Take a simple math textbook word problem and ALGEBRAFY it. (I love that new word!) A presenter at the NCTM algebra readiness conference used it. She showed us how to take a simple math word problem and provide other numbers as well as the one in the problem for students to solve the problem multiple times. Then students are able to make a generalization about the problem. For example:
Bill’s Airbrushed T-shirts is giving customers a 20% discount on all T-shirts. Find the discount on a T-shirt that had an original price of $12.
In addition to the textbook version, allow students to find the pattern when finding a discount on other prices of shirts.
Find the discount of a shirt that was originally priced at $13, $14, $15, $20, $50
If students write these in an organized way or use a table to calculate these amounts, they would easily see a pattern.
$12 x .20 = $2.40
$13 x .20 = $2.60
$14 x .20 = $2.80
$15 x .20 = $3.00
$20 x .20 =$4.00
$50 x .20 = $10.00
Math is all about finding patterns. Students can easily see several patterns above. Some will see the obvious pattern in the first few equations in which each product gains 20 cents. Students will also hopefully see the pattern of doubling the first factor and counting over two places to write the decimal. Then students can begin generalizing about multiplying any number by 20 percent. When students are able to generalize then the learning becomes their own personal discovery. Learning becomes fun again!
I am currently at a regional NCTM math conference on algebra readiness. I am going to share one of the things I learned at the conference. Use conjectures while teaching math to make the task deeper. For example, when teaching the commutative property, have students find at least three pairs of equations with factors that have switched places and allow students to draw a conclusion.
3×4 = 12
Ask students what they notice about the factors that have switched places. Hopefully, students will say that the products are the same when the factors have switched places. Ask students if this is always true. Allow students to experiment with their conjecture by using other examples. Ask other students if they can prove this wrong. When all minds are settled on the conjecture and agree, then reveal the name of their conjecture as the commutative property. Teaching with this method of discussing conjectures allows students to take ownership of their learning and be involved in the process of discovering mathematical concepts. Less reteaching will occur and your teaching will be closely aligned with Common Core Standards.
As I mentioned before, specific procedures are critical to a successful classroom. Each time of the day has different procedures, for example, math workshop time. Do students know what to do when they gather on the carpet, what to do with manipulatives, how to work in cooperative groups, how to speak during their work time, and what to do when they need help? If students are given norms in these areas, then the teacher’s time is maximized for instructional purposes instead of behavior management. Below is another photo from the classroom I visited for a lesson study. I like how this teacher’s expectations are clear for carpet time in this poster.
Here is my door for this year. I just finished it! It took a lot of work, but it turned out so cute. I took the idea from Greg Tang’s book The Grapes of Math. I recycled the grapes from another project in the past to use on my door. The grapes were made from purple and green construction paper circles that I glued together. I then punched a hole through the top with a hole puncher and put some green pipe cleaners through the top. To make the vine tendrils curly, I wrapped the pipe cleaners around a pencil. I recreated the grape vine with twisted brown bulletin board paper. The grapes were made from purple and green construction paper circles that I glued together. To stimulate math thinking, I added a copy of Greg Tang’s poem so that students will be encouraged to count the number of grapes that are displayed.
At this point in the year, most of us are acquiring sore muscles from moving furniture around and deciding how to arrange our desks. While moving your furniture, have you considered your traffic flow? Can you easily see each student’s desk when you walk in a complete loop around your room ? Arranging the room in a loop allows you to walk around the entire room easily enjoying proximity to monitor students work and off task behavior. If students are seated without the teacher being able to easily circle the room, often times some are left out when materials or papers are passed out because of the disjointed traffic Where is your door located? the pencil sharpener? book bag storage? paper trays? All of these factors determine how many possible distractions there are in the classroom. Fred Jones’ book Tools for Teaching has two chapters entitled Working the Crowd and Arranging the Room. These are excellent chapters which have taught me to be aware of the above factors to room arranging. Most schools have a copy of Fred Jones’ book in their professional library. There are a few pictures of his seating arrangements from the book online that may be of help if you don’t have access to his book.
Because rubrics are such a large part of our state testing, I decided to include a rubric with my behavior management card system. On our state testing a 4 is Advanced, 3 is Proficient, 2 is Basic, 1 is Below Basic, and 0 is an irrelevant response. To emulate the state testing rubric I made each card on my behavior system equal to a 4, 3, 2, 1, or 0. Students receive a score at the end of the week out of a total point value of 20. Students are allotted 4 points a day which equals 2o points for a 5 day week. If students get at least 18 out of 20 points, they receive a special treat on Friday. On Friday, I communicate students total score on a parent communication page attached to students’ weekly graded work. See the chart system in picture form below.
I came across an article by Ross Miller of Association of American Colleges and Universities yesterday, and it reminded me of how important it is to have high expectations for children. In this article it states that students may have equal abilities, but the student who is expected to achieve more will perform more highly. Teachers tend to attribute poor performance from a higher achieving student to bad luck while a low achieving student’s poor performance will be attributed to lack of ability. Americans tend to link ability and performance with little thought of student effort. Teachers in the U.S. tend to see low ability as something that is immutable. Contrastingly, Japanese and Chinese teachers attribute students’ learning more to the teaching received and to students’ effort. Since China and Japan tend to dominate the world in achievement, we could definitely learn from their high expectations of ALL students’ success.
I have always been a big fan of Greater Expectations–a way of instilling high expectations in your classroom with positive statements, cheers, proverbs, and songs etc. From this workshop about ten years ago I got the following words for the posters shown below. Every year I place these poems outside my door so that students can see them when they enter. I make reference to the posters often to let students know how bright they are and that I believe in their ability to succeed.