Brady 4.1 (g)

Activity 4.1 (g.)- Dyscalculia Readings

1.     One Fish, Two Fish, Pretzel Fish

This article discussed how a mathematical consultant and two teachers used the capture-recapture statistical estimation method and the lesson organizer routine to promote mathematical understanding. As a collaborative team, they taught students advanced mathematical content and skills. They used research-based strategies and student engagement to promote student learning.

They started off by reviewing data in terms of learning characteristics and skill levels. They extensively examined informal and formal records. They took this data and compared it to district guidelines. Next, the mathematical consultant recommended supplementing curriculum by using the capture-recapture method. To grasp this method, the teachers exposed the students to an activity introducing the concept of ratios and proportions. Calculators were provided to help with this activity, as well as exposure to real-world situational data. Cooperative learning, specifically through the use of group projects, was also implemented.

Lastly, the team implemented a lesson organizer routine, a routine that allowed the teachers to present the material in an organized format specific to student needs.  It created clear set guidelines and goals for the classroom using linking steps and review. From this process, student mathematical scores increased on average from 10 to 20 points.

2.     Connecting Math and Science for All Students

This article stressed using systematic connections between mathematics and science through the use of hands-on activities, problem solving experiences, and word problems. There were three different activities used explaining how teachers can combine the two subjects. The first activity was based on the concept of the multiplication/ division relationship and the scientific concept of force. It was hands-on which promoted student involvement. The second activity was focused on ratio and measurement. It called students to do several scientific experiments and record the results from the experiments. They were tally up and explain the ratio following these activities. The third activity explained the concept of proportions by requiring students to compare different objects with similar and different masses. A chart was used to document and compare these differences. All three of these activities were hands-on and interactive for the students. They were active participants using mathematical and scientific concepts concurrently. Doing so led to great understanding and practice.

3.     Teaching Students Math Problem-Solving Through Graphic Representations

This article explained how using graphic representations helps students with learning disabilities become better mathematical problem-solvers. Using a graphic representational technique, teachers can better support students in problem-solving skills. In order to implement this technique, teachers must follow and teach students several phases. Phase 1 is problem schemata identification and representation. The key aspects to this phase are for students to identify features of a problem and organize this information in a schematic diagram. Phase 2 calls for the actual problem solution. This calls students to select a plan to use the necessary operations, procedures, and steps to solve the problem. Once they have done this, they solve the problem. Finally, to ensure the success of this technique, teachers must remind students to go back and make sure they followed all the necessary steps to solve the problem and to double check their answer is correct. This strategy instruction is very structured and organized for all learners and boosts confidence in mathematical problem solving.

4.     Math Journals Boost Real Learning

This was my favorite article of the four I read, because I plan on using math journals now in my classroom. Math journals have many uses. They can be used for note taking, journaling experiences, writing problem solving stories, or class assignments. This article also gave several motivating ways to get students to write. These included problem solving, process prompts, language experiences, and classroom discussions. It also explained that journals can be used daily to once a month depending on the teacher’s preference. I know in my classroom, there often is a lot of anxiety and frustration accompanying new mathematical concepts. Giving students opportunities to voice these frustrations and communicate to me their learning needs would make more patient and empathetic as a math teacher. Consequently, my math curriculum would be more specific and helpful to all my students’ mathematical learning needs. 

Brady- 4.1 (f.)

Activity 4.1 (F)- Assessment Questions

1.     Name and describe the components of high-quality math instruction.

High-quality math instruction involves:

a)    A standard-based curriculum

·       Content and skills important for student learning

b)    An evidence-based instructional strategies

·       Effective research-proven strategies for teaching children mathematical concepts and skills

c)    Implementation with fidelity

·       Curriculum implemented according to researchers or developers’ intentions

·       Teacher training is necessary

·       Adherence to instructional procedures

·       Implementation required according to recommendations and time requirements

·       Instructional procedures skillfully implemented

2.     List all of the NCTM content standards and process standards and define the difference between the two.

Content Standards                                                            Process Standards

1) Number and Operations                                                1) Problem Solving

2) Algebra                                                                        2) Reasoning and Proof

3) Geometry                                                                        3) Communication

4) Measurement                                                            4) Connections

5) Data Analysis and Probability                                    5) Representation

Content standards are standards that focus on knowledge to acquire; whereas, process standards are ways to learn and use knowledge.

3.     View the video clip below and identify the evidence-based teaching strategy being implemented. Additionally, identify any effective classroom practices being used. Describe how each helps to build conceptual understanding of the topic being taught.

In this video students were to find the area of a shape. Several evidence-based teaching strategies were being implemented. Peer tutoring was going on in which two students worked together on this activity and each took turns helping each other. There also was cooperative learning happening wherein students were working to solve a problem together. The teacher provided the students an opportunity to work in groups to solve a problem they just learned about, in other words providing independent practice. They used a hands-on visual aid drawing they could write on to help solve this problem. After the teacher gave ample time to solve it, she came to each group, checked for understanding and praised the students for breaking down the problem into simpler steps, aka numbering. These steps helped students understand the topic effectively by making them active participants in the problem solving process.

4.     Of the effective classroom practices discussed in this module, select two.

a.              Describe their importance for teaching math.

b.             Discuss how you plan to use those practices in your own classroom.

Peer tutoring calls two students to work together on an activity. The students’ ability levels can be the same or vary. Research has proven that using peer tutoring promotes math learning. It gives each student involved an active role in their learning. Children receive positive reinforcement from this practice and it provides verbal interaction between students. Allowing this in the classroom provides the teacher more opportunities to check in and meet the needs of all students. I plan on using peer tutoring in my second grade classroom, specifically during more abstract concepts like making change in money, measurement activities, and complex word problems.

Another effective classroom practice discussed in the module was cooperative learning. Cooperative learning uses small heterogeneous groups (or groups of varying abilities) to increase mathematical learning. Students can discuss mathematical problems allowing understanding to start from the concrete level and progress to a more abstract level. Social skills improve through the use of this practice. Motivation, time on task, and self-esteem are also increased. I will use cooperative learning in class during my study guide and review days. Typically we have a two-day review period before a math test. I feel using cooperative learning will allow me to meet more individual needs. My higher mathematical learners will be able to reteach concepts taught earlier in the week to students who need extra support.

References

IRIS Center. (2010). Retrieved on April 15, 2011 from

http://iris.peabody/vanderbilt.edu/math/chalcycle.htm

Brady- Activity 4.1 (a. & e.)

Activity 4.1 (A & E)- Aligning with Mathematical Principles

Chapter 14, Mathematical Difficulties, explains why and how children learn math best. It goes into further depth expressing that some students with learning disabilities have great challenges learning mathematics. In this chapter, it gives several different strategies and accommodations to help and support not only these students, but also all students in mathematics. In this chapter, it recommended teachers align with several principles. Lerner and Johns (2012) listed these principals to include: early number learning, transitioning form concrete to abstract, providing opportunities for practice and review, helping students generalize concepts and skills learned, and teaching mathematical vocabulary (p. 468).

I watched three different videos in which instructors used several strategies, accommodations, and principles aligning with chapter 14. The first video I watched was entitled, “Addition and Multiplication Practice.” In this video, the speaker (“Math Tutor”) took the viewer through the mathematical steps in the addition and multiplication process. He started at the basics or concrete steps and took the listener into more complex or abstract steps. He solved two different problems, the first one easier than the second. The instructor in this video provided ample practice and transitioned from an easier problem to a more complicated one.

The second video I watched was “Elapsed Time.” Mr. Binkley, the teacher in the film, used a graphic organizer to solve an elapsed time problem. Specifically, he used a T-chart to organize the problem. He broke the problem down into steps, by starting with the basics and progressed to the more advanced steps. For example, he added the hours first and then he went by minutes, adding by tens and then by ones. Once the T-chart was set up he added up the column and solved the problem. Throughout the lesson he checked for understanding to ensure the student was grasping the concept.

The last video I watched was “Addition and Subtraction Problems on a Number Line.” Mucho Math taught this video. The instructor in this video took a complicated pre-algebraic problem and simplified it by using a number line, another graphic organizer. He explained that when simplifying expressions in math, students must work left to right. Throughout the video he stopped throughout the problem and also checked for understanding. He defined mathematical vocabulary as he solved the problems. He also provided several opportunities for practice.

All three of these videos implemented wonderful strategies to help learners be successful and confident when doing math. The instructors used several of the principles recommended in chapter 14. I especially enjoyed the second video of teaching elapsed time using a T-chart. Using a graphic organizer to break down an abstract problem like elapsed time is a wonderful strategy I can and will use with all my students.

References

Lerner, J. & Johns, B. (2012). Learning Disabilities and Related Mild Disabilities (12^thEd.). New York, NY: Cengage Press.

Math Vids. (2010). Retrieved on April 15, 2011 from

http://www.mathvids.com/nctmstandard/showlessons/1.com