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.

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 http://www.blogger.com/img/blank.gifwill 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.

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.

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!

Probability-Math 1512

This week we studied probability in class. During class we watched multiple videos and worked with e-manipulatives that focused on probability. A very broad definition of probability is the chance something will happen or not. I found the following video that breaks down the basics of probability:



Probability is a math concept that is important to know and understand because it is found so frequently in our lives. Every time we turn on the local news channel and watch the weather report we are dealing with probability. It is important that students not only know what probability is and how it can be found but how to interpret it and apply it to real-life situations outside of math class.

When it comes to teaching probability in the elementary school classroom there are many ways to alter lessons to make them relevant to the students in the classroom. Some of the more common ways to teach the basics of probability is to use some type of candy like M&M’s, Skittles, or gumballs.

PBS Kids puts a fun twist on the coin toss. They have a virtual coin toss page. Kids can turn to technology to complete a coin toss in order to better understand probability. Check it out by clicking here!

Ancient Number Systems- Math 1510

This week in my Math for Elementary Teachers online course we read an interesting article called “Understanding Place Value”. This particular article was about three elementary aged students who were just beginning to learn about ancient number systems, in particular Egyptian and Mayan number systems. The goal of teaching these students the ancient number systems was to help strengthen their understanding of place value. The very beginning of the article discussed the fact that many students do not have a firm grasp on the concept of place value. Once I realized that I would be reading about Egyptian and Mayan ancient number systems I was a bit put off. I didn’t really understand why we would want to teach these concepts to students in the year 2011.




After reading the article my mind started to change, with the key word here being started. I still wasn’t totally convinced that learning the ancient Egyptian number system was going to help young students learn our place value system. Later in the week I was working on my chapter homework and exercises came up involving ancient number systems. As I started working through them I became even more convinced that learning about ancient number systems could be beneficial. I enjoyed using the Egyptian number system in particular. It was easy for me to figure out and I understood the place values. Then I started thinking about how these could be applied to a younger student. As a 21 year old college student, I feel I have a better understanding on place value than the average 2nd or 3rd grader. Instead of simply wondering how children would handle, I went to find out for sure. I had my younger cousin, who will be a 4th grade in the Fall, come over and talk with me. I showed her my homework questions and asked if she had any idea what it was. She immediately started telling me what it was, how to do, and what it meant. I was completely shocked! I had no idea that she had learned this. I then asked her if learning this type of math had helped her understand our numbers more. She thinks it did. After learning the Egyptian math she was able to understand that when she sees the number 342 for example, she knows that the number 3 means that there are 3 groups of 100. After all of this I felt convinced that learning even the basics of ancient number systems is something that could be beneficial.

Really when it comes down to it, if learning ancient number systems can help young students understand place value even a little bit more, then it is worth teaching. In the words of my cousin “that stuff was fun”. One of the most important things in teaching is being able to grab the attention of the students. The Egyptian number system is fun and attention grabbing. Instead of writing numbers, students can draw little pictures. Not only can it be taught in a math class, but it could be taught in a social studies lesson when learning about ancient civilizations.

I found a really cool website that has information about Egyptian numbers. This site has interactive games as well as other historical information about Egypt. Click here to check it out!

E-Manipulatives: Graphs- Math 1512

This week in Math for Elementary Teachers 2 we worked with e-manipulatives that focused on different ways of graphing things. We worked with graphs such as pie charts and bar charts. Working with graphs and interpreting them is something that people can always practice. Graphs pop up quite a bit in our day to day lives and it is always important to understand them.

One thing that is great about working with graphs in the elementary classroom is that the lesson behind it can easily be turned into something that is relevant to the lives of the students and can be spiced up to grab the attention of the students. One of the more common graphing activities that I have encountered has been using candy of kind to create a graph. Providing a handful of M&M’s and asking students to graph the number of red ones or green ones is something that I have seen many times. It can also be applied to students themselves and graph things such as height, color of hair, or anything physical about the students. Like I mentioned earlier understanding graphs are an important mathematical tool. Graphs are found everywhere in the math world as well as the real world. When students are watching the news or reading the latest Seventeen magazine, chances are there will be a graph of some kind.

One of the interesting things about graphs is that they can be used in all kinds of different educational settings and subjects. Obviously they would be found in a typical math class, but what about other subjects? I have seen graphs in science classes, history classes, language arts classes, family and consumer sciences classes, and many others. The fact that graphs are in all kinds of subjects makes it even more important to be able to read them and interpret them.



I came across a great website filled was various e-manipulatives that have to do with geometry. The website has categories of e-manipulatives from young students all the way through high school students.

Different Math Curriculum- Math 1510

During the first week of class we watched a series of thought provoking videos. One of these videos is titled “Math Education: An Inconvenient Truth” and can be found below. This video was not only informative for me but also brought back a lot of memories of my elementary school math experience.



During elementary school my classmates and I were taught using the Everyday Mathematics curriculum. I can clearly remember being very frustrated with math. I can remember doing the work that was required of me but not understanding why I was doing it or what it meant. If I had to apply it in a setting outside of school I won’t know when or how. By the end of elementary school my math skills were not where they should have been. By the time I reached middle school and high school math I was so lost. There would be times when I would be working on homework and I would get so frustrated that I would almost start to cry. To this day I still struggle with multiplication and other basic math facts that I should know.



After watching this video (and others) I have come to realize that the choice of what type of math curriculum should be used doesn’t simply come down to traditional or reformed. The ultimate choice is a math curriculum that lies somewhere in the middle. Both extremes of math curriculum have their benefits. The reformed math curriculum forces students to think on their and become creative problem solvers. The traditional math curriculum teaches students the valuable skills that they need and keeps things simple. A mix of these approaches would be the most beneficial. If students have the most basic skills mastered, understand them, and can apply them, then they can begin to work on more abstract and creative problems.

For more information on Everyday Mathematics please visit The University of Chicago School Mathematics Project: Everyday Mathematics.

A Coherent Curriculum- Math 1512

During this first week of class we read an article called “A Coherent Curriculum: The Case of Mathematics”. This article really made me think about curriculum that is being used and what I could do as a teacher. The article opened up with a great analogy:

“Consider the agricultural prospects of two countries: In Country A, the nation takes the best that’s known about growing crops and translates it into clear, coherent, manageable guidelines for farming. These guidelines are distributed to all farmers in the country. Further, Country A makes available to all farmers up-to-date tools (tractors, balers, harvesters, etc.) and training on how to use these tools that allow them to implement the wisdom contained in the guidelines. Just as in any other country, some farmers have inherently greener thumbs than other; they find ways to surpass the guidelines and cultivate extra-rich cops. But the broad availability of the guidelines and tools puts a floor beneath farming quality. As a result, the gap between the most and least-effective farmers is not very great, and the average quality of farming is quite good. Moreover, the average quality slowly increases as the knowledge of the best farmers is incorporated into the guidelines. In Country B, the situation is very different. States, and sometimes towns, assemble a list of everybody’s favorite ideas about farming. The list is available to any farmer who seeks it out, but it’s up to the individual farmers to develop their own guidelines based on the list. The ideas are interesting, but there are too many ideas to make use of, no indications of which ideas are the best, and no pointers on which ideas fit together with other ideas. Plus, using the ideas requires tools-and training about how to use the tools. Few farmers have ready access to either. The result: A few particularly skilled farmers in Country B figure out how to farm productively. They are mainly the farmers in more affluent areas-they have been able to attend great local agricultural schools and can afford the tools suggested by their training. A few additional farmers-those with a special knack-do fine anyway, despite their lack of training and use of poor tools. But most of Country B’s farms aren’t particularly efficient, certainly not in comparison with Country A’s. In Country B, the gap between the most-and least-effective farms is huge, and the productivity of the average farm is far less than its Country A counterpart.”

When I applied this same analogy to teaching it makes a lot of sense. Why wouldn’t we have some sort of guidelines for everyone to use when it comes to what to teach? There is tons of information out there available to teachers and at times it can make it very overwhelming. Now bring in a new teacher. They may have the necessary knowledge they need to teach students, but how do they sift through all of that information to bring together effective lessons. Having a unified curriculum for everyone throughout the country would be very beneficial. It gives teacher the push in the right direction when it comes to planning and all students have been given the same learning opportunities. The thing to remember is that having a coherent curriculum isn’t taking away a teacher’s freedom to teach how they would like. An individual teacher can still pick and choose what activities they use in their classroom.

As a new teacher, I am not going to have a lot of say when it comes to curriculum choices across the district, state, or country. I am sure that there are many current teachers out there right now who feel the same way. The question that comes to mind is what can I do when I first step into my own classroom? One of the solutions that can to my mind is working within the school to create our own coherent curriculum. Not only can I work with my own team of teachers but I can work with the other teams of teacher that make up the other grades in the school. If we can all create our own coherent curriculum, at least at the school level our students will be taught consistently.

I came across an interesting article. Timothy D. Kanold, Ph.D. discusses a coherent curriculum. He is the Superintendent of Adlai E. Stevenson High School District 125 Lincolnshire, Illinois. Stevenson is the only high school in the state to receive four Blue Ribbon Awards for Excellence in Education from the U.S. Department of Education. He must have a good idea of how to implement a coherent curriculum and it is obviously working well. Check out the article by clicking here.

Welcome- Math 1510 and 1512

Welcome to my blog! This blog is all about my experiences and the knowledge I gain in the classes Math for Elementary School Teachers 1510 and 1512. These classes are crucial to my success as an elementary school teacher. Throughout the semester I will be posting about things that I have learned during the week, favorite educational blogs and websites that I have come across, and images and videos that relate to the topics that I have written about. Talk to you soon!