Math Strategies: Blog 4

When I first started this semester, I was able to observe the students in my placement work on several basic skills (such addition, subtraction, and multiplication).  During this time, the students worked on addition problems, and I noticed them using a method I feel I was not familiar with.  They would expand the numbers in the equation, add their place values separately, and then together to find the answer.  For example, 71+54=?  The students would separate the tens (70, 50), then the ones (1,4), and then add them (70+50), (1+4).  Then they would take those totals and add them together (120+5=125). 

            Another way a student can solve this problem is by adding 1 to 54, and changing 71 to 70.  So then the problem would become 70+55= 125.  Going off the expansion example, another strategy would be to subtract 1 from 70, 4 from 54 and add 70+50, 1+4.  Then add both sums together.   A different way would be to subtract 4 from 54, and add those 4 to 71 (causing 71 to become 75, and 54 to become 50).  Then 75 and 50 could be added together to find the answer.  Finally I know that 30+30=60, so if i took 60 from 71, I would have 11 left.  Then I could add those 11 to 54, causing 54 to become 65.  Now, I can easily add 60+65 because I know in the tens value 60+60=120 (because I know 6+6= 12 so I just add on a zero), and in the ones 5+0=5. So when I combine 120+5, I get 125.     

            When working on a different problem, (21*2) I noticed that one of the students changed the problem so that the smaller number was on top and the bigger number on bottom.  I noticed the student would do this for all their double digit by single digit multiplication.  One strategy that could have been used would have been to add, 21+21, instead of multiplying.  Another strategy would be to expand 21 (20, 1) and multiply each digit by 2 (20*2, 1*2) and then add the sums.  To make the numbers smaller, I could also split 21 (10, 11) and then multiply 10 by 2, 11 by 2 and then add those sums together to get the same answer.    Those are a few ways I can think of how to solve a problem like above using invented strategies.  

(pictures to be posted soon)

Blog 3: Talk moves

1.     This week has been a little out of the ordinary in my placement.  Illnesses and meetings have caused these two days to go by fast.  Even though the teacher may not be here, the students are and so is “MATH”.  However, I think there are two types of math.  The first type of math is the type your teacher teaches.  It’s the kind that either goes by the curriculum or to your needs, sometimes goes off a book, and is taught by the teacher him or herself.  The second type of math is what I sometimes call “substitute math”.  This math (as you probably have already guessed) is usually formulated with packets of review, math problems that have been seen before, TAKS (or STAR) questions from past tests, and is discussed when the teacher is out of the room.  This week, I saw both types of math in my setting.  The first day here, there was a substitute because my cooperating teacher was ill.  So, students worked on their problem of the day (which is sometimes done even when the teacher is present, but it is mainly “Daily 4” that they work on when they arrive), and a couple of TAKS related problems.  Now, even though these questions are formulated to resemble TAKS questions, I still think students can be taught how to solve these problems (such as a mini-lesson).  That however did not happen.  Students were given the problem of the day and worked on it alone (which is what normally happens), however when a student finished the substitute would then check the students work and go over it with that student alone until another student finished in which she turned her attention to the new student.  Once the students were finished they moved on to their TAKS problems and the same procedure took place.  However, she did project some “talk moves” when working with the students.  She would restate the students’ problem solving strategy, and ask the student if she explained it correctly.  I think I would have allowed students to share strategies with each other, and even ask if they could explain how they thought someone else solved the problem.   I also would have worked together on each of the problem.  I think having the students see different ways to solve a problem (even a TAKS problem) could benefit the student and can lead to higher thinking. 

2.     When the teacher was back in the room, students started working on “Daily 4” and different strategies to solving problems (such as algorithm, number facts, and expanding the numbers).  Before showing each strategy the teacher would ask the students how they would solve the problem.  Then she would explain back to the student and ask if that’s how they solved the problem.  Finally she’d ask if another student understood and if they could add on their own way or what they thought.  Some of the strategies the students would use were strategies the teacher explained, which would excite the student.  I think the teacher did a good job with the “talk moves”.  I don’t think I would have changed this lesson.  I really liked how she allowed the students time to solve it their own way, and then asked the other student to explain.  Finally she showed several strategies they could use, and she stressed they could use whichever strategy they prefer.  I think this is important because sometimes students feel like they are restricted to one strategy when in fact they are not.  It still allows a sense of exploration, but provides help if needed.