Substitutes

I know that substitutes are necessary to keep the schools running, but what I don't understand is the lax requirements.  Case in point: our sub today wasn't sure how to evaluate -8 - (-4) because she hadn't done subtracting a negative number lately.  While I understand that is not something one does every day, she is a fully certified teacher for K-8, and she subs in preschool through high school.  How do we expect our 7th graders to learn the basics in math if their teachers aren't comfortable with the basics in math?  If I become a high school math teacher, I'm going to find a sub that I can trust - or else have a foolproof plan for when I get sick.  Egads.

Two-way communication

Today I saw another great stride for D.  Last week, after meeting with him and his mother, I had seen an improvement in work ethic.  When we assigned 3 figures to graph (testing for similarity), he chose to graph all 5 figures, which must have taken a bit of extra time because the coordinates needed to be calculated for each figure.  Today when we taught mental tricks to calculate 1%, 2%, 5%, 10%, 25%, and 50% of a number, I handed out a worksheet for the students to do.  Unfortunately, their skills were not as developed as I thought, and the problems were taking more time than I had planned for the students to complete.  I changed the requirement to finishing 3 multi-step problems, and then students could transition to Math Whizz, an online math program. D gave me his worksheet, and then asked if he could have it back to work on the additional problems.  He said "I want to do more of these."  This from someone who doesn't view himself as able to do math. I can't wait to email his mom and tell her what a terrific attitude her son has!

What's in your hip pocket?

Today I showed up at school and found out that my cooperating teacher was staying home sick and a substitute was taking her place.  Since I was more familiar with the material, I taught the classes today and the substitute helped with grading quizzes, etc.  My cooperating teacher had written the outline for today's classes on the board yesterday, and we had gone over the plans together yesterday, so I felt prepared for the classes.  Except for one detail: our 4th period class was supposed to start with a puzzle, and I didn't know what that puzzle was.  I searched her notebook where she keeps papers, looked through the folders on her table where she organizes the papers for the day, and still no puzzle appeared.  After searching for many minutes, I emailed her and asked where I could find the puzzle, and she responded by saying she didn't have anything specific, but planned to come up with something.  Oh, I can do that!  We did 2 quick puzzles out of Michael Serra's Mathercise, one on directions (N,S,E,W) and one on reading a sentence correctly.  I thought they would be too easy, but several students struggled with the ideas.  I think we need to do more of them!

Change in performance

I was thrilled today when D brought in his homework, and he had done above and beyond what we had asked of the class.  There were 5 figures to graph to evaluate for similarity, and we had divided the class into two groups: one group did the baseline and two distortions, the other group did the baseline and two different distortions.  Within each group, they should have found 2 similar figures and one impostor.  Most of the class had excuses about why they hadn't done it, and we ended up giving them class time this morning to finish their homework.  Imagine my surprise when D shows us all 5 figures completed.  I publicly acknowledged his hard work and my CT actually gave out candy for students who did the homework at home.  I hope this signals a new work ethic.  Perhaps last week's conference with D and his mom made a difference.  His attitude certainly made my day!

Two ideas that struck me

From chapter 9 in our methods book, I found two ideas that really struck me as worthwhile.  One pertaining to gender equity said that, in general, girls are less comfortable with calculators and technology than boys.  I remember during my freshman year of college when I started my engineering classes that all of the boys were eager to program on computers and I had no experience with any programming.  Not only did I feel intimidated by the boys already having the knowledge, but I felt that somehow I had missed something in high school that I was supposed to learn, and it made me reluctant to ask for help.  So this tidbit of information really struck home with me.  Today during a practice session with linear functions, I encouraged the students to use our graphing calculators.  Two girls chose to use them, so I felt like I made a step in the right direction.

The other idea I liked was to find mathematical problems from different cultures to share with my students. With our diverse student population ranging from Vietnamese to Ukrainian to Gabonese, I'm eager to search for useful math ideas that will shed light on their various cultures.  I think it will be healthy for all students to see the ways math is used in different situations.

Catching up is hard to do

Students who have realized that the end of the trimester is only a few days away are now bringing in missed assignments they think will bring their grade up.  However, our standards-based grading only counts tests and quizzes for grades, so showing us their homework doesn't affect their grades.  Other students are asking to retake tests, so we have set up times before and after school, as well as during lunch tutorial, for students to come and take a different version of their unit test.  It seems odd to me that students who go to the trouble of taking another test have not made an effort to study the questions they missed on the first test. In some cases, the students miss questions that are very similar to ones they got right the first time.  Or they'll get the same questions wrong that they missed the first time (not every question is different).  I wonder if it's due to parental motivation that the students are retaking tests; it hasn't brought up anyone's grade so far.  We had one student planning to retake the test tomorrow, but now school is cancelled due to snow.  There's always next trimester!

It doesn’t count if it doesn’t stick

I saw this comment today when we had snow predicted (and school got out two hours early), but when I first read it, I thought about how appropriate it is for teaching.  In teaching to the students, it doesn’t count as valid teaching if the concepts don’t stick with our students.  We are working on how to make similar figures in 7th grade math, and I’m stressing that similar figures need to have the same scale factor for each dimension.  I keep asking “what number do you need to multiply by to go from the old figure to the new figure?” and defining this as the scale factor.  We did multiple examples with both rectangles and triangles, and demonstrated the scale factor is bigger than 1 when we are going from a small shape to a large shape, and the reciprocal going from the big shape to the smaller.  At the end of the class, I gave the students an exit ticket with two sets of triangles: one set was similar shapes because each side was multiplied by 2 to get the other side, and the other set had triangles whose dimensions were changed by an addition of 1 to each side.  Five students out of 24 got it wrong, so at least the majority were following along.  But for those five, why did they think those triangles were similar?  The right idea didn’t stick.

Low point

So I'm gone from home more than 12 hours straight due to teaching school and going to school, I haven't seen my husband today since he was gone at a meeting by the time I got home, I've had an hour-long fight with my son about one thing after another, there's two loads of laundry to fold and I'm wondering for the umpteenth time: what did I get myself into?  I have a lesson plan to write for tomorrow, another one I need to change based on what happened today, a unit plan to write for methods and I'm beat.  Why did I want to do this?  This is too much!  I hope the sun shines tomorrow because I need it!

Finding mistakes in my teaching

My cooperating teacher and I have been co-planning our classes together, and I take her plans and flesh them out into more formal plans for methods class. However, I'm only doing that for the Algebra and CMP2 classes, not for our Study Tech class.  So when I started teaching Study Tech today, I realized that I didn't have a detailed feeling of where our class needed to go.  Frequently, we are previewing or reviewing concepts these students will see in their CMP2 class.  We were working on equivalent fractions today, something all of the students struggle with to some degree.  I reviewed the worksheet that they had for homework by asking students how they solved the problems, and then we gave the students another worksheet to practice with positive and negative numbers.  After 5 minutes of working with the students, I saw they needed more scaffolding, so I asked them to write down each time the fraction they multiplied by to get the equivalent fraction (ie, 5/5, 3/3, 8/8, etc.) Most students kept working on the problems, but in going around to assess their progress, none of them were writing down the intermediate step.  I didn't make that step mandatory, so they weren't doing it, even though it would have helped most students understand the process. I wish I could go back and reteach this lesson, making sure that students write down the ratio they are using to find their answer.  Next time, I'll know!

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!