Math Talk Moves

 So, today is TAKS Tuesday in our Math class.  This means that the students attempt to solve one TAKS word problem on their own as a sort of warm-up for the class.  You can see the problem projected on the overhead below.  Today the class is solving a problem that involves the skills they've learned in the latest unit: place value.  I've taken pictures of many of the students' solutions; most of which involve lining up the 4 answer choices to determine their size, and subsequently determining which number resides between the two numbers stated in the problem (5,800,000,000 and 5,700,000,000).  

In the end you can see the teacher discussing the problem on the doc cam, and the students volunteering to explain their methods for solving the problem.  I heard some "Yes, but..." statements, and a few "Yes, and..." statements when the teacher heard some of her preferred methods for solving the problem.  One thing I appreciated was her comment towards one of the students with adapted materials.  She praised the student for using the place value chart they have in their adapted materials folder (see last week's post) to line up the possible answers and determine which was correct.  She did not mention the obvious - the fact that certain students are provided these charts at all times - but she pumped him up for being clever enough to use
the idea of a place value chart as a strategy.  I thought this was a
sweet way of  putting the spotlight on this student's
cleverness, and disguising what makes them different from others in the classroom.  I also heard the teacher asking students to use the revoicing strategy, and the restating someone else's strategy.  The latter was used primarily to call out students who were off-task and not listening.  Though, occasionally she asked a student who is struggling to repeat their neighbor's strategy, in the hopes of them picking up some new tips.  In the cases where it was a behavior management tool, I still see it as beneficial for those who are paying attention to hear it explained again, by someone else and in different words. 

If I was to do anything different, I think I would have used more "Yes, and..." statements to encourage those who are not used to talking through their thought processes.  Many of the same students offer their strategies each time there is a discussion, leaving little opportunity for those shy or struggling students to explain their though process (even to themselves).  Before I got into the habit of telling others "why" I chose a certain strategy or "how" I solved a problem, my answer would have been something like, "Just cuz...it's what you told me to do."  Blooms taxonomy explains that the highest level of thinking involves teaching; I find that includes even teaching

yourself.  I also believe that by asking them to apply their reasoning to others' reasoning, their are further activating their higher thinking.  It's very difficult to compare and contrast your thinking to another person's.  You have to truly understand their logic once you truly understand your own.  And that's a tall order!

Stepping Into Teaching

So, here's (1st picture) one of my students working on a place value game in their General Education Math class.  The game involves taking turns rolling a 9-sided die to fill up a certain amount of place value blanks.  First, the group of students (4 kids at their desks which are already grouped together) decides how many place value blanks they want to work towards. Example: this group here decided they wanted to work towards the hundredths place since they had to include a decimal in their game for today.  They take turns rolling the die, and place the number they rolled into one of the blanks; it's their choice where to place it.

Here (2nd picture), my student placed an 8 in the ones place.  As the teachers and I walk around we ask the students to identify the place values of the numbers they've rolled.  This is an excellent way to informally assess students' understanding of place value.  It's also a prime opportunity for students to teach each other and/or model their strategies.

Afterward (3rd picture), the students line up in order from least to greatest, or vice-versa.  Here the teacher has partnered with two struggling students as they play.  She later left them with the group at the next table once she felt they had a sufficient understanding of the concept.  This group then had 6 students in it which made for a challenging team collaboration, but also a very rewarding challenge for the group in the end. 

Here's (4th picture) the first group's finished work.  Afterward, they expanded their problem to the thousands place (before the decimal) and the thousandths place( after the decimal).  It also became a contest as to who could write the largest number; the nine on the 9-sided die became a coveted roll.  Note to class, this was not a teacher-planned competition.  It appears that the "greatest" amount meant more than place value to my students!

Finally (5th picture), once the game had ended the students returned to their seats to correct their quizzes for partial credit.  They're allowed to use their books to help solve the problems, and they work alone or with a teacher.  One decision I greatly appreciate is my teacher's choice to give full credit on homework if the students correct their work (with a red pen) while they go over it the day it's due.  As long as the student tried and is willing to learn from their mistakes, she says there's no reason not to give them a 100%.  If they didn't even attempt it, they have to make it up at a later time without full credit.

Shown here and below (6th picture until last picture) are the accommodations my students with IEPs use for every task.  They're laminated folders with several different charts, mnemonic devices, and facts pasted onto them.  the students may use them during any activity; quizzes, tests, warm ups, group activities-anything!   I think they're really wonderful tools for these students who are working towards accountability and self-monitoring.  

So, it's obvious that I don't have pictures from the halls, walls, or facade of the building...truth is I didn't feel comfortable taking these sorts of pictures.  There's always a class in the hallways and their artwork lines the walls; there wasn't a good picture to take if I had to avoid faces and names!  Regardless, my school is very laid back, friendly, and proud of their students.  Everywhere you look there's a student's name posted for a chivalrous deed (the school's mascot is a knight, so they earn notoriety/respect- their name is announced on the morning announcements if they're caught performing a chivalrous deed), examples of the class' projects, and educational posters (ex: 3 Science questions for the month; students can turn in their answers to the front office for a raffle held at the end of the month.)  It's a warm place; one I consider applying to even if Steve and I move to Central Austin.  We shall see. :)

Response to Readings Class 9/2/10

1) Problem solving involves exploration and discovery.  While there is a need for some prior knowledge, it's not necessary to teach the skills to solve the problems first.  Teaching occurs during the trials, mistakes, and final understandings after the explorations.

2) My personal feelings towards math will impact my teaching skills and the way my students view me as a competent, comfortable teacher.  If it's clear in my actions or expressions that I'm not confident in my skills, this is easily passed on to my students. They in turn may become nervous, unconfident learners.

3) Students, given the proper guidance and problems to solve, will not have to reinvent the wheel.  Much of the responsibility falls on the teacher's shoulders to keep the discussion moving at a decent pace, keep the discussion on topic, and keeping the students motivated.  It can be done!

4) When a student has struggled with a concept for a long period of time, a good idea may be to have a peer offer to help, or to ask probing questions which might lead the student onto the right track.  Sometimes a simple hint, leading question, or statement can guide someone to new insights and possibilities.

5) I read this article so long ago that I can't remember specific examples. I know that the researchers used modeling to assist students' learning; more specifically, they used manipulatives.  They also allowed for student discussions in small groups during the problem solving activities.