to more challenging problems. Thus, this strategy encourages students to think creatively because it requires students to create new simplified problems that they can solve to determine if there is a pattern that can be applied to a more difficult problem. It also encourages students to think critically because students need to determine what the pattern is.

The narrator of the video points out that the thought process that the students were using is much like the thought process of a mathematician. This is because mathematicians typically analyze simpler problems in order to develop a pattern that can be applied to more complex problems. Since this is what “real world” mathematicians do, I feel that this is the type of mathematical thinking that students really need to learn in school. Thus, it is important that videos like this one exist to show prospective teachers how they should teach mathematics to meet the needs of twenty-first century learners.

I particularly liked the teaching strategies that Janet Walter employs. This is because I believe that it is important to encourage students to become active learners. When students become active learners they rarely become distracted. Also, by becoming a part of the learning experience, students generally develop a deeper understanding of the material. Unfortunately, I have experienced many mathematics courses that are not engaging. In the type of mathematics class that I am describing, the teacher typically acts like a “sage on a stage”. He or she gives students the information necessary to solve problems, and then the students are asked to take notes and solve problems using those notes. In this type of mathematics courses, classroom discussions about mathematics questions and problems are a rarity. In essence, students are not asked to think deeply about problems in this type of class. They are simply asked to do a process that was clearly mapped out by the teacher. Since this style of teaching simplifies the job of a student, it is not common to hear of a student who complains about this method of instruction. However, this style of teaching is not the most effective way to get youngsters to learn mathematics. Thus, I am glad to see that this video encourages new teachers to break this mold and get students to think about mathematical problems.

Lastly, I think the most important thing that this video demonstrates is that if teachers give students the opportunity to become active learners then there is a good chance that the students will have fun. I have heard many students tell me that math is boring, math is hard, and math is inapplicable to their daily lives. This is likely because students are often not asked to participate in mathematics lessons in ways that encourage them to think deeply about a problem. I think the strategies presented in this video have the potential to change this type of reaction to mathematics. By employing the strategies demonstrated in the video, teachers can get students to think like mathematicians, develop a deep understanding of the material, and enjoy what they are learning.

Week 4 - Virtual Manipulative - Number Puzzles

Hi Everyone,

Number Puzzles Virtual Manipulative

I love the Number Puzzles Virtual Manipulative for several reasons.

First, it challenges students to solve relatively difficult math puzzles. For each puzzle, students need to come up with a strategy. For example, they must consider whether it is better to put a high or a low number in the vertex of a triangle? Keep in mind that this changes depending whether the sum for each side of the triangle is large or small.

Second, this virtual manipulative forces students to do computation. I feel that most students will find it annoying to have to keep typing numbers into a calculator. Thus, they will challenge themselves to do the computation in their heads. Obviously, the ability to do computation in one's head is a very important skill, and thus, this virtual manipulative helps students build this skill.

Third, these puzzles are fun! I allowed my middle school students to play these puzzles during lunch, and they loved them. I do not think they even realized that they were doing math. Thus, if you want to trick students into doing computation in their heads then this is certainly one of the best ways to do it.

I suggest that you try this virtual manipulative at home. You will find that it is actually very entertaining.

Sincerely,

Marc

Yola Website

Hi Everyone,

Up to this point, I have been using a Google website. I like Google because I am familiar with it. However, I just created a Yola website, and I realized that Yola websites are much better than Google websites. You will be surprised just how user friendly Yola websites are.

Check out my new Yola website:

Marc Vogel's Math Manipulatives 1 Yola Website

I have already posted the two Pattern Blocks lesson plans that I created on my Yola Site. I also posted the supporting documents. Thus, you can find everything that you need on my Yola site to conduct two lessons with Pattern Blocks in your respective classrooms.

I will post the lesson plans that I create in the future on this site, so I suggest that you check it regularly.

Sincerely,

Marc

Updated Blog

Hi Everyone,

Throughout my blog, I converted the web addresses that I posted to links. I hope this makes it easier for you to find everything.

Sincerely,

Marc

Week Three - Backyard Improvements Lesson Plan

This lesson plan, like the lesson plan from week two, uses Pattern Blocks.

Marc Vogel's Week 3 Lesson Plan

Marc Vogel's Yola Website (Contains Lesson Plans and Supporting Documents)

If the link above does not work then copy and paste the following link into the address bar:

http://sites.google.com/site/mathmanipulativeslessonplans/home/lesson-plan-for-week-three

I based this lesson plan on the Backyard Improvements Lesson Plan, which you can find under the Patterns and Functions link for Grades 7 - 8 on the Super Source CD-ROM.

Reflection on Perimeter Search Lesson for Week Two

As you know, I demonstrated the Pattern Search lesson in class this past Monday. When I tried it with two of my high school students that stopped by after school it was very successful. I feel that I was able to meet all of the objectives of the lesson. The interesting thing is that the students never seemed to realize that they were doing mathematics. To them, the activity was like a game. One would think that high school students would not want to play with blocks, but the reality is that they enjoy working with manipulatives as much as elementary school students.

For anyone who wants to become a mathematics teacher, this lesson is a good way to reinforce the concept of perimeter. Students generally enjoy a challenge, and they enjoy a challenge that involves manipulatives even more. To students, the activities in this lesson are more like "fun time" than they are work. Thus, it is easy to get students engaged by using this lesson.