Start with the basics

We gave our Study Tech students an online assessment that was targeted to material taught in the 6th-8th grades, and many of them did poorly on the test.  These are students who got a 1 on the MSP test at the end of 6th grade.  Because we want to clearly define where they are now in order to show improvement later, we also gave these students the online assessment for grades K-5.  Several of our students scored at the 3rd or 4th grade level in certain subjects, particularly working with fractions and finding equivalent fractions.  This topic is going to come up again in later math, so we really want to make sure they understand this basic idea.  Our realization that we need to go back to concepts they should have learned in 3rd grade opened our eyes to the level of basic math skills these kids are missing.

What is your math identity?

Last Tuesday's methods class touched on the concept of math identities: what is your relationship to math?  How do you see yourself - good at math or not? Does the idea of solving math problems bring you peace or anxiety?  The article we read really got me thinking about our Study Tech kids, students who struggle at math and have been labeled as "not meeting standard."  Every day, I aim to make math relevant for these students because they clearly believe that math is not important to their future. If we can show them how math is relevant, then I think they may be more self-motivated about their learning.  In particular, there is one student who I'm tutoring who is bored or sleepy during every class. He can do the work, but has trouble getting started.  We gave students a sudoku puzzle to do after finishing a quiz because they needed to stay quiet as the other students worked on their quiz.  I was surprised and delighted when I handed my tutored student a sudoku, and he said "Oh, I love these. I have a book of them at home."  Now I have a hook to work with! I want to give these students a chance to see themselves at mathematicians, so they will have more self-confidence to tackle math problems.

Optimal planning

Now on the fourth iteration of my plan for this Friday's observation, I keep coming back to what I'm going to present and what the students are going to do, how they are going to learn, what do I scaffold and what do I leave for them to struggle with.  At first, I had the straightforward, direct-instruction lesson with times for students to work out the problem and I would randomly choose students to answer.  Then I added an entire scaffold on the relationship of a container's volume to height, including borrowing a graduated cylinder from science and comparing data points from the cylinder with a two-cup measure. There's a problem in the book that asks students to match a container shape with a graph, and I saw this as a great mini-lesson in spatial reasoning, which I know from the research may come more easily to boys than girls.  Then I added think-pair-share to the questions, which would give the students an opportunity to interact and get some informal feedback from each other.  And I copied some worksheets which students could do in class and then hand in, allowing me to provide (non-graded) feedback to them for the following Tuesday.

Then I talked it over with my CT and realized that our main focus on Friday is to review for Monday's test, and I need to cut back my plan to keep the new material to 20 minutes or less.  Back to the drawing board!  The worksheet will be used for after the test on Monday, I'll pull some relevant questions from the book for Friday, I'll rewrite the plan and run it past my CT again tomorrow....  Where's another hour of sleep for tonight?

Scaffolding vs. telling

As I'm working with W on adding and subtracting integers, I feel good because I like helping. I try to ask questions to help her understand her strategy, and not give her the answers.  For instance: "How do you subtract a negative?"  I realized yesterday that I have probably helped her too much because as I went around the room checking students' understanding on a review worksheet, she grabbed my wrist and "no, you can't leave me."  Oops! 

I have told the students during instruction that they need to find the best learning tool for them and work with that.  We have shown them several different analogies for working with positive and negative numbers, and given them time to practice with black & red chips, hot & cold cubes, black & red cards, gaining and losing yards in a football game, but it still seems that students will see an equation and jump to an answer without thinking about what it means.  I don't want to tell them the answer, but I'm confused on how to scaffold the learning process.  After we taught a lesson that a negative times a negative equals a positive, I asked them to solve -3 + -8 (with emphasis on the +) and had several students enthusiastically respond +11!

Switching gears

Today I began a lesson in our algebra class on solving absolute value inequalities with a straightforward visualization: a skateboarder going a constant 20 ft/s (really? who makes these numbers up?) is coming towards a bystander who is 100 ft away.  When will the skateboarder be 60 ft away from the bystander (who is not moving)?  The class came up with the concept that there are TWO times the skateboarder is 60 ft away, one on each side.  I compared the bystander to Zero on the number line and explained that the absolute value of a number is how far it is from zero.  I wrote absolute value on the board with a definition, and proceeded to show an equation (absolute value of x = 5).  Several students stopped me to say "what is absolute value?"  It totally threw me for a loop because in my mind, I was already headed towards the inequality part of the lesson, and here the students were telling me they didn't know what absolute value was.  I spent much longer than I intended on the basics (since if they don't get those, the rest is useless), and we didn't even START the group quiz that was going to take the last 45 minutes.  Argh!  We plan carefully, but not carefully enough.  It makes me wonder what are they teaching in elementary school?

A day of tricks

It can be hard to capture the attention of kids the day after Halloween with the world of math. We had wild kids in all of our classes today, and our intentions for math-centered instruction was diverted by discipline issues at times.  Also, I was preparing for my observation on Wednesday, so I spent the planning period incorporating my teacher's feedback.  However, as I went to save the file, I saw an erroneous message that my hard disk was full.  I spent my lunch trying various methods to save the file so that I could send a copy to my clinical faculty.  I was not able to save the file, so I printed a copy, restarted the computer, and spent an hour this evening redoing my revisions.  In addition, I tried to print a color copy at school today, only to discover that the color printer was not working (although it looked fine in the print queue).  All this drama drove home the fact that it's important to plan ahead of time!

Teaching to the plan

I've had the opportunity to teach several classes now.  Frequently, my cooperating teacher will share what she had in mind for the class period and ask me if I'd like to teach.  I enjoy working with students and sharing analogies that I think will help them, so I usually jump at the chance to teach.  The problem is, what she has in mind does not usually get completely transferred to my brain before I start to teach the class.  With algebra, the textbook is more traditional and I'm comfortable with all of the ideas and the overall learning target for each day.  However, with CMP2, I feel that the text does not adequately cover the main ideas and we need to supplement with additional information.  Twice, I have taught the CMP2 class and discovered that I skipped an activity that my cooperating teacher had in mind, but was not clear to me.  I'm learning first-hand that it's important to thoroughly plan beforehand!