Mathematical Practice #2

Eight Mathematical Practices

This is the second one

Reason abstractly and quantitatively

We need to be able to break down the problem and be able to represent the problem in what makes sense be it pictures, words, symbols, etc. I wasn’t as concerned about the answer as I was about the process. I wanted to see their work, how they came to the answer that they had. I got more the line that “I did the work in my head” more than what I can count.

Drawing representations of problems in whatever manner made sense and then label the sketches. Manipulatives often help in understanding of problems. I tried to let students figure out what to do with data themselves instead of giving them an algorithm that solved the problem but didn’t give them an understanding of the relationship of the numbers.

Mistakes matter

I have been thinking about the new year that is fast approaching. I am excited to be heading into a new year, but I will miss my summer vacation. I want to have conversations with my students and help them through their mistakes. I have recently discovered the benefits of making mistakes and have found how much I have learned from my own mistakes.

Far too often I hear from students that they just want the answer. They look up answers on #photomath and think that is all that they need to pass the class. I do not want to concentrate on the answers but rather to concentrate on the process. It is one thing to get a correct answer but does having the correct answer mean that they have the understanding of the process. I think not. I want them to understand the relationship of numbers and patterns.

I liked the idea last year of having an Algebra Boot Camp. We need to practice math if we are going to learn math. We need to exercise our math brains to develop and strengthen them. I have a big job in front of me, but math is too important to let it slide. This is the keys to all other subjects.

1 of 8 mathematical practices

There are Eight Mathematical Practices

This is a brief explanation of the first one. I will be talking about all of them.

Make sense of problems and persevere in solving them

We need to first, understand the problem. This means to read and try to figure out what the problem is asking. I started playing this toy blaster game on my phone recently because one of my kids suggested it. One thing I noticed was I can go through and match all the colors and not meet the objective. I had to look at what my objective was and go for those items. If I just matched colors, I would not necessarily meet the objective.

Why do I need to learn math? Reason #1

In anticipation of the new year that is just about to start, I am thinking of this age old question that I have probably gotten more than any other question, (including my kids asking, Why?).

Between my five Algebra 1 Periods, the students I work with in Robotics, the lunch time students, after school students, class of 2020 students that I advise, this is the most often question that I get. Why do I have to take math? I am never going to use it.

I am going to write down a few of my answers that I plan to give them. If you come up with more, please, make a comment.

The first thing that I thought of was they need to pass this class because it is a requirement for graduation. Then they have science classes they need to pass for the same reason. If students do well in math, they will have the advantage over the students in these classes.

I feel that reason is really a cop out. Of course they have to pass the class, but that is not what they are needing to hear.

The first real reason I have is that it builds their brains. I know that the more math I learn, the smarter I seem to feel. I have to agree that I am not comfortable with that math headache that I get. There is this particular side of my head that when I am really working on critical thinking about problems, it hurts. At first I didn't like it and thought something was wrong. Then I began to relate it to the learning I was doing. It was just like when I go to the gym. I was building my brain. I was exercising my brain just like I exercise my body.

Math helps develop critical thinking skills. This is a necessary skill to have in the real world. I don't think I am helping my students by giving them 100 problems to solve one way, but I need to come up with problems that will help develop their thinking. If I can do this, then I believe that they will be more successful.

Correction Procedure?

If mistakes are important to our brain's growth then why not give Students the opportunity to correct their mistakes to earn credit. I found this on MathGaraffe.com

What procedures do you use for students and making up their mistakes, if any?

Do you think this type of procedure makes a difference?

Is half credit appropriate? 

First day activity

If making a mistake in math helps our brains to grow (see Mistakes post), then we need to change the way we handle student mistakes in the classroom.

How do we change the way a student thinks of mistakes in the math class?

This is an activity I plan to try the first day in my Algebra 1 class this year.

Take a piece of paper. Put your name on the paper.

Write on the paper your feelings when you make a mistake in math.

Crumble it up.

Now take that crumbled piece of paper and throw it at the board with the feelings that they have when they make a mistake in math.

Now, go retrieve your paper.

Unfold the paper and smooth it out.

Turn the paper over to the blank side. Take a colored marker or pencil and start to trace the lines of that crumbled piece of paper. This represents the new synapses that grow in your brain when you make a mistake.

Now take that piece of paper and put that in your notebook for this entire year to remind you that mistakes are just proof that your brain is growing.