Becoming a Teacher

In my dreams of becoming a teacher, never did I think I would want to spend my days working on math. I have never been opposed to math, I've just felt more comfortable working with students to become strong readers and haven't spent near the amount of time working on math skills. I was also never a "math kid" so I guess that might be why I have always thought that I was just not a math person until reading an article posted by my instructor. More likely, it was a self-fulfilling prophesy which allowed me to avoid taking time to educate others. I wish I could take all that time back so I could balance the time and effort that I put in to educating children equally. In my research for math websites, manipulatives, activities, methods, etc. I've found so many opportunities that I would have loved to use in past scenarios. When I complete my schooling and have my own classroom, I will be well-prepared for a variety of tasks, skills and other online activities for my students.

One area that I have feared is the process of setting up a curriculum based on the Common Core Standards. In my concern for this, I asked some teachers I work with to give suggestions on how they set up their curriculum and this was a site that was recommended Common Core Curriculum and I'm so glad it was. The site is called TenMarks and even the "free" version is very workable and easy to use. I was able to pick a grade and standard and then find practice problems, assessment tools and strategies to help build the necessary skills to meet the benchmarks. I encourage everyone to watch the demo on the attached link as it gives a great breakdown of how the site can benefit all teachers.

It has taken me a while to reacquaint myself with some of the strategies that I have been learning over the last few months and it makes me wonder how I can coach my students to be the best they can be. One example of this is working with fractions. It has been a really long time since I have had to add, subtract, multiply or divide fractions. Now that I have had to take the time to relearn these skills, I am reminded of some of the gimmicks my own math teacher used when I was in school. For instance, whenever we multiplied fractions (meaning crossing out like terms), she referred to it as "playing Zorro" by crossing out any terms that were similar and reducing fractions so they were easier to work with. We always laughed at her gimmicks but it obviously worked because here I am, 20 years later, remembering how to "play Zorro." I can only hope that when I am teaching my students, that I can be as impressionable as she was to me. In the following example, I am attempting to display how to "play Zorro," as you can see the initial numbers we are working with are two eights, and eight twelfths. Since there are like terms within these fractions, we can play Zorro by crossing out 2 and 12 and reducing them to 1 and 6. The second step is to reduce the 8s to 1s because they cancel each other out. this makes multiplying this fraction much simpler.


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Manipulatives

With tools like the Internet, I have found a plethora of manipulatives online that would be useful in my classroom. In many cases, classrooms are short on supplies, manipulatives and the like. Fortunately, we are blessed to have sources like the Internet, computers, tablets, etc. which provide us with virtual manipulatives. Sometimes these manipulatives may be less "hands on" and don't work as well for certain children. In other cases, for children who are more technologically advanced, these may be more beneficial.

In my recent searching for new ideas besides using just the same old unifix cubes and base ten squares, I thought I'd find something fun and different for my students. I came across this wonderful math Pinterest board by Ruthie Sheppard and it was exactly what I was looking for. She has a variety of websites pinned as well as games, activities or projects the are perfect for the elementary classroom. One board that I found particularly interesting was linked to the website Kids Count 1234
more specifically the Math Centers and Games link which is full of manipulate games and worksheets that you can print off and use in your classroom. I LOVE free printables and this site is full of them. Clear 10 is probably my favorite one on this site (I tried so hard to display this printable but no matter what I tried I couldn't figure it out).

I know that with manipulatives, comes eager children and anxious bodies tend to create problems that can be prevented with high expectations and proper planning. I found this video helpful in the preparation aspect of organizing a classroom for manipulatives and setting expectations with the students from the start.

 

 



One final website I'd like to share with you is K-12 Manipulatives which is full of a activities that have kept my second grade daughter busy for the last week. This site is run by Utah State University and is loaded with math manipulative activities for all ages. These activities would be incredible to use on a Smart Board or other interactive white board device. Some would be perfect for an entire classroom while others would be best for individuals or small groups.

Multiplication

As I continue to reaquaint myself with elementary level math, I am reminded about the many varieties of multiplication. When I say varieties, in referring to the idea that sometimes it's easy, others it's hard, sometimes multiplication complicates things and in other cases it simplifies things. That does not even begin to touch on the ways to solve a multiplication problem. You can put the numbers side by side (2x2=4), you can stack them on top of each other, you can use the lattice, grid or box method or even the Japanese stick method. The hardest thing for me to remember is that the simplest method for me may be much more difficult for someone else. I guess when it comes right down to it, the best method is whatever works to get the correct answer. Sometimes repetition works better for some, such as multiplication facts. Here is a great hands-on website to work on these facts.

Multiplication was always pretty easy for me, but I see students struggle with traditional multiplication on a daily basis because they forget to bring down the zero to start the tens column or the miss numbers when adding the final answer. I though I'd take a little time to reflect on the lattice method for two reasons. The first one being that the lattice method is very new to me. I had only recently been taught this method and I see why math teachers are actively teaching it now days. The second being that it is almost fool proof. I say that with caution because I realize we HAVE to know our multiplication facts on order for it to work so smoothly, but it truly is so simple! You know, I guess it would be okay to have a multiplication chart available for students who struggle with their facts as the bigger goal is to come up with the correct answer, through whatever resources are needed. I attached a video by Khan Academy doing a demonstration of lattice multiplication.

This is one of those methods that can be simplified and easy for the younger child learning multiplication or for the 5th or 6th grader who is mastering the skill.




An example for those new to lattice multiplication

A reproducible worksheet to master the skill

Decimal Places and Rounding

Whether you are six years-old or a sixty-six years-old, place value and especially those with decimals can be quite annoying and unnatural to work with. There are many sources on the web to help with remembering place value and truly mastering it. The following video is fun and would be a great way to get students out of their seats and interactive while teaching this concept. I also asked around to some of my own sources (for instance-my sister, the "math specialist" teacher). ;) She highly recommended this arrow card site as it really gives students the opportunity to create their own numbers and manipulatives while working on place value.

When working on adding or subtracting it is sometimes difficult for students to remember to line the numbers or decimals up correctly. It then becomes even more confusing when multiplying and dividing because they don't always have to be lined up in special ways as long as the end result is in the correct format. I also really enjoy the breakdown of this video to help introduce the decimal places and the value of each place. It would likely be geared more toward 5th or 6th grade students (even though it is a little juvenile), but definitely beneficial. Remembering the difference between terms like tens and tenths, can be difficult.

The www.decimalsquares.com/dsGames/ website has an activity called Place Value Strategy where students can spin a wheel and place a number in the tenths, hundredths, thousandths and ten thousandths place with a goal to make the largest number out of those spun. Students could play this against the computer or they can play with a friend. It would be fun to see how different ages might use different strategies to make the larger number. In many cases it can be frustrating trying to remember the correct place value of decimals, fractions and percentages. One activity that I have found on the web that students can use to help them learn and remember the correct place on the number line is this equivalence activity. It does not allow students to place the number, fraction or decimal on the incorrect place value so students can see their errors immediately and correct them.

Problem Solving Strategies

In the many years that I have taken or taught math classes, the most complicated and often complained about problems, are the word problems. So it's time to pose the question...what can I do to make these problems simpler for my students? There are many strategies out there and we could probably make up some of our own, but I'm going to go with one that I have seen to be effective in classrooms that I have been in and has proven to simplify the wording and complication of these frustrating riddles. The method I'd like to suggest is the CUBE method or in some cases the CUBES method. CUBE is an anagram to help break the word problem down into simpler, more recognizeable, "math-related" terms.

In my research, it appears this method originates from The Teacher Garden where she has used this, along with other methods to simplify problem-solving techniques.

CUBE is broken down into four parts:
C-Circle the numbers
U-Underline the important words in the problem
B-Box the question
E-Eliminate unnecessary information

Okay, to demonstrate this method, let me give an example word problem so I can simplify it through the CUBE method.

While Jamal was at basketball practice his coach asked him to take attendance. He looked around and noticed there were 20 pairs of shoes. Jamal thought that didn't add up because he knew there were 12 players on his team. When Jamal counted everyone he realized there were only 11 people there, including his coach. How many teammates were not at practice that day?

C-If I could draw a circle around the numbers (however blogger doesn't allow this) I highlighted it.
U-I underlined information that might be important
B-Instead of drawing a box around the equation (because Blogger doesn't allow this) I highlighted it.
E-I would eliminate the first sentence, and basically anything that isn't circled, underlined or boxed.
S (if you choose to include it)- Solve and check to make sure the answer is correct.

 

Now, in order for this method to truly work, reinforcement is necessary! You can't just display a picture like this on the wall of your room and think the students will just pick up on it. I have found it most effective to work through mulitple word problems on a daily basis and to revisit similar problems at least weekly. Take the time to coach your students on how to use this method and then push them to try it on their own. Before long, your students will be using this method in their daily work, without prompting.

Math is Confusing!

As an adult, looking back, I have never remembered elementary math being so difficult or confusing. It seems the more I "'re-learn" the more I'm lost. In elementary school, I couldn't wait to work on Roman numerals, fractions, or my favorite-guess and check. I also enjoyed the patterns, riddles and problem-solving worksheets that we got to do on special occasions. Unfortunately, once we started working on problems that I felt were "too tough" I gave up and lost interest in math. In time I overcame these frustrations and I was eventually able to grasp concepts, thanks to teachers who spent a lot of class time (and sometimes before or after school) answering questions and working through problems, step by step. I guess it's important to note, that I am a VISUAL learner. This was most obvious in math as story problems were my nemesis.

Whatever method works.

I have noticed the mathematical world is putting a lot more focus on the properties of addition, subtraction, multiplication and division, than I recall from my own time in school. I currently work in school where the middle school math teacher uses gimmicks in her daily lectures to help her students remember these properties. Since I am not one who memorizes things well and I prefer to read, take notes, and draw clues while studying, I am more apt to remember things that I have gone over time and again. Though I am not as experienced as a teacher who has been teaching math for 20+ years, I hope to come up with some of my own techniques that will make it easier for my students to not only learn, but retain these skills. It is my goal to find techniques that work for everyone, on an individual basis. I recall many classmates who were capable of quickly doing mathematical problems in their head, yet I was the opposite. I was desperately in need of a tool to assist me in solving the problem, whether it be pencil and paper, a manipulative or in some cases, a calculator.

Have fun!

I also hope to help my students develop of love of math. Even I math is not my favorite subject, I hope I can influence my students in a way that might make them love it. I find it ironic that I do really enjoy algebra and more difficult math concepts, as long as I have a formula to go by. In some cases, the more complicated (to some extent) the better. So as I embark on this adventure of becoming an elementary teacher, I hope to learn many things that will make me the best teacher I can be. I look forward to finding websites, activities and other blogs that will allow me to reach out to those who have a better understanding and a comfort level of teaching math to children of all ages.