Monday, July 18, 2011

Measurement- Math 1512

This week we continued with the geometry unit. One of the things that we talked about was measurement. We worked on finding the area and perimeter of shapes, conversion between two different units, and understanding measuring different things.

When I was in school learning about using rulers and different types of measurements I struggled quite a bit. When I was in 1st and 2nd grade we worked on using rulers and measuring different line segments. One of the things that was most confusing for me is the fractions involved with measuring. We hadn’t yet learned about fractions and when we took measurements dealing with ¼, ½, or ¾ inches, I didn’t know what it meant. I didn’t understand that ¾ was larger than ¼. Once I reached 3rd grade we stopped learning about measuring and rulers and jumped to finding perimeter and area. I still hadn’t fully understood measuring and how to use a ruler. I felt so left behind and lost during this section of math class. Once third grade was over so was learning about measuring. I never worked with measuring again until the 6th grade. During wood shop class we spent the first two weeks learning about measuring the fractions that go along with taking measurements.

Now that I am older and more familiar with fractions and measuring, I understand how important it is to know about measurements and conversions. There are so many real life situations that could be given as examples for why they are important. One of the first things that comes to my mind is moving into a home. When someone moves into a home they often time update things like paint and flooring. In order to be able to purchase the correct amount of supplies the new home owner would have to know how to calculate the area of a room. When the same home owners move furniture into the house they are going to have to know how to measure. Another example that comes to my mind is driving a car. Having a good understanding of distances and measurements is important when driving a car. A driver needs to know how far away they are from another car so that they can keep a safe distance. Without a good understanding of measurements or distance a driver wouldn’t be able to do this.

I found an interesting website that students can use to practice finding area and perimeter. Click here to check it out.

Saturday, July 16, 2011

Modeling Math Meaningfully- Math 1510

This week one of the articles that we read was called “Tying It All Together: Classroom Practices That Promote Mathematical Proficiency for All Students”. The article talks about a lot of important concepts that teachers can utilize to help create proficient math learners but there was one that stood out to me the most. One of the concepts covered was called “Modeling Math Meaningfully”. The idea behind this is that when students use multiple ways of showing their work and the answer to a math problem, they create more connections. This technique has students using manipulatives, pictures, real-life scenarios, verbal symbols, and written symbols in order to create connections and understanding.

Why does using multiple ways of solving the same problem work? It works because more understanding is being created. When we solve a math problem only one way, a lot of times we aren’t really sure what we did or why we did it. When students have to prove their answer in more than one way they are proving that they truly understand the concept at hand. If they can show understanding through drawing a picture, talking about it, and showing it with manipulatives, there is a deeper level of understanding and more confidence. Many of the math students who are not confident in their abilities (ME!!!) feel that way because they lack true understanding of the math that they are working with. Even if they can solve a problem and/or work through different formulas and problems they don’t truly understand. It is essential that students know what they are doing, why they are doing it, how they are doing it, and how to apply those things outside of a structured classroom activity.

What does all of this mean for my future classroom? After reading this article I be using the method that the author suggested for modeling math meaningfully. My students will not only be required to show their work but they will be required to show it in multiple ways. If I am holding them accountable to showing their work I also need to hold myself accountable. I need to provide plenty of opportunities for students to explore math and allow time for them to work out the problems at hand and really think about what they are doing and why.

One of the ways that students can solve problems is with manipulatives. Often times teachers can run out of ideas or not know how to use them in the classroom. Scholastic provides some excellent links to provide teachers with tips and ideas about how to use manipulatives effectively.

Monday, July 11, 2011

Prealgebra Strategies- Math 1510

This week one of the topics we discussed was prealgebra strategies. We watched a video with young students working with different strategies such as solving word problems and coming up with their own language in order to understand the math problem at hand. Prealgebra strategies can be helpful for very young students because they are being introduced to reasoning skills early on and have more opportunities to practice them before they encounter more complex math problems.

While I was watching the video on prealgebra strategies I found myself thinking back on my days in elementary school math classrooms and my feelings towards math. When I think back on the things that I learned during math class I can remember solving word problems that were similar to the word problems in the video. I can remember solving word problems from 1st grade on up to 11th grade. Each year the problems became harder and harder. In 1st grade we would solve word problems using small numbers such as adding 3 and 2 to make 5. Once I reached the upper elementary grades word problems involved adding three digit numbers or more and multiplication and division. By the time I reached high school the word problems were very complex and involved various formulas and procedures. As I moved through the grades math became more of a struggle for me until I grew to hate math. I am realizing now that everything that I had learned was simply a continuation on everything that I had previously learned. In my mind I was learning something new every year. As a 1st grade I never realized that I was actually doing a form of algebra and as an 11th grader I never realized that the algebra that I was learning was something that I had experience with already. As I thought about my experience more my mind drifted to something that the class had discussed before and that is having a coherent curriculum. Many times my teachers would use different names for the same things or alter steps in solving the same problem. This was beyond confusing for me. I think my relationship with math would have been very different if my teachers based their lessons off of a coherent curriculum.

Should we be using prealgebra strategies in elementary classrooms? I believe that we should. Prealgebra strategies enhance a student’s ability to reason and use their logic skills. If they are able to develop those skills starting from an early age and be stronger problem solvers later, why shouldn’t they be used? If students are able to write and solve their own word problems they can be more confident when they come across a word problem that they didn’t create. Teaching these strategies early on can help create more confident math students and more confident math students means less negative relationships with math.

I found an interesting website for word problems. This website generates word problems based on the season. If your classroom wanted Spring time word problems, simply click on the Spring link under the appropraite grade level and it will generate problems for you.

Humor in Math Class- Math 1512

This week we focused on humor in the math classroom. Humor can add to any class and at any grade level and helps keep the students interested on what is going on in the classroom. This week we watched several humorous videos and were provided with a list of links regarding humor in the math classroom. Of course this was a fun thing to study this week but it also made me think about why it is important to have humor in class and my own experiences with math and humor.

Like I had said earlier humor can add to any class and at any grade level. With that I said I think math is one of the classes that can greatly benefit from a little humor. Math is one of those classes that revolve around facts solving problems. Math class is also labeled of the more boring and serious subjects in school. A little bit of humor can totally transform a math classroom. One of the sure fire ways to grab the attention of students is to be funny. By sharing a joke or two and lightening the mood with a funny story or comic students feel the pressure ease off and are more able to concentrate. Keeping the mood light and fun makes the time pass quickly and makes learning fun.

I had my own experiences with humor in the math classroom. Math has always been the one class that I struggled in. Because I struggled in math, it was also my least favorite class to go to during middle and high school. I could just feel my mood drop when I knew math class was coming. All of that changed during 7th grade. I had the BEST math teacher that I had ever had that year. He was one of the funniest teachers that I had ever met. He started every class period off with a funny joke, comic, or story of some kind. When it came time to teach the lesson he did what he was supposed to do, but he did it with a smile. Math class was fun for the first time. As I began to enjoy going to math class, the topics that we were learning about began to be easier for me to understand. I felt at ease when I was in class and that feeling followed me home when it came time to do homework. The fun things that happened during class popped into my head when I was doing homework and made it a bit easier to get through. When I did come across a topic that I needed a little more help on I felt good asking for help. I knew my teacher was willing to help me and would do so happily often times with a joke a two. My 7th grade math teacher changed my whole year when it came to math. I wonder if he really knew the impact his humor had on me and the rest of the class.

I found a fun website that has many different types of jokes. They specifically have a section devoted to jokes that are realted to different school subjects.

Saturday, July 2, 2011

The Lattice Method- Math 1510

This week we learned about different multiplication strategies. One of the strategies that was covered was the lattice method. The lattice method is one of many different multiplication strategies that people can use. The following video is a demonstration of how the lattice method works.

I have had previous experience with the lattice method. During 5th grade the lattice method was one of the multiplication methods that we learned how to use. In the 5th grade I found the lattice method completely confusing. I was never able to figure out how to use the lattice to find the correct answer. I quickly gave up on the lattice method and relied on the traditional multiplication algorithm. When I saw the lattice method, now as a college student, I immediately became nervous all over again. I knew that I wasn’t able to figure out how to use it in the past and I assumed it would be the same thing again. This time around I was surprised to find that I enjoy using the lattice method. The lattice method is easy for me to understand now. In my own opinion I don’t find the lattice method any easier or more difficult than the traditional method, it is just another way to multiply.

The question that may pop into many heads is, why should the lattice method be used when the traditional method works just fine? Both methods will provide the correct answer but for many students the lattice method is sometimes easier to work with. The lattice method breaks down the problem into smaller pieces to work with.

I found a kid friendly website that breaks down the steps of the lattice method clearly. This would be a great website to show to parents. Many parents aren't familiar with the lattice method and this website would be a great tool for them to use along with their kids when they are using the lattice method at home.

Geometry- Math 1512

This week geometry was introduced. When most people think of geometry they think of shapes. Geometry does involve shapes but things like angles and lengths of sides are also discussed in geometry. Geometry is a great mathematics topic for people who are visual learners. They are able to draw out the different shapes or angles and see what they are working with.

When I think of geometry my mind immediately goes to the different types of angles (right, acute, obtuse, and straight). I found a video that breaks down the different angles and what degree category the different angles fall into. When I first began learning about angles in elementary school the hardest thing for me was trying to remember which angle aligned with the different degree categories.

As I have continued to watch videos, read the readings, and work on the different homework problems in the geometry unit, the things I have learned in elementary and middle school are beginning to come back to me. I hope the video helps jog your memory and get your mind thinking about shapes and angles again.

I discovered a fun website that has different geometry games and e-manipulatives for kids. This particular website also has other math topics for kids such as fractions or multiplication. Check it out!

Cooperative Learning- Math 1510

This week we watched an interesting video showing students in a classroom working in cooperative groups. Cooperative learning is often compared to group work but they are very different strategies. Many times in group work one or two students end up doing the work while the rest of the group sits back and doesn’t put any effort into the work. Cooperative learning utilizes groups but holds every group member accountable. The following video gives an overview of what cooperative learning is and how it works.

When I think of cooperative learning I can think of many different benefits to using this method. One of the benefits of this method is that students are actively engaged in their learning. Instead of sitting at their desk passively listening to the teacher lecture them about a particular topic, students can dive in and explore and make sense of what they are learning. Cooperative learning also teaches students social skills and allows them to practice their skills in a safe environment. As students continue through their education and make their way into the working world they are going to have to learn how to work well with others. Cooperative learning teaches students how to listen to what other people have to say and make compromises. It also teaches students that it is alright to ask for help or admit to any mistakes that may have been made.

Although there are several benefits to using cooperative learning there are also several disadvantages. One of the first disadvantages that came to my mind would that it could be a source of arguments and frustration within the group or the classroom as a whole. Nobody likes to be wrong. The same is true for students in a classroom. They don’t want to be proven wrong. If the group chemistry is not strong arguments can break out quickly. If there is a lack of structure among the groups things can quickly get off track. Students need to have structure within the class and the group so that they can stay on task and complete the job. If the structure is not there then there is also the risk of turning into your average group work with only one or two students doing all of the work.

The following video provides tips on how to effectively utilize cooperative learning in the classroom.

I found a website that is hosted by the University of Missouri that is filled with links related to cooperative learning. This website has pages and pages of links with more information about cooperative learning as well as activity ideas. Check it out!