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.