Error Analysis

I believe that the error analysis activities were the most beneficial thing we have done in this class. Prior to taking this course, I would have checked the answers to see if they were either right or wrong. It had never occurred to me that there are patterns in the errors that are made. I never realized how much I could learn about students in my class just by analyzing the errors they made and determining where they did not understand the concept. It is important for teachers to spend time and consider the educational needs of each student. I also learned that I am able to make notes on different concepts that I may need to spend more time on the following year.

I thought it was beneficial to me, as a future educator to know different strategies for solving addition, subtraction, multiplication, and division problems so that I am able to instruct students with various techniques depending on their knowledge and competency with each mathematical skill. Before the error analysis activity, I hadn't really realized how often students can trip up on multiplication problems that I find to be pretty simple.

Technology

Technology has been used throughout this entire course in many different ways. We discovered and used a Wiki to collaborate as a group and complete projects electronically. We then learned how to use a GoogleDoc when working on a group project. We also used math applets and learned how they can benefit students. The SmartBoard and computers were used throughout the course as well.

I thought that the use of the different types of technology throughout the semester was very beneficial. I am naturally comfortable with using technology. I enjoy knowing how technology works, and how to fix or resolve any problems or questions someone is having with technology. I thought it was interesting to use a new technology for an assignment. Some may have been frustrated when learning to use new technology. I feel that the use of technology in this class is beneficial to me as a future educator. It is important to incorporate technology in the classroom very often. I believe that it is important for teachers to have a full understanding of the technology they are assigning their students to use. After having the opportunity to use Wikis, GoogleDocs, math applets, a SmartBoard, and other technology used in the class, I have more of an understanding of what technology tools should be used in certain situations.

Prior to this class I had used a SmartBoard a few times in high school. I always thought that a SmartBoard was an awesome tool to have in the classroom. Throughout the semester, we used the SmartBoard in almost every class session. I learned so many things about what a SmartBoard can do, and how they can be used by the teacher and students to aid in the students' learning. Before I began this class I would have never thought of using a blog, Wiki, GoogleDoc in my classroom. I didn't really know what a math applet even was. This class has taught me of many different ways that technology can be incorporated in the classroom to aid the students.

"Graphing Calculators as Tools" - Mathematics Teaching in the Middle School

Browning, C. A., & Garza-Kling, G. (2010). Graphing calculators as tools. Mathematics Teaching in the Middle School, 15(8), 480-485.

Graphing Calculators as Tools includes several graphing calculator activities and focus on what we believe are four powerful ways to use this technology as a tool to explore mathematical idea:

1. Collecting or generating raw data
2. Examining multiple cases
3. Providing immediate feedback
4. Showing graphical and numerical displays

Teachers can use these ideas effectively through TPACK (technology, pedagogy, and content knowledge). The interconnection and intersection technology, pedagogy, and content knowledge. The article discussing different ways of investigating algebra through the use of graphing calculators and technological tools. Students use graphing calculators and stand alone motion detectors to investigate linear relationships and other functions. Students can make connections to positive and negative slope. The accessories available for graphing calculators allow students to physically investigate linear relationships and functions with motion sensors. The calculator they creates a graph from their movement. Students can then analyze the graph of their movement. Students investigate geometry and measurement using the SMILE application. SMILE has the potential to strengthen students' understanding of angle and angle measure. Students also use graphing calculators to investigate data analysis and probability. Students can use the graphing calculators to use probability simulations where they develop estimates of experimental probabilities for the problems they are interested in investigating in a more efficient way that using traditional tools.

I thought that this article was very helpful and useful for classroom teachers. I liked that the article provided a multitude of activities that use graphing calculators. I also liked that the article included activities that utilized different graphing calculator accessories with the calculator. The accessories available for graphing calculators allow students to strengthen prior math skills/knowledge, as well as learn new mathematical skills and concepts. The article is useful to classroom teachers because it specifically explains how certain applications on the calculator can help students grasp a deeper understanding of mathematical concepts and skills. I thought that this article presented very interesting and engaging activities, but it is very expensive to purchase enough graphing calculators for the class. Even if only a few calculators were purchased, the cost of the applications and accessories used in the activities are also costly. I liked that the article addressed how the activities and math skills explained in the article to the NCTM Content Standards.

"Supporting Language Learners" - Teaching Children Mathematics

Brown, C. L., Cady, J. A., & Hodges, T. E. (2010) Supporting language learners. Teaching Children Mathematics, 16(8), 476-483.

Supporting Language Learners is an article that describes many different instructional practices that will help support English learners. The article begins with a heading stating "incorporating these instructional practices for two math tasks into lessons to support English learners to an excellent, equitable program." The strategies described in the article are not exclusively for English learners, and regardless of their cultural background the strategies can provide support for all students. The strategies are grouped in two main categories: strategies to support English language acquisition and strategies to promote low-anxiety classrooms. Linking new concepts to past experiences is beneficial to students. There are advanced organizers that help language learners make that connection. Expository and comparative are the two forms of advanced organizers. Developing students' vocabulary by identifying words that might cause confusion for the students and address the words during the lesson. Teachers should use visual cues to help students develop their vocabulary. Visual cues include diagrams, props, photographs, drawings, models, and real-world objects. Make sure to adjust your teacher talk. Repeat important explanations and directions to improve ELL's comprehension. Slow down when speaking, but not so much that it sounds unnatural. This is the most simple and most helpful strategy for ELL students. Simplify sentence structure, be consistent with words and phrases when giving directions. The article then provides an example of two tasks that utilize the first group of strategies. The second category is strategies that promote low-anxiety learning environments. Teachers should use predictable routines. Use signals to indicate the close of one activity and the beginning of another to aid students in understanding expectations. Contextualize when giving directions. Simultaneously using physical demonstration with verbal explanations help language learners understand. Language learners appreciate peer help and support, and the volunteers feel a sense of satisfaction in helping. The teacher should provide guidance to the volunteers and distribute responsibility in the group.

I thought this article presented very helpful information that would be useful to a classroom teacher. I thought that this article presented information that was very general and could be applied to all subjects and in a lot of different situations in the classroom. I was somewhat disappointed that this article did not relate to mathematics instruction more specifically. I have learned about these strategies in prior classes. I liked that the article included a list of words, relating to mathematics skills and operations, that cause confusion in ELL students. It was helpful to see the strategies used in the examples provided in the article, even though they were very basic.