Posts tagged ‘Math Discussions’

Utilizing Mathigon Site in the Classroom

“Math is like going to the gym for your brain. It sharpens your mind.” By Danica McKellar

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Mathigon is a new STEM website that consists of interactive eBooks, videos, slideshows and animations, with the aim of making advanced mathematics more accessible, entertaining and applies real world application. This website is FREE, works on all devices and has a Chrome App extension and can be made into an iOS App (by saving to home screen). Follow them on TwitterFacebook and Google Plus.

You can choose from a variety of activities, lesson plans and slideshows that have been designed specifically for the classroom. This site is created out of the UK but meets many Common Core Math Standards,  Math Practices and NC Science Essential Standards.

One of my favorites is the ebook,  “World of Mathematics” which was also 2013 Lovie Awards Gold Winner. It is a great, engaging way to add non-fiction text, class discussions and writing tasks into the math or science classroom. Another favorite activity, that the students also love, is the Math Treasure Hunt (Middle of Page).

“This essay (The Value of Mathematics PDF) explores the practical, intellectual and cultural value of teaching mathematics at school, examining a wide range of research and with many examples.”

Mathigon is still being developed but many of the activities to coming soon look very promising such as Mathemagic, Carnival of Mathematics and more ‘chapters’ in the ebook called Motion and Matter.  I would love to hear what you think of this new site and how you will incorporate it into your classroom.

Work Sited: About Us – Mathigon | About.” 2012. 4 Jan. 2014 http://www.mathigon.org/about

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More Math Reasoning Needs to be in Elementary School

“Mathematical reasoning is essentially about development, justification and use of mathematical generalizations.” Jo Russell

Many teachers come to me for advice about teaching students to problem solve. I know that having a strategy is helpful for many students, but I also think it comes down to reasoning skills as well. I think mathematical reasoning is one of the biggest over looked skill taught in math. We need to start teaching more logic and reasoning in elementary schools so when the students start algebra, it makes more sense to them because they have a stronger background. This will eventually help students with problem solving as it will build critical thinking skills a vital 21st century skill.

There are two types of reasoning, deductive and inductive, that we need to teach. Many teachers don’t realize the importance of these math reasoning skills. Below I explain why!

Inductive reasoning involves going from a series of specific cases to a general statement. I like to relate inductive reasoning to a series of pictures and you have to figure out which on is the odd one out and why. We need to start teaching this type of reasoning in Kindergarten. Having the students look at four pictures and then asking them which picture does not belong, helps with inductive skills. In first, the teacher can do the same but this time asking the students what the ‘rule’ is about the pictures. Each year you add a different and harder element to inductive reasoning so by the time they are in the upper grades, they can figure out why a rectangle can not be a rhombus.

Deductive reasoning is a type of logic in which one goes from a general statement to a specific instance. I relate deductive reasoning to the game clue. When I am teaching reasoning, I like to start off teaching with Abbott and Castello Video- Who’s on First? (http://ow.ly/90Zhd) I have the students draw a picture of a baseball diamond in their notebooks, modeled after the one I have on the board. I then tell the students to just listen to the video, many of the students don’t even know who Abbott and Castello are so it is a great time to bring in a little history! After they listen to it once, I tell them to listen to it again and fill in the positions of the baseball team they are talking about. This is a great way to introduce reasoning and logic in grades 3 and up. The students don’t relate it to a math lesson right away because it doesn’t have numbers in it, yet they are still solving a problem.

You can find logic and reasoning throughout the Math Standards of Practice for the Common Core under….

#1. Make sense of problems and persevere in solving them.

#3. Construct viable arguments and critique the reasoning of others.

#6. Attend to precision.

#8. Look for and express regularity in repeated reasoning.

To view all the Math Standards of Practice (with more detail description) and the Math Common Core click here. http://www.corestandards.org

Math Discussions and the Importance of it in the Classroom

“If two wrongs don’t make a right, try three.”  ~Author Unknown

I think often teachers forget how important discussion in any subject is but especially in math. I believe many educators don’t always realize the benefits of discussion and see it as a ‘time waster’. Math discussion to me is one of the most important things to be taking place in the classroom. When students discuss math they are able to clarify their own thinking and learn from others. The teacher can also informally assess if the student’s truly under stand the concept or just walking through the steps to solve it.

Asking students to talk about mathematical concepts and problem solving doesn’t happen over night. The educators need to make a safe learning environment so the students feel comfortable to share their thoughts. This includes showing and allowing the students to solve math problems in more than one way. The classroom needs to have clear, high expectations and the students need to treat each other as equals through respect.

Once you have a safe learning environment math discussions will flow and the students will start to hold each other accountable by asking each other ‘how did you get this or that’ etc. This is also a great way to infuse the 21st century skill of communication.  The key to great math discussions is asking the students to explain their mathematical thinking which also incorporates the 21st century skill of critical thinking.

When I was visiting a math classroom this week, 2nd grade, the students were working on finding the missing addend in math problems. A little girl, Jessica*, was showing the class how she solved the math problem. The teacher was doing a great job of asking her guided questions of getting her to explain her work. I was watching and walking around looking at other students work as well and saw many students got it right but solved it multiple ways. Once Jessica was done showing the class the teacher was ready to move on to there math workshop time. I jumped in (I don’t do this in all classrooms, but with this teacher I knew that I could) and said, “I see Frank* has a different way of solving this problem. Frank can you go up to the board and show us what you did. I also see that Sam* did a different way as well, can you show us what you did too.” The students went up to the board and showed and explained their work all getting it right. I then asked, how many of you solved it the way Jessica did, 10 hands went up. How many of you solved it Franks way, 6 hands went up. How many of you solved it Sam’s way, 4 hands went up. I then asked who solved it the right way? No one raised their hands. I waited (one of the hardest things a teacher has to do-30 seconds feels like 10 minutes some times!) after a few seconds of their little brains turning, Steven* said, ‘all of them, as they all got the same answer.’ I then asked, “Is there more than way to solve a problem?” Most of the class shouted out yes.

Here is just a snip it of one classroom and how the discussion lead to understanding there can be more than one answer. It also showed the students that didn’t do it Jessica’s way that it was okay; where if we didn’t have that discussion they could of thought they had done the problem wrong. This did take about 8 minutes off of their workshop time but the benefits were priceless.

Teachers need to realize the benefits of math discussion and the only way to do that is making more teachers aware. Facilitating math discussions involves engaging students in sharing and listening, questioning and responding, and agreeing and disagreeing. It also gives us, the teacher, an opportunity to really understand the students thinking. This should be occurring within and through the teaching process. Students will also benefit from hearing what others say and see that there is more than one way to analyze and solve a problem. Classroom math discussions also give you the chance to clear up any misconceptions the students may have.

Do you allow time for math discussions in your classroom?

*names changed to protect identity.

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