Cooperative Learning

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Cooperative Learning

What is cooperative learning and how can it be implemented in a classroom. Lets look at this idea broadly and narrow it down. From what I have observed and read is that first and foremost as the teacher we need to know our students. I know I taught a lesson this past fall and I did a random name draw to create groups. My cooperating teacher was a bit on edge at first thinking two students who didn’t work well together were put together. When I was drawing the names I knew these students didn’t work well, so I made sure they were all in different groups. 

You really need to know your students. If you have all the bossy kids together they won’t work. All the shy kids together won’t work either. You can do random picks as well from time to time to have students who normally may not work together to allow them time together, sometimes kids can surprise us.

I know I’ve discussed with teachers the number of students in a team or group and the majority say 4-6 per group. More than 6 I have been told just isn't as effective when it comes to group work. Also, that you should assign roles for each student. I remember one teacher she would set colored clips on the desks. We would each pick one out; she would than put the task on the board and what each color represented. One person was the recorder (the writer), another the go-getter and putter away of supplies, pen-holder (so everyone had a chance to share before the writer could write) and many other different jobs depending on the task. I felt this was a great way because each time you could end up with a different task, even if you always picked the same color. 

Some ways to incorporate cooperative learning are through think-pair-share. Students are posed a question and think about it individually, than they pair with a classmate collaborate than share as a whole group. Another way is by having clock buddies. You have students set up a clock with other classmates names on them and when you want students to work cooperatively you can call out “Work with you 2 o’clock buddy” this way you don’t have to worry about a student not being picked.

Check out the article from the U.S. Department of Education regarding cooperative learning. Cengage Learning also has a great website you can read up to learn more about Cooperative Learning.

Response to YouTube Videos... What's your take?

Response to YouTube Videos... What's your take?

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It was a great perspective to see all three videos, Math Education: An Inconvenient Truth , Math Education: A response to “An Inconvenient Truth” Part 1 , and Math Education: A response to “An Inconvenient Truth” Part 2 It was great to see the different sides. The College Professor sat a bit on both sides of the fence. In this last video he discusses that math is being taught as abstract. Students developmentally do not start thinking abstract till they hit their early teens. Yet we are expected to teach students in the elementary grades to think abstractly. Students only worry about the here and the now. If it isn't relevant to me today, than why I should learn this... so you say I will use this in the future; my future is in 10 minutes when I go out to recess and if I should play with Bob or Jill. 

He goes on to say that math is useful, that it isn't a bunch of formulas. Rather that students need to think things out. It's the thought process and the understanding of numbers. He really didn't know the books that were being used, but what he could understand of the books and the few he knows, is that the books are trying to make math sensible and useful for students.

He goes on to make another good point; teachers don't always buy into the books. If the teacher teaching the math, from said book, doesn't buy into it than it won't be taught that way. I know many teachers who say yeah we did it the book way the first year and now I modify it to my liking. It seems to me and to the author of the second and third YouTube video, that we as adults, yes, even us teachers, can't get past the way we were taught math. I know personally I learned by a formula method. This is the formula memorize it and that’s it. I can tell you, so I memorized others I had no idea. 

He makes a point that you can't change the curriculum without changing the national tests. I feel that this shouldn't be true, unless they are looking for a specific formula, than yes this would be true. If the goal of the test if for students to answer the questions, show their work and get the question right, than we as teachers using other forms of learning math shouldn't sweat national tests. If these tests require specific formulas to pass, well than buckle up, for the next nine months you will be teaching for a test. Sadly most of the tests are at the beginning of the year and don't reflect your teaching and a summer break in their as well. 

I loved that he said the ultimate goal is for students to understand numbers, make sense of them and to also know the algorithms. Math needs to make sense for it to stick and for us to want to attempt to try it again down the road or to take interest in it again. Once the numbers make sense and you can look at a problem and work your way through it, than that is the time to practice. I would rather spend time teaching kids to think about the numbers and then having them practice and really understand, than to have to try to figure out where they went wrong and try and correct a process that they have wrongly engrained. 

You need to know how to think or you don't trust the process... if you don't trust the process would you keep trying or give up?... step in to an elementary students shoes for a moment to answer that question... Even as an adult, I'm not sure I would...

THINKING BLOCKS

Thinking Blocks

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The Thinking Blocks manipulatives were fun and educational at the same time. With using these manipulatives you could use them as a way to gauge where your students are with comprehension on each section. I probably wouldn’t use it to gauge where students are at comprehensively, but I would use them as a tool that students could use after they had learned the concept.

I feel that if used as a tool and not as a main way to teach the lesson the Thinking Blocks could be helpful for students. I would maybe make this one of the stations during a math lesson and have other stations that student’s would rotate through. I feel that this way I could have different techniques that the students can go through. Some students work best with manipulatives right in their hands and others work better when they work with their peers and some would better their understanding through the website manipulatives.

I’d probably introduce this into a first grade classroom and continue through the second and third grade. Kids today would not have a problem with the technology. All the students would need to be taught how to use the website, so this would be important step to cover first. I would model the website to students as a whole before I would send them of to do on their own. I would make sure that I had charts and 100 tables, as the first graders are still working on numbers. I guess I would see how they did with it, if they struggled I would hold off till second grade. 

Week 4 Blog Post - Multiplication Method

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Videos - Multiplication Method

Week 4 Blog Post 

I really liked the videos (Lattice Method, Russian Peasant Method, and Cool Multiplication Technique) for the different multiplication methods. In the first lattice method video it was really nice to see the breakdown and how he explains to set up the lattice. When he incorporated the decimal that seemed like a great way for students to learn where to place decimals at the beginning. I feel that we expect kids to know right off the bat that oh you just count over and how many spots the decimal was originally over. I have seen many a blank stares. But if you would start it with the lattice method and begin explaining how it works and see how it is two over and two over, that’s there it ended up in your final answer. I just think there may be a few more Ah Ha moments in the classroom with this technique.

The second video the Russian Peasant Method was really interesting. I liked that with this method not only were you working with multiplication of a problem but also working on halving and doubling numbers. I feel that this would help students practice halving and doubling numbers without it being a practice as if we were drilling students with cards. This method is a nice way for student to check or even perform the multiplication problem. I feel that some students may like this way better, specially if they do not know their multiplication facts well. The halving and doubling may be the hardest part, but than you get to the bottom and all you have to do is add to get your answer.

I know when I was a student all we had was the standard algorithm and no other way. I remember we wrote our numbers for our multiplication facts on the back of the paper for the answers, than we cut them out and drilled until we knew our facts. Also, those dreaded times test, do you remember those? When it came to the bigger multiplication of two, three and four plus digit numbers, we relied on the standard algorithm and the hope that you remembered those facts that you drilled over and over. I know I myself would have been better off using different methods to find answers to the problems. It was sad to watch students who figured out other ways to answer the problem and not get the points because it wasn't the standard way. It is refreshing to know that teachers are working with students and helping them understand the process through multiple techniques.

The last video was good for a laugh. I’m sure there are many kids out there that wish they could just compute a question to get an answer, I know I've had my moments.

Here are a few other multiplication methods I found on You Tube check them out, they may come in handy some day. The last one reminded me of my first post and different methods that were used for place value in different cultures. 

Gelosia Method of Multiplication  - Lattice Method

Amazing Method of Multiplication

Egyptian Method of Multiplication

Place Value MAB for iPad

Great way to include technology into a classroom, specially when schools are going one to one with iPads.

There is a greater push to bring technology into the classroom. We live in a day and age that nearly everyone has their own smartphone, iPad, kindle, laptop or computer, even televisions are wired to the internet. With having so much technology at out fingertips, why not incorporate within the classroom. Now just using an iPad in a classroom is not going to integrate technology unless it is used properly.

I found this application Place Value MAB for the iPad. This application is used for students to learn place value with MAB blocks. What are MAB blocks? MAB stands for Mutli-base Arithmetic Blocks. MAB blocks are blocks that show base ten number values. There are many types of these blocks, some come as wood, plastic and even foam. In this example it comes as an application that can be manipulated.

What are the MAB blocks? There are multiple blocks that are used.
There is the:
One unit = One
One long= One Ten
One flat = One Hundred
One cube = One Thousand

The application gives you a quick run down of what MAB is, the units that are used and the terminology and values of the blocks. The application also gives examples and games that show you how this application can be implemented within the classroom.

If you are still confused as to what MAB is please check out this website they explain what MAB's are, how to get students to work with them and how to help students to understand how ten longs can equal one flat and so on, as well as an activity link.

Understanding Place Value

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Understanding Place Value

Blog Post One by: Michele Jarosch

Having students understanding place value early on in elementary school is essential. It is a primary concept students need to know and teachers work hard with students, yet place value, as numerous studies have shown, is elusive and a hard concept for students to grasp. Just like students who make connections between sets, envisioning the set, matching that to a number and than being able to write that number, and understanding they all mean the same thing.

Place values take time to learn. In the article Understanding Place Value the authors introduced students to other place value systems. What is a better way to learn our own place value systems, than through learning and understanding other cultural place value systems.

Students are allowed to use manipulatives to understand and learn place value as well. Here are a few YouTube examples of using base 10 blocks to understand place value.

Place value blocks intro

Base 10 blocks lesson 1 Intro and Explore

Place Value with Base 10 blocks

My first experience with another form of place value wasn’t until last fall in my grad Math Methods course, maybe having learned these earlier on I may have been a better Math student. Being able to incorporate this idea of introducing other place value systems may really help students to understand our own place value systems.

Incorporating these other place value systems not only helps students with the Math of place values and the knowing for standardized testing. Integrating the Math aspect of place value systems along with the History of the system, time and people, Geography of where developed and what the land was like, Culture of who these people were and what they did, Music of the time frame, Art of the time period, and more all in to a unit. Incorporating all of these together you are not only teaching some lesson on place value, you are allowing students to discover place value and build upon that knowledge, actively ingrain the information.