Does Writing Help Improve Understanding?

  I have always been told if you can explain it in your own words, you show you understand the material, at least in English.  I wondered if the same thing applies to mathematics?

First of all, research indicates that improving a students ability to both read and write increases their learning.  In addition, writing can reveal misunderstandings, holes, and other issues with a person's understanding.

Most of us have never been trained to include writing in our math classroom.  I am the first to admit, I tried to have students journal their thoughts early on but I discovered they only copied their notes.  Since then, I've learned ways to sneak it in so they cannot just copy the notes.

Many students can solve any problem you give them but the minute you ask them how they got the answer, they tell you its done.  Others come up with the correct answer, only because they made an error in their calculations.  They don't care the process was not correct. I get told "I was close enough."  I try to explain close enough, especially in real life, could mean a bridge falling down or a building crumbling to the ground.

In addition, it may not be the actually writing that is important, instead it may be that writing requires students to think about their ideas and communicate those ideas.  When we require students to begin writing in the math class, we have to make sure to create a situation so students are willing to take a risk. 

I finally figured out how to implement more journaling in my class.  I give a warm-up at the beginning of the class period.  Since I collect these every week, I can have them write something on the back every day or every other day.  I do not include enough writing in my classroom but after reading two articles listed at the bottom, I have ideas.

Some of the suggestions include:
1. Have students explain in writing, how they solved a problem.

2.  Create solutions as if they are writing a textbook.  This would include the explanations associated with each step of finding the solution.

3. A short essay on what do you mean when you are asked to prove something.

4. Letters to the teacher to explain the student's confusion in regard to material taught.

5. Write a letter to someone who was sick that day to explain the material covered that day so the student does not get behind.

6. Create writing tasks which have students explaining their work complete with examples.

7. Free writing where students write for a short period of time on a set topic. 

8.  Teach students to apply the 5 W's (who, what, etc) when they write on a specific topic.

9. Have students work collaboratively to create a written explanation of their thinking.

10. Have students write a letter to help someone who is struggling with the material.  How would they explain the process and the concept.

This site has some very good detailed suggestions on using writing in the classroom.
Here is another one.   I have always been told if you can explain it in your own words, you show you understand the material, at least in English.  I wondered if the same thing applies to mathematics?

First of all, research indicates that improving a students ability to both read and write increases their learning.  In addition, writing can reveal misunderstandings, holes, and other issues with a person's understanding.

Most of us have never been trained to include writing in our math classroom.  I am the first to admit, I tried to have students journal their thoughts early on but I discovered they only copied their notes.  Since then, I've learned ways to sneak it in so they cannot just copy the notes.

Many students can solve any problem you give them but the minute you ask them how they got the answer, they tell you its done.  Others come up with the correct answer, only because they made an error in their calculations.  They don't care the process was not correct. I get told "I was close enough."  I try to explain close enough, especially in real life, could mean a bridge falling down or a building crumbling to the ground.

In addition, it may not be the actually writing that is important, instead it may be that writing requires students to think about their ideas and communicate those ideas.  When we require students to begin writing in the math class, we have to make sure to create a situation so students are willing to take a risk.

I finally figured out how to implement more journaling in my class.  I give a warm-up at the beginning of the class period.  Since I collect these every week, I can have them write something on the back every day or every other day.  I do not include enough writing in my classroom but after reading two articles listed at the bottom, I have ideas.

Some of the suggestions include:
1. Have students explain in writing, how they solved a problem.

2.  Create solutions as if they are writing a textbook.  This would include the explanations associated with each step of finding the solution.

3. A short essay on what do you mean when you are asked to prove something.

4. Letters to the teacher to explain the student's confusion in regard to material taught.

5. Write a letter to someone who was sick that day to explain the material covered that day so the student does not get behind.

6. Create writing tasks which have students explaining their work complete with examples.

7. Free writing where students write for a short period of time on a set topic.

8.  Teach students to apply the 5 W's (who, what, etc) when they write on a specific topic.

9. Have students work collaboratively to create a written explanation of their thinking.

10. Have students write a letter to help someone who is struggling with the material.  How would they explain the process and the concept.

This site has some very good detailed suggestions on using writing in the classroom.
Here is another one.

Implementing digital apps

Tuesday I downloaded 4 different notebook apps so each of 4 classes would have their own set of digital notebooks as these iPads are shared.  For two periods I had the students write down notes and for one period, I had them write what they knew about midpoint, distance and angles.   The biggest thing I forgot to do was plan time in so they could explore the application before writing things down.  Just for your reference I downloaded SAS Notebook, Goodnotes, Inkflow and Popplet lite.  It turns out Inkflow comes with a 10 page instruction manual the students read.  When they started writing, I had students help answer each others questions on using the app such as "How do I delete something?"  "How do I start a new notebook?"  This way I don't have to answer things. 
I am hoping to have students use these apps as their digital journals. 
In the future, I plan to have them create posters, foldables, take pictures of certain worksheets and use the annotation abilities to highlight certain important items.  I am going to try to have them create posters or word salads on line and import the finished project into the journals. I am hoping this way, it becomes more interactive than just a straight writing exercise.
Only time will tell how it works.  I have one more period today and we'll see if we even get to the app as it is a shorter period than usual due to a pep rally.

Foldables, origami and geometry.

Today in Geometry we had a blast doing origami.  We just started learning about points, lines, planes and intersections yesterday.  Rather than bore them with standard learning activities using points, lines, planes and intersections, I decided to incorporate origami.  After the warm-up I showed a video on the science of origami which was quite fascinating.  Dr Robert Lang, a person who can fold just about anything from a single sheet of paper, shared how origami has helped in science.  I didn't know that the way a scorpion is made in origami is the same type of folding used to put the airbag in the steering column.  The video was only 1:46 long but the kids were so interested in the material, they asked me to show the video again.
I had loaded two origami apps onto the iPads earlier this month.  One is Origami instructables while the other is "How to make origami" .  Personally, I prefer the latter because each step allows you to have the app show the actual fold if you want more than just the directions.  My students had so much fun, they didn't want to put away the iPads when the bell went.  Tomorrow, I will have the students create a summary of how they used point, lines, planes and intersections in this activity.
A couple weeks ago, we had a short after school class on Foldables created by Dinah Zike.  I wasn't sure my high school students would buy into them but they did.  They were focused and on task.  For Algebra II, we will be filling in the information over the next couple of weeks while in College Prep math, we created a foldable for the 6 basic trig ratios including as they relate to the unit circle.  It was awesome. I think that high school kids still like to make things and don't often get the chance unless they are enrolled in an art class.  I have to pull out my book on using foldables in math.

Interesting perspective on teaching math.

I was doing research on the internet to find some real world math problems that I could have my students do and I stumbled across this blog http://blog.keycurriculum.com/2012/03/what-do-you-wonder-real-world-math-problems-are-everywhere/
In it, the author has a short video of Annie Fetter from the Math Forum in which she says we should use senarios with questions like What do you notice? and What do you wonder? You are not after the students to actually solve it just look at it and find information.  The class has a discussion on it and then for homework you have the students write about what they talked about in class that day.  Toward the end of the entry are three websites, one of which has some great things to use for that. 
This is a cool way to integrate writing into the classroom while being able to assess student thinking and understanding of certain math ideas. 
I am always looking for new ways to integrate writing and to assess student understanding.  My students due to cultural influences are afraid to make a mistake and want you to check all their problems.  I need to help them be less afraid of making mistakes and being willing to work independently.
If anyone has ideas or scenarios I could use in a High School math class, I would love to hear.

Infographics + finding information.

Most of my students are below proficient in writing.  That is the last part of the state test they tend to pass.  I was playing with infographics yesterday and had a great time.  In the process I decided that I am going to see about importing infographics into a program such as subtext and adding some questions so that my students have to find the information and reply using complete sentences.  I can also add in some compare and contrast activities.  Since many infographics have actual stats, it falls neatly into math.  Right now, the students get out early on Wednesdays so teachers can have their weekly meetings.  The length of the classes on Wednesdays are perfect for this activity.  I think I will also do one word problem on Wednesdays using the KWC process. They need to work on taking the time to find information rather than asking me immediately for help.
Tomorrow and Friday, my ebook on Amazon is available free. 

There is a push for my students to do more reading and writing so they do better on the standardized testing.  I've been thinking about how to include in my classrooms.
1.  Word problems - Use the KWC  after underlining the important sections.  Perhaps even have a short video or illustration included so my students can see what it is.  My students tend to be so remote that they have little or no prior knowledge of some of the situations.  For instance driving the car from Philly to NYC.  We don't have cars and they have no idea of the distance involved.  So I  end up rewriting the problems to use boats, snow machines or ATV's.  If I included a map, perphaps a google trip using google world so they could see the actual routing that might build some prior knowledge.  They could fill out a short pdf form for the KWC and then on the bottom write in an explanation for how they came up with their answer.  This would add reading and writing into my math class.
2.  NASA math problems.  I've tried these but the students do not do well with them.  Again, if we had a pdf form to help them organize information, pictures or videos on the topic so they can "see" what is being talked about and perhaps have them create a video to record how they came up with the answer, it might help them improve their mathematical vocabulary.
3.  Finding real life problems such as telling how long a body has been dead using logs and temps.  Include a web page with the information so students can find the equation used to determine the time since death.  Provide them with a scenario where they are the corenor and they have a body.  They discovered that the body temp is such and such and they make a report on how long the person is dead. 
These are just three ideas I came up with to incorporate more reading, writing, and technology into my lesson plans for next year.  I did not mention iPad apps because there are several that could be used.

Neat app for word problems.

Found a new app called Subtext.  It allows you to take a book or web page or document and layer things like questions, quizzes, assignments, etc to make it more educational than just reading.  Right now they do not do PDF's but they are working on it and hope to have that facet available by next school year.  I've heard great things about it and it seems to be mostly used for literature or reading.  I tried to think of where I could use this actual application in my math classroom and at first thought about worksheets.  Once they get the PDF feature up and running that would be a possibility but this morning, it hit me.  Word Problems.  Most of my students take the numbers provided in the word problem and guess the operation, hoping for the correct answer.  If I used word problems with this application I could incorporate the KWC  (What do I want to know, what do I need to find and what considerations or special conditions do I need to keep track of).  This is something I could easily layer into the material.   Honestly I do not do enough on word problems and this could give me a tool to help them practice doing word problems.

Back to learning menus

I've been giving a lot of thought to learning menus and writing.  I've worked hard this year to increase their verbal communications by asking why, how did you come up with that answer, and other questions. I have been projecting warm-up and standardized test questions on the smart board.
Unfortunately, they are not as strong on the written, so I am toying with the idea of having students create pamphlets or jingles/raps or create some sort of digital presentation on showme, iphoto, or make a pod cast. 
In the past when I've had students create digital presentations, they've struggled with the creativity.  Many of these students have grown up in an oral culture and have little if any printed material in their homes.  So if I ask them to create a printed ad, I'll have to show them an ad and discuss the parts.  The nice thing is that I can bring a few magazines along to give them ideas and they can take photos to keep a record for themselves so they have a guide. 
This is something I'm going to be working on over the summer so I set it up properly and introduce it slowly over the year.  Maybe start with a choice of two digital projects and increase the number of choices over the school year.
If anyone has suggestions on setting up and using digital learning menus, I would love to hear from you.

Prime numbers

I keep hearing that we need to relate math topics to real life so students can see where the concept is used.  I had my 9th grade algebra I students go to Safari and research the answer to this question.  "How is prime factorization used in real life.  they found these answers.
1. Cryptography - developing and breaking codes
2. Internet security
3. Credit cards
4. Random number generators
5. breaking thing into parts
6. Magicians use them
I have a small class. Two of the students gave up on looking and one always takes her time.
This exercise gave them an opportunity to do research on a topic and find out more about real life.  I think I am going to integrate more of this next year along with having them write more.  My students score low on the writing and need to see you use it in other subjects.
I am hoping to do a bit of mind mapping on prime numbers on Monday.  It will help them develop some thinking skills they are low on right now.

Nice web site for use with the iPad

I use several math sites in my classroom but over the next few days I will focus on three of them.  Two of these can be used with the iPad and the third required the use of Rover the last time my students used it.  I'll talk about each of the websites over the next three days.
The first website is www.mathisfun.com  After I've introduced a topic such as prime factorization, I will often use a QR code to send my students to read the material on the website.  Most of the topics have a small quiz at the end of the reading section which I have the students do.  I do not grade them on how many they got correct, only that they did it.  Its a second way to expose them to the information.
I was reading on a website that it is good to provide both written and verbal instructions so that when students are not listening to verbal directions and they ask "What am I supposed to do?  you can point them to the written instructions.  I have put the written instructions into a QR code and had the students use the iPad to read it. It actually worked quite well. 
The same website suggested giving students choices in the classroom including choices of writing prompts.  I am going to try the writing choices out with the Journalize or the Notes program.  I am having fun trying to find ways to increase writing in the Math classroom. 
Tomorrow will be www.aaamath.com

update on two apps and a new one.

I spent some time going through the Boss T Maths I downloaded the other night.  It appears the one I found are just samplers rather than the full versions. The first one, Expanding and Factoring, shows you how to expand the distributive property or factor it from the expanded form to the original problem.  The examples are for a(b + c),  a(b-c),  (b+c)a and (b-c)a.  The app provides some vocabulary and a geometric representation.  Once you get to the practice problems, you can access the ones for the first examples but the others are locked and  you need to purchase the full priced app.  You can access the first practice problems for factoring ab + ac and evaluating ab + ac.  Again, if you want to any of the other problems you have to upgrade.  I was rather disappointed in that I was unaware of this being a lite version rather than the full version.
The special binomial products is set up in the same manner as the other.  You have to upgrade to access all parts of this app.  I think I could still use this effectively with my students for reteaching or guided practice using the examples.  Although I cannot access all of the practice problems, I can always create problems with the answers contained in a QR code so once my students have finished the problems, they can check their work.
I found a book making app Book Magic.  It allows kids to make their own books.  I can see this being used by elementary students to create books on shapes,  processes,  etc.  The app comes with basic shapes and it also allows the students to draw pictures, import photos or other material.  This is a bit too simple for older students. 

Journaling

I am looking at incorporating journaling in my math classes as it is important to include more writing in my class.  I found a nice program Journalize which I got on the day it was free.  It looks just like a journal but it allows you to import pictures, etc and I am thinking it would be great if I could have students keep journals in some manner so they can write about what they are having trouble with, write a letter to a penpal explaining what they did in class, create a drawing and import it.  Make it more friendly than the usual write it down on a sheet of paper or keep in a book.  Too many of my students loose their pencils, binders, etc.  The less paper I have to have them deal with, the more they turn in.
I found two programs from Boss T Math.  One is on the distributive property and the other is on special binomial products.  It comes with instruction and quizzes and seems to be done in a very mathematical way.  I have downloaded them and will play with them over the weekend.  This company makes 7 more and all but one are free at this point in time.  I'll give you a report on the two apps on Monday