Math Bully

During the first week of October (Oct. 1 - 5, 2012), New Jersey held its second annual "Week of Respect" which was created as part of the state's anti-bullying law. During the week of respect, we are asked to include something in our lesson plans that reinforces the importance of treating all people with respect. I was thinking about respect and the importance of respect in the math classroom and I realized that the kind of bullying that I usually see in a math classroom is students laughing when other  people make mistakes. I think it is very important that my students feel safe in my classroom and know that if they make a mistake that they will not be ridiculed. So for my lesson on respect I decided to talk about "math bullying." I start out the lesson by asking my students what they think a "math bully" is and that usually elicits some interesting comments. My definition of a "math bully" is something who laughs or ridicules another person when they make a mistake. Then I share with them some quotes that I found on the importance of making mistakes in the learning process.

Making mistakes simply means you are learning faster.

   --West H. Agor

Constant effort and frequent mistakes are the stepping stones of genius.

  --Elbert Hubbard

Mistakes are the portals of discovery.

--James Joyce

The many who achieves makes many mistakes, but he never makes the biggest mistake of all - doing nothing.

--Benjamin Franklin

Never say, "Oops." Always say "Ah, interesting."

--Author Unknown

It's okay to make mistakes. Mistakes are our teacher - they help us to learn.

--John Bradshaw

I have not failed. I've just found ten thousand ways that won't work.

--Thomas Edison

After we read the quotes together I shared this Respect Pledge:

And then I invited all the students to cut out a geometric shape and write their name on the shape and add it to the Respect Pledge classroom mural at the back of the room. I like the fact that this activity gives us a chance to do a quick review of some geometry vocabulary while at the same time it illustrates that we are all different and unique and we come in all shapes, sizes and colors.

ISN Organization

I tell the students from day one that I don't like to waste time. On the first day of school I show them an almost empty bottle of shampoo and a nearly empty jar of peanut butter and I ask them to guess what that means about me, especially in math class. Someone usually raises their hand and says "You don't like to waste time," but I have gotten some other interesting and creative responses! On the first day of school we practice passing out papers along the rows, a la Harry Wong. We also practice passing papers back in and moving the desks to get into their "pods" for group work. I read a post during the summer which had a photo of how desks are arranged for group work. I thought the configuration was brilliant because students only have to turn the two front desks to face each other and not the back two desks. It also creates a u-shaped group which allows all the students in the group to see the teacher and board easier when instructions are given to the whole class.

I started using math journals in my classes several years ago and with all the great ideas I have gotten from math teacher blogs, the journals have been morphing into interactive notebooks. I am so excited to try foldables this year and other note taking activities. This year I am encouraging my advanced students to take their journals home every day to study and review what we covered in class. In my general classes, I allow the students to leave their journals in the classroom. I laminated some 2-sided signs for math journals, calculators and responders indicating to the students, as they walk in the door, whether they should get these items before they go to their seat. For example, one side says Math Journals Today and the other side says No Math Journals Today. I just flip it over as needed for each class. 

One thing that I have liked about math journals that stay in class is that students always have something to take notes and do practice problems in no matter what their binder looks like. But keeping the journals in the classroom presents other challenges--getting them out and putting them away every day can be time consuming and chaotic. In order to make this classroom procedure efficient, I designate a place in the classroom for each class period so that the journals are easily accessible and available to every student every day. On the left is a picture of the journals for one class period before I labeled them. On the right is a photo of the journals after I labeled them. I write the class period, color-coded, on the left and then write the last name of each student in black sharpie (I covered the names of my students with a piece of paper). This helps each student find their journal quickly and easily as they come into class and it helps me find and relocate any journals that are returned to the wrong pile.

            

I Have Who Has Games for Math

Several years ago when I found these I Have Who Has Cards on Mathwire.com, I definitely wanted to try them in my classes. I have used the multiplication facts, Algebra Variable Expressions and Geometry decks. This is a photo of some cards from the multiplication facts deck from Mathwire.com.

Each student has one or more cards on their desk and the teacher keeps any card to start the game. Begin by reading the clue on the starting card "Who has 3 x 8?" The student with the answer "I have 24" reads the answer and also the new clue below it. The game is over when you have run through all the cards and on the last card a student reads the last clue "Who has 8 x 6" and the teacher, still holding the first card, reads the answer "I have 48."

The students enjoy this game and are very engaged because they really have to listen and concentrate as each card is read, especially the students who have 2 or more cards to keep track of. I like to time the class with a stopwatch to see how fast they can run through a deck of cards and I make it a competition between my classes or try to improve the class time on subsequent days.

Last year I decided to assign a creative end of the year project to the students after I read this post from I Hope This Old Train Breaks Down and several students chose to make their own I Have Who Has deck of cards for their project. I really enjoyed watching these students figure out how to make the cards so they would work out correctly and then choose the information they wanted to put on each card. Their presentation to the class was having the class play the game they made!

Here is a link to some more I Have Who Has Cards on Mathnstuff.com which include: signed numbers, geometry (area & percent), calculus and directions for making your own cards or having students make a set for the class. The book pictured below has 38 games for 5th and 6th grades including: decimals, fractions, percents, data analysis, probability, square roots, exponents, etc., which would all be great review topics for 7th and 8th grade math classes. The book also contains directions for playing the game in different ways. For example the deck Extreme Mental Math has a maze worksheet for each student to complete during the game. "As your classmates identify the answers, draw a line to each number to complete the maze."

Has anyone else used these games in middle school math classes? What decks have worked well for you and what strategies have you used to make it an effective learning activity?

I have created a template for students to use to make their own set of I Have, Who Has? cards. Students really enjoyed making their own cards and then running the game themselves.

My First Foldable!

The students made their first foldable in class on Friday. The students started out class by writing in their notebooks about which classroom activities helped them learn the most. Then we discussed the pyramid of learning and retention. I gave them the list of activities from the pyramid in alphabetical order and asked them to guess which activity was the most effective in terms of learning and then which activity was the least effective. Then I showed them the pyramid with the percentages and we discussed how some classroom activities are more active and some are more passive and that when students are more active, they learn and remember more. Then the supply managers got out the supply bins and we folded, cut, colored and taped the first foldable of the year.

Click here for the template.

Third Time's the Charm!

They say that the third time's the charm and I really believe that if students can successfully complete problems on a new concept three different times, then they are on their way to mastery. The first time is guided practice in class, the second time is independent practice at home and the third time is reviewing the concept the next day during the Do Now or homework review.

I have read many interesting and thoughtful posts on the homework and homework policies. It seems that many math teachers believe that independent practice is important but struggle to find the best system that works well for both students and teachers. I have definitely had that struggle.  I have tried many different strategies--some have worked well and some not so well and some have worked well but have taken up too much class time or too much of my time outside of class. Once again I want to try some new things this year in order to find the best system possible.

Start:
1) Assign fewer problems. I usually assign odd problems from the textbook and remind students frequently to check their answers in the back of the book in order to see if they are on track. I am thinking about assigning fewer problems this year (10-15 instead of 15-25). In fact, I LOVE the idea of assigning just one problem that is very rich. For example, I really like this surface area problem from Accessible Mathematics by Steven Leinwand. "Doctors estimate the amount of skin each person has using the formula S = 0.6h^2 where S is the number of square inches of skin and h is the person's height in inches. Use the formula to determine a reasonable estimate for how much skin you have. Then validate your result using a a referent such as an 8 1/2 x 11 sheet of paper and using surface area formulas. Discuss the reasons for the differences among your three estimates." (pg. 51)
2) More Productive Homework Review. By assigning fewer problems, I hope to make homework review more productive by asking students to show and explain their solutions to the class. I am starting school with a unit on problem solving and after working on one strategy in class, students will be assigned a few problems for homework. Students will also be asked to pick one problem and write out a detailed solution to show and share with the class. Then when we review the problems in class I can quickly ask students to bring solutions up to the ELMO to show the whole class and explain. And then I can ask other students if they have other ways to solve the same problem.
3) "Flipped" Classroom. I would like to experiment with using some ideas from Flipped Classrooms. Of course teachers have been doing a low tech version of a flipped classroom for years by assigning some reading from the textbook before a topic is covered in class. Any student who does this kind of preparation can gain so much more from the classroom presentation/lecture/discussion on a new topic. I want to encourage students to come to class "ready" to learn something new by having some previous exposure to the topic. As part of the homework assignment I plan to give students a link to a video on the topic we will be covering the next day in class. Khan Academy is one resource that I will use for these videos.

Continue:  
1) Daily homework check. Continue to check homework very quickly at the beginning of class by walking around the room and initialing or stamping homework that has been completed. I want this process to take less than a minute or two and so I don't "grade" the assignment at all (I do that later) and just give them a stamp if they have the homework on their desk at the beginning of class.
2) Weekly homework check. Collecting all homework assignments on Friday and entering a weekly homework grade based on effort and completion of the work and following the homework guidelines. When I "grade" homework I look for a proper heading, completion of all problems assigned, effort, marking problems right or wrong, making corrections and showing work.

Stop:
1) Grading every assignment every week. Last year I though to myself, if I still collect all homework assignments, but only look carefully and assign a grade to half of them I could save myself a lot of time and students would still know that I expect homework to be completed and would still get the benefit of independent practice. And since students are fairly consistent about doing or not doing homework, a homework grade based on only half of the assigned work would be an accurate reflection of their effort and homework completion. I plan to randomly decide each week if I am going to check homework and assign a grade or simply give them a check in the gradebook for turning in the assigned work.


I love my new homework board. I got the idea from Math = Love. THANK YOU. I plan to invite students to come up with quotes and math expressions for the calendar for bonus points. I have wanted for a long time to include motivational quotes about life and math and calendar math in my classes and I think I have finally found a way to make that part of the regular classroom routine.

Card Trick

I plan to use this activity in class on the first day. Besides being an interesting challenge, I think it can be used to the show the power and magic of mathematics. It is also a great way to introduce problem solving and different problem solving strategies including draw a picture or diagram, look for a pattern, logical reasoning, work backwards and PERSEVERANCE.
Prepare thirteen playing cards, all the same suit. Then place the cards in a specific order so that when you flip over every other card you will reveal the cards in descending order. More specifically, when you flip over the top card it will be a King, and then the next card is placed at the bottom of the pile still face down.  The next card flipped over is a queen, and then the next card is placed at the bottom of the pile, etc. This process repeats until you have revealed all the cards in order from King to Ace.
When you show this trick it seems deceptively easy and students jump in and think they have it right away. Then the fun begins! When they "run through" the deck the first time, the pattern usually works up to 7, but then breaks down after that because they didn't take into account that some of the cards would come to the top of the deck multiple times. It is exciting to watch students struggle with this problem, try different strategies, get more feedback directly from the cards, and then try again.
I plan to show this trick towards the end of class on the first day and let students try to solve the problem. I am hoping some students will go home and work on it at home and then show how they solved it in class the next day.

                              

I plan to show the students how to solve this problem by drawing a diagram.


____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____

Using this diagram we can fill in the cards that need to be in each position. You simply write in the K, skip a line, Q, skip a line, etc. Then when you reach the end, start over and continue to skip a blank line each time.

This is a great activity for math class, but I think it could also be used effectively in other classes or advisory groups.

Math Anxiety

There are two books I read this summer that were very interesting and helped me form a set of goals for the coming school year:  Learning to Love Math:  Teaching Strategies That Change Student Attitudes and Get Results by Judy Willis and Accessible Mathematics:  10 Instructional Shifts That Raise Student Achievement by Steven Leinwand

        
In the first book the author discusses the importance of reversing negative attitudes about math as a critical step toward learning. "If your students are anxious during math class, information entering their brains is less likely to reach the conscious thinking and long-term memory parts of the prefrontal cortex, and learning will not take place. . . . Under stressful conditions, emotion is dominant over cognition, and the rational-thinking PFC has limited influence on behavior, focus, memory, and problem solving" (pg. 10). The book gives lots of suggestions for helping students overcome math anxiety and learn to love math. One of my goals this year is to give special attention and focus to any student who has struggled with math in the past and exhibits math anxiety when they come to math class. For example, one thing that has bothered me in the past is returning tests and quizzes to students with low scores with a big ugly stamp on the front requesting a parent signature. It feels like adding insult to injury when the student hurriedly turns the test over on their desk or hides it in their binder.
                                                   
                                                        

This year I want to do things differently.  If I feel like I need to make the parent aware of the test or quiz score, I am going to send an e-mail. (Note: all grades are available to view by students and parents on our school grading software.) But more importantly I am going to request a short individual conference with the student to discuss the grade and together form a plan for improvement. Hopefully these individual conversations will help me understand whatever is preventing the student from mastering the material and will help me make adjustments throughout the year.

I like all the ideas in the second book. I am going to try to do all 10 of the instructional shifts mentioned in the book. Here is a copy of the list from the front cover of the book:

1) Incorporate ongoing cumulative review into every day's lesson
2) Adapt what we know works in our reading programs and apply it to mathematics instruction (focus on explanations and don't stop with one word or numerical answers to problems).
3) Use multiple representations of mathematical entities.
4) Create language-rich classroom routines.
5) Take every available opportunity to support the development of number sense.
6) Build from graphs, charts, and tables.
7) Tie the math to such questions as: "How big?" "How much?" "How far?" to increase the natural use of measurment throught the curriculum.
8) Minimize what is no longer important.

9) Embed the mathematics in realistic problems and real-world contexts.
10) Make "Why?" "How do you know?" "Can you explain?" classroom mantras.

One idea I have for working on these instructional shifts is to make a poster for each unit covered in class. These posters will include vocabulary and key concepts and will highlight the most important information covered in class and included in the interactive student notebooks. I have some wall space around the room that is very high and difficult to reach. I am planning to bring a small ladder to school so that after we finish each unit I can hang the posters so that they form a border at the top of the wall around the room. Hopefully these posters will be a continual reminder of what we have covered so far and how much they have learned!

Active vs. Passive Learning

I read The Teaching Gap several years ago and was very intrigued by the differences between typical instruction in U. S. and Japan classrooms. I was especially interested in the different approaches taken to problem solving. In Japan "the teacher presents a problem to the students without first demonstrating how to solve the problem." Whereas in the U. S. "the teacher almost always demonstrates a procedure for solving problems before assigning them to students" (pg. 77).

I have tried from time to time to give my students a "challenge" and then, using the work produced by students working on their own or in small groups, teach the lesson. I have found some success with this approach, but I have also noticed some deep-seated resistance to this method among my students. That resistance has taken the form of giving up, wasting time, complaining and most worrisome believing that they will learn more effectively if I just explain to them how to do it.

When I was reading the book I frequently thought, I wonder what a classroom that follows these teaching methods looks like? How does it start? How long do students spend working on a problem? What do student explanations look like? How do the students work in small groups? How does it end? etc. I was really interested when I saw a blogpost recently about the TIMSS video study and included some short clips and some analysis. (I don't recall the author of the post, and would appreciate it if anyone can provide the link.) When I was searching for the post later I discovered that 53 of the TIMSS public use videos have been translated and are available on TIMSSvideo.com.

I watched two different videos on the same topic and compared the different approaches taken by the teachers. My plan during the first week of school is to show some very short clips from both videos to my students and ask them to compare the two different teaching methods.

From the Japanese lesson on finding missing angle measurements I want to show:
00:00 - 00:15 Opening bell and bowing
4:45 - 5:30 Student explains the first method of three presented on how to solve review problem
10:15 - 12:00 Teacher explains the new task to students:  write a new problem with certain conditions
23:30 - 24:00 Students get into groups to compare problems and choose one for class to solve
32:00 - 33:00 Teacher takes one problem from each group to copy on the board for all students to solve.
51:00 - 51:25 Teacher ends class

From the U. S. lesson on finding missing angle measurements I want to show:
00:00 - 1:15 Opening and review
15:00-17:00 New set of problems is presented
21:10-22:00 Teacher works with individual student
27:30 - 30:00 Teacher ends independent work and discusses problems with class
30:30 - 31:30 Teacher reviews integer rules
44:45 Teacher ends class
48:00 Teacher dismisses class

After watching the videos and discussing the differences, I would like to do an experiment with my students. I will divide them into three groups. One group will turn around and face the back wall and only be able to hear. One group will be able to hear and see and the third group will hear, see and copy what is given. I will read (and show) 20 mathematical terms. After a short break (I will do something completely different here), I will ask students to write down how many words they can remember from the list that was given. We will compare the number of words that students can remember from the three different groups. It will be interesting to see if the percentage of words remembered is close to the percentages shown in the Learning Pyramid shown below. Note: I know there has been some doubt about the accuracy of the percentages in the pyramid and whether they are supported by actual research. This model was presented and used as the foundation of a education graduate course I took called Curriculum and Practice in School Environments. I am concerned about using inaccurate information, but I think research strongly supports the idea that active teaching methods are more effective than passive teaching methods and I think this graphic conveys that concept very well. I plan to have the students fill out a blank graphic of the pyramid of learning and retention for their interactive notebooks.



                                             


                        



                       

I am hoping that by showing these videos and talking about the differences between passive and active learning that my students will understand why I might ask them to struggle with a problem before I simply show them how to solve it. I want them to know that struggling with a challenging problem is not bad, in fact it is probably the most effective way to learn new material and develop problem solving skills. I am hoping that by explaining the value of this teaching method at the beginning of the year that my students will buy into the idea and that my attempts to use this method will be more successful.

Who wants to be a Millionaire?

I am starting my 5th year of teaching this fall. Last year I wanted to focus on student motivation and so I made a bulletin board with this title "Who wants to be a Millionaire?" and I decorated it with play money from various board games from home. On the second day of school I played the music to the game show "Who Want to be a Millionaire?" as the students walked in the room. Then I showed the students some data of average lifetime earnings at different levels of educational attainment. I found the data from a report published by The Georgetown University Center on Education and the Workforce. A bar chart in the report shows that the median lifetime earnings of a student with no high school diploma is $973,000 and $2,268,000 for a student who earns a bachelor's degree. After discussing the information in the chart, I asked the students what is the total value of their education. After determining that a college degree is worth more than a million dollars ($1,295,000), I wanted to break this down into something that would make sense to middle school students so I guided them through a series of calculations to determine the value of their education per year, per day, per hour and per class period.  We used these facts in our calculations: 12 years of education from secondary school (including 5th grade) to college education, 180 school days, 6 hours of school each day (excluding lunch) and 8 class periods per day. The results were truly astounding. Students found that if they graduate from college on average their education will be worth $107,917 per year, $600 per day, $100 per hour and $75 per class period.

Last year I used the $100 per hour theme throughout the year by giving out $100 bill pencils for prizes for student of the month and for other student achievements and exceptional effort. And I often reminded the students that by giving their best effort in class they are earning $100 per hour in future earnings. This year I plan to extend that by putting $100 bill stickers in students' notebooks and writing them notes recognizing their efforts in class.

Important Note: As an economics major in college I learned about opportunity costs and that is definitely what I tried to focus on during this discussion of money and earnings. I tried to emphasize to the students that money has value in the sense that it represents opportunities.