Choose your TAs wisely

In one class that I've observed, the female student TA positioned herself near a couple of boys and spent the entire period chatting with them.  I would tell them to be quiet during the teacher's direct instruction (which took most of the period), but they rarely stopped talking for more than a minute.  (Perhaps the fact that I'm only here for a short time meant that I had no authority in her eyes.)  The TA informed me that she was in Running Start, so she goes to college in the morning before she comes to the high school, and then she works 20 hours/week after school.  It surprised me that someone with that much motivation would purposely disrupt the class.  I guess I saw it as disruptive, but maybe the TA didn't.  I don't know if teachers can choose their TAs, but if you can, make sure it's someone who will add to the class environment, rather than detract.

Good tip for continuity from year to year

One teacher I observed today has students summarize their notes for a chapter test in a specific notebook.  The teacher provides composition books for each student (with their name labeled on the spine), and the notebooks usually stay at school, but students are allowed to take them home on the night before a test. The students can take one to two pages of notes to summarize the main ideas from the chapter, as well as diagrams or formulas.  Tomorrow, the students can use the notebook during the last 10-15 minutes of the test.  At the end of the school year, the students have a notebook that contains all the major ideas from the course, and they can take that with them for the following year of math, building continuity of math learning.  Have you ever forgotten the unit circle values for sine and cosine?  Flip back to chapter 2 of pre-calc, and you'll have all the important points right there.  The other advantage of the notebook is the process of making the summary is a great tool for studying.

A warning in high school

I helped out in a math class for seniors who need to pass this class to graduate.  It's called EMP, short for Evidence of Math Proficiency (I think).  It used to be that the students would learn all year, and then try to pass a single test at the end of the year, but there wasn't a great success rate for that.  Last year, they tried putting together a math portfolio with work throughout the year, and they had a 94% success rate.  Unfortunately, the state decided it cost too much to evaluate the portfolios, so now the students have tests throughout the year, but the test directly follows the teaching of the material.  Yesterday's lesson was on scientific notation and Mrs. G led the students through the methodology of converting numbers into and out of scientific notation.  I was helping some of the students during the working time, just verifying they understood the concepts. 

After class, I asked Mrs. G if I could come back later in the day to help with her 2nd EMP class.  She said "yes, but don't look at the work or offer help to the students in these 2 left rows, as they may become violent; just work with students on the right side of the class."  I hadn't thought offering help could provoke such a strong reaction - now I know to be careful!

Observations on Learning

The students I have been observing are in our regular 7th grade math class, as well as an extra math class for students who have not met standard in 6th grade (called Study Tech). I can tell W. is learning when she voluntarily answers questions, provides an alternative solution, explains a strategy to a friend, holds up her hand to show she understands a concept, and writes review notes in her notebook, color-coded to show different ideas.  I saw her having difficulty learning when she was turning around to chat with friends, when she showed an inability to focus on math, and when she came back to a previously-worked problem and couldn’t explain her steps.  I observed D. sharing a factor tree on the board, and working through a fraction multiplication problem.  He was not learning when he put his head down on the table, did not bring in his homework, was joking with friends, and when he could not complete the quiz.  Much of the difficulty for this student seems to be his disorganization.  He comes to class with a binder full of papers, which are not organized by subject or have a discernible order.

In the Study Tech class, I watched the students during an activity where each pair of two students had rods made from blocks to help understand fractions: some rods were color-coded to show halves, some thirds, some quarters, etc.  Each pair of students held up their rod when we asked for specific fractions.  This activity was designed to help students understand common denominators.  I watched as they tried to add one third and one quarter with the blocks, and the students responded with blank looks.  After a few attempts to add different fractions, we had the students put the blocks away because they didn’t seem to be helping, just confusing the students.  This was an example of a hands-on, interactive activity that I expected would be helpful for students uncomfortable with fractions, but in reality, the students seemed confused by the blocks.

On another day, the teacher was discussing how to divide fractions, which should be a review topic for the seventh graders.  I expected the most difficult part for the students to be remembering that dividing is the same as multiplying the reciprocal.  However, during the work session after the instruction, I checked in with several students and the main misunderstanding came from converting a mixed number to an improper fraction.  The parts that I believe are going to be hard may not match what the students believe is hard.

All of the teachers that I have observed genuinely care for their students, and this seems the most important characteristic for a teacher to have.

Different methods helps learning

I like that my middle school uses block periods for four days each week because I know several districts who are transitioning to block periods; however, it can be a challenge to motivate students for 105 minutes of math.  My cooperating teacher is experienced with block period scheduling, and she uses many different techniques throughout the period.  There are times when students work quietly on their own, completing a worksheet or problems from the book.  At other times, the students have white boards to show their answer to a problem at the front, and student are allowed to work with partners.  One student who was reluctant to fill in a worksheet became very motivated when we switched to an online game, even though the math task (rounding decimals) was the same.

Another technique that has helped us assess whether the students understood place value or estimating fractions has been to hand out notecards with different numbers on them, one to each student.  Then the students self-order themselves into a line, based on their understanding of whether 15/7 is greater or less than the square root of 3 in the case of the algebra students.  This gives the students a chance to get out of their seats and work with their classmates to determine relative values.

The students have also come to the board to demonstrate their factor trees, which allows students to see each other as teachers. The teacher usually asks the class if there are any other ways to find the solution, so students can see several methods all create the correct answer.

Starting school with *students*

I started student teaching last week; it's exciting to have students in the classroom after all the training we've been doing with other staff.  Due to all the interventions that my middle school puts in place, we've been mainly focused on procedural stuff in the beginning and we haven't been able to do math yet.  We did a group ball toss activity to learn names: the students enjoyed it, and it helped me remember most of the students' names on the second day. 

In the seventh grade classes, we had groups of 4 students work on a puzzle that spelled TEAM.  It was not obvious that the puzzle pieces spelled a word, so several groups tried to fit all the pieces into one shape.  Only one group out of each class got the word spelled out in the 10 minutes that we gave them to work on it.  We used this opportunity to discuss what works well to solve problems as a group: everyone helping, trying different strategies, drawing in each person in the group.  My teacher gave the students guidelines about how to work in a group, and showed a powerpoint that detailed conversation tips for groupwork.  One ground rule that she stipulated that I would not have automatically thought of was that every person in the group needs to agree on their question before they ask the teacher for guidance. This encourages the students to talk among themselves before turning to outside sources for assistance.  I noticed a couple of groups that did not include everyone, but the majority of students seem to have experience working within groups and shared the process.

Cool math ideas

I had the privilege of attending a training for high school math teachers last week, led by Kristine Lindeblad. She's terrific; if you get the chance to participate in a training by her, by all means, go for it!

She started by giving us a survey, which we filled out, crumpled into balls and threw around the room to insure anonymity. Then we created human bar graphs to show the results, and whoever had the largest shoe size, most number of siblings, born the furthest away got to report out. We then created two different graphs to show two of the questions, and put TAILS on each of them (Title, Axes, Increments, Labels, Scales). Kristine staged which graphs were shown to the class, and asked us to provide an affirmation and a probing question for each graph. I liked that the exercise built community, gave us an idea of what areas were most important for these teachers, and modeled affirmations and questions, which is a great way to give positive feedback.

We did several other activities throughout the day, and at each step, Kristine kept the focus on our learning, modeling what a student-centered classroom looks like. She asked good questions, but always kept the atmosphere positive and encouraging. She had us read parts of Never Say Anything a Kid Can Say! by Stephen Rinehart, which is a great reminder for me: I need to ask more than I explain. One tip that I will take to heart is "Don't carry a pencil" because then you can't write out the solution for the student; he or she needs to do the writing (and learning!) themselves.  I can't wait to try some of these ideas with the students.