There are times when we have to reteach material to certain students. We know we should reteach it using the same methods but what can we do to make reteaching material more effective?

When reteaching content, it is suggested the teacher break the material down into small chunks so students are able to process and learn the material better. Once they show understanding and mastery of the first chunks, you can introduce more chunks until all of the topic has been learned. If at any point, students show they have not learned the material, try using alternate explanations or problems.

One way to assess understanding is to use a short quiz or questions to determine student misconceptions. This give a starting point so the teacher can focus on eliminating the misconceptions before moving on.

When reteaching it should consist of controlled, coached, and independent practices. Controlled practice is when the teacher models and guides the students, usually the first step. Coached practices are when the students are working more independently and the teacher moves around coaching students while providing feedback, and suggestions. Finally, independent practice refers to being able to work independently with little coaching or feedback.

It is suggested the independent practice should not be graded but used to analyze strengths and remaining weaknesses. It is the weaknesses which provide the area of reteaching to help students become proficient.

Some days, there is simply not enough time to analyze student understanding to create a proper lesson plan. Fortunately, there are three easily used strategies for reteaching which can easily be inserted into the lesson.

1. Error Analysis where the teacher posts questions with errors and the students work in small groups to find the errors. Once they identify the common error, they become more aware of it and can often find it in their own work. I like this because students often have to be trained to find errors in their work.

2. Create short activities which help students clear up small areas of misunderstanding. These activities should not be graded, they are just for eliminating misunderstanding.

3. Think aloud where the teacher models their own thinking aloud while mentioning common misconceptions along with explaining why you do what you do.

Tomorrow, I'm looking at something new to me. Re-engagement seems to be more student centered while reteaching which seems to be more teacher oriented. More on that tomorrow.

# Thoughts on Teaching Math with technology

## Monday, January 16, 2017

## Sunday, January 15, 2017

## Saturday, January 14, 2017

## Friday, January 13, 2017

### Practice Makes Perfect or Does It?

How many times have you hear the phrase "Practice makes perfect."? I've heard it from my grandmother, my parents, my teachers, just about everyone. I even heard it the other day from another teacher. He commented the new math program did not have enough practice problems.

I realized one thing about practice and that is you have to learn to do it correctly the first few times or you will impress the wrong moves in your muscles or in your brain. If a student learns the process incorrectly, it takes about 21 days to relearn it correctly. Imagine 21 days.

Have you taken time to actually analyze the mistakes of your students? I haven't but I have noticed that certain students make the exact same mistake every time they do the problem. For instance, when rewriting a two variable equation into slope intercept form, they always combine the x variable and the constant into one term. Every time. This means they have the incorrect process imprinted in their brain and it becomes harder to reteach it.

This means you have to reteach the concept which is almost like having to break them of one bad habit and replace it with a better habit. This means you have to reteach the material and have students practice the correct process over a 21 day period so hey have a chance of learning to do it correctly.

Sometimes, they develop the incorrect process because they were absent while other times its because they didn't learn it properly the first time or perhaps they got careless and just started doing it wrong. It doesn't matter because we have to make sure students learn and practice it correctly.

I'm figuring out I have to break it down so they practice say the last step on their own, then I have them do another step plus the last step independently until they can work the whole problem on their own. In addition I try to spread the lesson over several days while practicing previously taught material. I use homework as another place to practice previously taught material so they have a better chance of learning it properly.

The current thought on this topic is not "Practice makes perfect" but "Perfect practice makes perfect." Next week I'll provide some ideas for helping students learn the material correctly the first time and looking at effective ways of reteaching.

Feel free to comment and let me know what you think about this idea.

I realized one thing about practice and that is you have to learn to do it correctly the first few times or you will impress the wrong moves in your muscles or in your brain. If a student learns the process incorrectly, it takes about 21 days to relearn it correctly. Imagine 21 days.

Have you taken time to actually analyze the mistakes of your students? I haven't but I have noticed that certain students make the exact same mistake every time they do the problem. For instance, when rewriting a two variable equation into slope intercept form, they always combine the x variable and the constant into one term. Every time. This means they have the incorrect process imprinted in their brain and it becomes harder to reteach it.

This means you have to reteach the concept which is almost like having to break them of one bad habit and replace it with a better habit. This means you have to reteach the material and have students practice the correct process over a 21 day period so hey have a chance of learning to do it correctly.

Sometimes, they develop the incorrect process because they were absent while other times its because they didn't learn it properly the first time or perhaps they got careless and just started doing it wrong. It doesn't matter because we have to make sure students learn and practice it correctly.

I'm figuring out I have to break it down so they practice say the last step on their own, then I have them do another step plus the last step independently until they can work the whole problem on their own. In addition I try to spread the lesson over several days while practicing previously taught material. I use homework as another place to practice previously taught material so they have a better chance of learning it properly.

The current thought on this topic is not "Practice makes perfect" but "Perfect practice makes perfect." Next week I'll provide some ideas for helping students learn the material correctly the first time and looking at effective ways of reteaching.

Feel free to comment and let me know what you think about this idea.

## Thursday, January 12, 2017

### Sum of Interior Angles Hands On.

The first two days of this week, I had students work on an activity designed to help them arrive at the formula for the sum of interior angles. The first day, I passed out this great worksheet from Great Math Teaching Ideas which has all the regular polygons from triangles to decagons already done and ready to go.

I printed off the three page activity put only passed out pages two and three with the polygons.

The first step is to have students use a protractor to measure one angle and use that to find the sum of the interior angles. This step has them learning to use and reinforce the use of a protractor.

For the next step, I had students divide the shapes into smaller triangles with the lines starting from the same vertex. This provides students a chance to create the 180 degree part of the formula. When everyone had this completed we discussed using the knowledge that triangles have 180 degrees with the number of triangles to calculate the sum of the interior angles.

I asked students to compare their answers which lead to a discussion on why there might be differences between their answers with the protractor and the calculated answer. It was a great discussion.

I passed out the first page with the chart for names of the polygon, number of sides, and sum of interior angles. I added two more columns, one for number of triangles and one for each individual interior angle. One column was added in front on the left side and one at the end on the right.

Once the chart was completed, I asked questions which lead to the (n-2)180 formula. They added it to their notes and finished class by answering three of the four questions at the bottom.

Yesterday, they had a chance to apply the actual formula with a worksheet. Let me know how you teach this. I prefer activities to introduce topics. Thanks you all.

I printed off the three page activity put only passed out pages two and three with the polygons.

The first step is to have students use a protractor to measure one angle and use that to find the sum of the interior angles. This step has them learning to use and reinforce the use of a protractor.

For the next step, I had students divide the shapes into smaller triangles with the lines starting from the same vertex. This provides students a chance to create the 180 degree part of the formula. When everyone had this completed we discussed using the knowledge that triangles have 180 degrees with the number of triangles to calculate the sum of the interior angles.

I asked students to compare their answers which lead to a discussion on why there might be differences between their answers with the protractor and the calculated answer. It was a great discussion.

I passed out the first page with the chart for names of the polygon, number of sides, and sum of interior angles. I added two more columns, one for number of triangles and one for each individual interior angle. One column was added in front on the left side and one at the end on the right.

Once the chart was completed, I asked questions which lead to the (n-2)180 formula. They added it to their notes and finished class by answering three of the four questions at the bottom.

Yesterday, they had a chance to apply the actual formula with a worksheet. Let me know how you teach this. I prefer activities to introduce topics. Thanks you all.

## Wednesday, January 11, 2017

### iPlugmate

The other day, a friend showed me this awesome thumb drive with a plug for ipads and iphones and a usb one. It is called iPlugmate and its made by a company called HooToo. I think he got it off of Amazon during one of their lightening deals.

I borrowed it to transfer some photos off of an iTouch to my computer and it was wonderful. I didn't have to plug it in, bring up iPhoto, connect them and wait.

I had to download an app for the free app and I was ready to go.

As you can see it comes with a plug on each end, the i device on the wider end and the USB plug on the narrower end. The caps are attached to the thumb drive so they do not get lost.

I simply plugged in the drive to my itouch and instructed the app so save certain photos on it so I could use them on my computer. The first time I used it, it took me a bit to realize I had successfully transferred the material because the light indicating success is in the middle, right next to transfer interrupted.

Once the photos were transferred, I unplugged it and plugged it into my computer. It was easy to transfer the photos into iphoto. I ejected it just like any other thumb drive.

Here is a closer look at the plugs on this thumb drive. It comes with 32 GB of storage which is enough for what I need. I can see using it in class.

I often have students do things on the iPad and I have had students mail the presentation to me via e-mail but now, I can just pop it on here and directly transfer it.

There are times our internet goes down so I do not have to wait till it comes up. I can use it at home to transfer material from my i devices to my computer and back without hooking it up with the cord.

To say the least, I think it was a great investment for me. If you've been looking for something like this, check it out on Amazon. Just look for iPlugmate.

I borrowed it to transfer some photos off of an iTouch to my computer and it was wonderful. I didn't have to plug it in, bring up iPhoto, connect them and wait.

I had to download an app for the free app and I was ready to go.

As you can see it comes with a plug on each end, the i device on the wider end and the USB plug on the narrower end. The caps are attached to the thumb drive so they do not get lost.

I simply plugged in the drive to my itouch and instructed the app so save certain photos on it so I could use them on my computer. The first time I used it, it took me a bit to realize I had successfully transferred the material because the light indicating success is in the middle, right next to transfer interrupted.

Once the photos were transferred, I unplugged it and plugged it into my computer. It was easy to transfer the photos into iphoto. I ejected it just like any other thumb drive.

Here is a closer look at the plugs on this thumb drive. It comes with 32 GB of storage which is enough for what I need. I can see using it in class.

I often have students do things on the iPad and I have had students mail the presentation to me via e-mail but now, I can just pop it on here and directly transfer it.

There are times our internet goes down so I do not have to wait till it comes up. I can use it at home to transfer material from my i devices to my computer and back without hooking it up with the cord.

To say the least, I think it was a great investment for me. If you've been looking for something like this, check it out on Amazon. Just look for iPlugmate.

## Tuesday, January 10, 2017

### Writing Open Ended Questions

Yesterday, I talked about visible thinking. One of the suggestions
was to use questions that had no one right answer so students had to
explain their thinking. Unfortunately, it is not always easy to find
questions that meet the criteria so its important to know how to change
questions from having only one answer to a more open ended one or create
your own questions.

Lets first look at taking specific questions found in the textbook and turning them into more open ended questions.

Take a process question such as "Calculate 47 x 25" and rewrite it to read "Calculate 47 x 25 in two different ways.". Or take a question like "I have a quarter, a dime, and three nickles in my pocket, how much do I have?" and change it to "I have 5 coins in my pocket, how much might they be worth?"."

Instead of finding the volume of a rectangular prism measuring 2.1 by 8.2 by 3.4 and rewrite it so the student is asked to create a word problem where you need to find the volume of a rectangular prism in order to solve it. You could also rewrite it to require students to find all the possible dimensions of a rectangular prism with a volume of 120 m^3.

Next lets look at techniques for creating open ended questions.

1. Think of Jeopardy where the answer is given and the contestant provides the question but in this case there is more than one answer. An example might be "Area of 30 square feet" which gives four possible questions such as "What is a rectangle that is 3 by 10, or 2 by 15, or 1 by 30 or 4 by 5". This will be a student's first thought but it also allows for questions like "What is a triangle with a height of 10 feet and a base of 6 feet."

2. Use examples that have wrong answers and have the students decide where the mistake is and how to correct it. It might be a question like "George thinks 24 + 37 equals 51 but Jill says its 511. Who is correct? Explain your answer." In this case both answer are wrong so they have to explain that. It could also be a question involving one person seeing five rectangles in a design while the other person sees three rectangles and two squares. The student has to help settle the disagreement.

3. Get menu's or price lists from real world places and have students calculate things like "How much would a school lunch cost if it were bought at this restaurant?" Get a news paper and ask students to speculate on the relationship between the space articles and ads take up on a page.

4. Use the Tell Me All technique which simply asks students to write down what they know on a topic such as fractions, roots, factoring, etc.

Tomorrow we'll look at creating good "Which one does not belong?" questions. Let me know what you think.

Lets first look at taking specific questions found in the textbook and turning them into more open ended questions.

Take a process question such as "Calculate 47 x 25" and rewrite it to read "Calculate 47 x 25 in two different ways.". Or take a question like "I have a quarter, a dime, and three nickles in my pocket, how much do I have?" and change it to "I have 5 coins in my pocket, how much might they be worth?"."

Instead of finding the volume of a rectangular prism measuring 2.1 by 8.2 by 3.4 and rewrite it so the student is asked to create a word problem where you need to find the volume of a rectangular prism in order to solve it. You could also rewrite it to require students to find all the possible dimensions of a rectangular prism with a volume of 120 m^3.

Next lets look at techniques for creating open ended questions.

1. Think of Jeopardy where the answer is given and the contestant provides the question but in this case there is more than one answer. An example might be "Area of 30 square feet" which gives four possible questions such as "What is a rectangle that is 3 by 10, or 2 by 15, or 1 by 30 or 4 by 5". This will be a student's first thought but it also allows for questions like "What is a triangle with a height of 10 feet and a base of 6 feet."

2. Use examples that have wrong answers and have the students decide where the mistake is and how to correct it. It might be a question like "George thinks 24 + 37 equals 51 but Jill says its 511. Who is correct? Explain your answer." In this case both answer are wrong so they have to explain that. It could also be a question involving one person seeing five rectangles in a design while the other person sees three rectangles and two squares. The student has to help settle the disagreement.

3. Get menu's or price lists from real world places and have students calculate things like "How much would a school lunch cost if it were bought at this restaurant?" Get a news paper and ask students to speculate on the relationship between the space articles and ads take up on a page.

4. Use the Tell Me All technique which simply asks students to write down what they know on a topic such as fractions, roots, factoring, etc.

Tomorrow we'll look at creating good "Which one does not belong?" questions. Let me know what you think.

Subscribe to:
Posts (Atom)