Multiple Methods in Math (1510)

Thinking back to some of my years in grade school, I remember how overwhelmed I became during math class when I saw how many different approaches there were to a math problem. It seemed as though the class was shown how to solve a multiplication problem one way, and then the next day we were introduced to a whole new method. Learning numerous methods to solving a math problem had its ups and downs.

Everyone likes options. If you can't seem to grasp the first method, there will always be another method to fall back on. Every student is an individual and unique learner. It is great to provide students with options to choose from.

Providing too many options for students can also have it's downfall as well though. If we were to show students all of the methods to solving a multiplication problem, I am not too sure that they would be able to distinguish between them all after awhile. Maybe there is a happy medium, where teachers can provide their students with options to choose from, but not all of the options. I found one great website that shows videos and describes a few different approaches for addition, subtraction, multiplication, and division. Everyday Mathematics Methods

Analyzing Data (1512)

Last week I had the opportunity to learn more about analyzing data. This included different types of data displays, relationships, averages, and decision making. The section that I found to be the most interesting to me was on data displays.

I was amazed to see all of the different ways to display data. There are frequency tables, dot plots, bar graphs, histographs, circle graphs, and so many more. I began to remember learning about many of these data displays when I was in grade school. With all of the different types of displays, I wonder how students are able to keep them all straight when they are introduced in a single section.

When teaching a unit on data analysis, I think it is important for students to be introduced to the different types of data displays, while also learning how to read them. If you know how to read the information being shown, you can understand and describe relationships within the data, as well as the spread of the data.

Probability (1512)

Probability is the measure of how likely an event is going to occur. While going through many of my textbook chapters, I find it hard at times to relate what I am learning to the real world. I amazed at how many connections I have been able to make between probability and my own life experiences.

An experiement is a scenario involving probability that leads to outcomes or results. An outcome can be described as the result of a single trial of an experiment. To find the probability of an event, the following formula can be used:
              

Probability Of An Event

P(A) = The Number Of Ways Event A Can Occur The total number Of Possible Outcomes

Many probability problems involve the use of cards, dice, marbles, coins, and spinners. These items work well to represent sample spaces and outcomes. While working on many of the problems in this chapter, I found drawing out a tree diagram to be the most helpful in many scenarios. This diagram allows you to layout and see all of the outcomes in the sample space.

Take some time to practice probability!

Estimation Skills (1510)

Teaching students how to use estimation in relation to math has several benefits to their education. According to The National Association for Child Development, “teaching your child how to use estimation in math can significantly improve their learning curve.” Estimation is also a great way for students to think about, access, and apply their previous learned math knowledge.

Estimation skills can be useful throughout all years of an individual’s life. Shopping in the grocery store you may need to estimate how much your bill is going to be. Estimation also relates to distances and time. For example, you have to drive to a location and be there by a specific time. Most likely, you will estimate how far you are driving and how long it will take so that you know when you have to leave.

There are some great ways to incorporate practice of estimation skills into everyday math lessons. Two that I have come across are interactive games, and printable worksheets. I hope to use many resources such as these in my future classroom.

Base-Ten Blocks (1510)

Base-ten blocks are a great math manipulative that can be used to help students add, subtract, and understand place value. The blocks come in four different sizes as shown in the photo above. Common names for the four different sizes are blocks (1,000), flats (100), longs (10), and cubes (1).

Another use of base-ten blocks is seen during the act of trading blocks. It is important that students understand that one block is equivalent to ten flats, one flat is equivalent to ten longs, and one long is equivalent to ten cubes. Students will become familiar with trading base-ten blocks in order to have the appropriate blocks when representing a number.

I have whitnessed base-ten blocks being used in classrooms a few different times. I was surprised how effective they were in helping students understand place value, addition, and subtraction. The students also seemed to be much more interested in what they were doing, because they were actually working hands on with the blocks. However, I did observe one downside of the blocks with a few students; they were more interested in building with the blocks than using them for math.

Math 1510/1512

I am two weeks into the classes Math for Elementary Teachers 1 & 2. I am very excited to be taking these classes because I feel as though there is so much that I can learn from them. I have started to build a math knowledge base from the chapters in the textbook, while also taking part in class discussions regarding various topics.

Classes such as these are very important and beneficial for individuals such as myself, that are pursuing a career in education. Educators have to know and understand what they are teaching, as well as how to go about teaching it. There is much more than a single characteristic that makes for effective teaching, and I hope to learn about many and put them all together to use today and in my future.

One excellent learning tool that I have had the chance to work with in both of these classes already was emanipulatives. Seeing as this is an online learning class, many of us are unable to work with actual models, blocks, tiles, and other objects in order to explore and solve math problems. The emanipulatives is a sort of virtual manipulative, or the next best thing. It has really helped me to visualize a math problem when I am solving it. There are many great math manipulative websites out there for students of all ages to use at home or even in the classroom.
Here is a link to one of them: http://www.mathplayground.com/math_manipulatives.html