Friday, July 30, 2010

Create a "thinking" environment immediately

I have heard teachers comment that students can't (and do not) think - all they want is to know what the right answer is. Well, I disagree. I do believe many students are hesitant to share what they are thinking and there is the natural fear of being wrong in front of everyone. After all we do not like to be wrong in front of everyone, why should they? Consequently, it is important to create a safe and comfortable "thinking" environment in your classroom.

I start on day one by setting the expectations and guidelines. Now, I am not a big fan of handing out a page of rules and regulations. I do discuss the importance of respect and then I ask them the following question.



I give the students a few minutes to work on this (depending on the students math background I may need to discuss that a square is a rectangle) and then I write the numbers from 1 to 15 on the board. I ask for a show of hands how many students think there is one rectangle, two rectangles, etc. and I do a tally on the board. When I get to 15, I will ask if anyone has a different answer and will place that on the board, if there is one. This is the first day of school, so students tend to be fairly quiet and there is not much conversation going on. I will then ask if anyone would like to change their answer. I do this as I am sending them a message that it is okay to change your answer. Next I will count the tally marks and usually it does not equal the number of students - there are always a couple of students who hesitate participating in this activity. Consequently, I will announce that there appears to be a few people who hadn't decided yet and did they now want to vote. Finally, I do the problem (count the rectangles) and demonstrate my method. As I am doing this I will hear various comments like "Oh, I forgot that one" or "I didn't see that one". We will then discuss their strategies.

When I finish I point out three very important things:
1) If the students got the problem wrong, do they now understand? I discuss the importance of speaking up, asking questions, and never leaving the classroom confused.
2) It was NO big deal if they were wrong! We are all going to be wrong at some point in time. Everyone was polite and respectful and that is how this class will always run!
3) Non participation is unacceptable. I do stress that I will not embarrass them, but I can't read their minds so they will need to help me by participating and sharing what they are thinking.

Consequently, I have the built the foundation of a safe and comfortable "thinking" environment through an activity. I encourage the students to copy the problem down and have their parents try it.

In my next post I will provide the answer to the question and will discuss how to continue building this safe and comfortable "thinking" environment.

Monday, July 26, 2010

Word Walls in Mathematics

Mathematics is filled with confusing vocabulary! For example, the word median is used with statistical measures (the middle term in a set of data that is in order numerically) and in geometry (the median of a triangle is the line segment from one vertex to the midpoint of the opposite side). Ask students to find the difference and you might want them to subtract two numbers or you might be asking them to tell you how the numbers differ - odd vs even, prime vs composite. Begin a geometry unit and you have new vocabulary coming at the students fast and furious. So, how can we help our students master the vocabulary as quickly as possible. First, as I mentioned in my previous post, use the vocabulary correctly and use it often. Second, try putting a word wall up in your classroom. There are many ways to design a word wall. You might want to start with the vocabulary word, followed by the definition, followed by a visual. You might want to incorporate the visual within the word. Examples of this can be found at The Broward County Public Schools - Exceptional Student Education page. You will need to scroll down to they yellow link - Mathematic Word Wall. You will need Adobe Reader to view the document. I would suggest that when you begin the school year you have a word wall started. As the year progresses have the students take charge of the word wall. The possibilites are endless - be creative and have fun with it!

Thursday, July 22, 2010

Goodbye Plug and Chug, Hello Substitute and Evaluate

Mathematics is a very challenging discipline for many people. So, why do textbooks and teachers make it even more confusing by communicating poorly? Our students are capable of understanding the concepts if we would use the proper terminology. For example, why do we tell students to plug and chug? What does it really mean to plug and chug? What we really want the students to do is substitute the value into the expression and evaluate. I know what you are thinking, what is the big deal? After all, students knew that when you told them to plug and chug you meant place the value in for the variable and perform the order of operations. Well, have you thought about what happens when on a standardized test the directions say to substitute and evaluate? Have you noticed that students try to solve algebraic expressions? Why? They do not understand the difference between an expression and an equation. Here is another example. How many books and teachers ask students to reduce a fraction? Doesn't reduce mean to make smaller? Does the fraction actually get smaller? No, the fraction is equivalent! No wonder students have difficulty understanding the concept of a fraction. What we should be asking the students to do is simplify to lowest terms. One last example, how would you read -3? If you said minus three, doesn't minus mean subtraction? Isn't this really negative three or the opposite of three?

Don't feel bad if you are guilty of poorly communicating the mathematics to your students. In many instances we are mimicking what was in the textbook and relying on how we were taught mathematics. I would encourage all math teachers at all levels to think about the terminology they use. If you are in the habit of using mathematical slang or poor terminology, try to break the habit as soon as possible. Discuss this issue with other math teachers at your school. If everyone begins to use proper terminology, students will also use proper terminology and you will see them make great strides in being able to communicate mathematically.

Sunday, July 18, 2010

The Beauty of Mathematics


When trying to intrigue my students about mathematics, I take time to discuss both the beauty and the importance of mathematics. Every year I try to find time to discuss fractals and show them math in nature. The Fibonacci Sequence is always a favorite of the students. They are always amazed at how many places this sequence shows up! It really doesn't take long to show the students a few things or have a class discussion. If you can show YouTube videos in your school, take a few minutes to search the archives - there are some great videos out there. If YouTube is blocked at your school, don't abandon the cause. I myself plan to open the school year with this poster that I made.

Tuesday, July 13, 2010

Continue the Excitement!

So, you have caught your students’ attention with the 11 trick for double digit numbers and maybe showed them how to work with larger whole numbers times 11 (multiply by 11 expanded) as shown in Fantastic Math tricks. Now what? If you know that at some point in time during the school year you will need to simplify fractions and you will work with percents, I would suggest you build the skill of working with 25. I convince my students that they can do division with a double-digit divisor in their heads!! How? The double-digit divisor is 25. First, I will ask them how many quarters are in $1.25, in $3.75, in $8.25 and in $10.00. I tell them to take the dollar amount times 4 and then add in the number of quarters needed for the cents. Yes, I do make sure I am working with a multiple of 25. Then I will relate this to 125 ÷ 25. I tell my students the 25 is a quarter and the 125 is $1.25, so how many quarters are in $1.25? Relate math to money and students will catch quickly! In no time at all your students will be doing 1175 ÷ 25 (answer is 47 as there are 44 quarters in $11 and then you need three more for the 75 cents) and 2050 ÷ 25 (answer is 82 as there are 80 quarters in $20 and then you need two more for the 50 cents). What you have done is empowered your students – they are in control of the numbers as opposed to the numbers controlling them. By mastering the skill of working with 25, your students will find it easier to simplify fractions like 275/1000.

Friday, July 9, 2010

Create Excitement for Mathematics on Day One

I know it is the middle of the summer, but it is never too early to begin planning for the new school year. One of the things I try to do each year on day one is "hook" the students and show them the beauty and power that mathematics possesses. I teach high school math (all levels - remedial to AP) and am always amazed at how easy it is to build excitement for math and empower my students at the same time. One of the first things I show them is how to multiply a double digit number by 11 in their head. For example, 54 X 11. I tell them to take the 5 and 4 and split apart ( 5 __ 4 ), to find the number that goes in the middle they need to add the 5 and 4. So, 54 X 11 is 594. What if you get a double digit number when you add the two digits? A carry is produced. For example, 67 X 11. Split the 6 and 7 ( 6 __ 7 ), add 6 + 7, this gives you 13. The three goes on the line and the one is the carry over to the 6. So 67 X 11 is 737. My students of all levels find this amazing! However, please take the time to show them why this works! There are many math tricks that can be used. Finally, I end my class by telling the students that they are in control of the numbers and they should not let the numbers control them!