Blog #20: Manipulative Reflection

1. How do you know students deepen their understanding while using manipulatives?

In order to know if  students are gaining understanding through their use of manipulatives is to give students pre and post assessments before and after working with the manipulatives. These assessments can either be formal or informal. For example, if students are using the pattern blocks for the identification of the properties of shapes, the teacher can verbally ask students how many sides, what are the sizes of the angles, etc. about each shape both before students work with the manipulatives and after. If students perform significantly better on the post test, the teacher knows that the work with the manipulatives was effective.

 

2. How do you know if the students can transfer their understanding from manipulatives to other situations?

The teacher will need to provide students with multiple situations in which students can use and transfer their knowledge . These multiple situations should include real-world, higher order thinking problem solving. For example, students are working with the snap blocks to create bar graphs based upon data they collected from the following poll: What is your favorite sport? Students collected the data by asking several classes within their school and then created their graph using the different colored snap blocks. The teacher, to see if students can apply their newfound knowledge, asked students the following questions: 1) Which sport did the people like the most? 2) Which sport did people like the least? 3) Was there any sport that you were surprised did not make the list? 4) What do you think is the most popular sport in the country? Using this type of questioning, students can analyze the information they collected and then expand upon it.

 

3. How can you assess that understanding or growth?

Assessment for working with manipulatives can be informal or formal. As long as the teacher tests students before and after they work with the manipulatives, the data collected will show student progress. For example, students can be asked to use the cuisenaire rods to set up addition and subtraction problems. The teacher will walk around to students desks and make a checkmark on a checklist for students who have accurately solved the problem. Students can be evaluated based upon the number of problems they got correct in comparison to the total number of questions.

 

4. When students work in groups, how do you hold each younster accountable for learning?

I am a firm believer on providing students with individual roles when working in groups. Each student should receive a designated duty to perform while within the group so that the group completes the assignment accurately and on time. Student duties could include recorder, time keeper, material runner, leader, etc. The student roles will largely be determined by the type of activity. The idea is that students are holding one another accountable for completing the work of the entire group. If one person does not effectively fill their assigned role , then the work of the entire group suffers. This creates positive peer pressure for all students to pull their own weight within the group.

 

5. When students work in groups, how do you assess each younster's depth of understanding?

Student depth of understanding can be assessed by asking students to take turns answering questions within their groups. In other words, students should each be responsible for a specific question in which they can utilize their group members if they do not understand the question or do not know the answer to the question but ultimately it is their responsibility to answer the question. The teacher, while asking the questions, can keep track of student responses on a simple chart that contains student names. Additionally, students can be asked to individually write out their reasoning for answering a group question individually. Therefore, they may write phrases such as, "Our group decided to start by…", or "Our group decided on this answer because…". In this manner, students are responsible for their own understanding of the work of the group and teachers can use their written explanations to assess understanding.

 

6. How are you improving students' problem solving skills with the manipulatives?

It is often easier to understand a concept by visually representing the concept. Manipulatives allow students to visually represent a variety of different types of problems. Unlike two dimensions drawings, manipulatives provide students with tangible materials to hold in their hands and to manipulate. 

Blog # 19: Curriculum Plan Reflection

When I first read over the requirements for the Curriculum Plan, I was extremely nervous. The task that lied ahead for my group and myself seemed daunting and overwhelming. However, once my group and I began working on the project we realized that it was not as scary as we originally thought. After the first work day in class, we were able to get a significant portion of the assignment completed and our progress continued from there. After the final work day in class, our group decided to split up the workload in order to finish the assignment and begin filming the video. Each group member completed their portion of the workload by the deadline decided upon by the group and we were able to film on the final meeting day.

I was very satisfied with the final result of our curriculum plan project. We were able to create a complete and thorough curriculum plan for three years. We determined the most logical method of separation was by dividing our curriculum plan based upon how the common core standards were arranged. The standards of the same categories were kept together and we combined each semester based upon the two larger standard categories that best aligned with one another. In the end our curriculum plan was logically organized and would be successful in a real classroom.

Blog #18: Technology Blog

The technology that was the most useful from this class was the SMARTboard presentations. The SMARTboard is one piece of technology that has been neglected in our Bradley education, in my opinion. We have received some instruction here and there when questions have come up or a classmate has used the SMARTboard in a presentation but nothing much beyond that. It was nice to be able to learn more about the special features of the SMARTboard and to practice doing them in class. Most of the teachers that I have met in the field do not use the SMARTboard because they have not been taught how to use it. In one experience, I asked to use the SMARTboard to teach a lesson and the teachers did not know how to turn it on! I think we all need several opportunities or seminars to be taught and to practice with the SMARTboard, so that all teachers can make use of them in the classroom.

The videos that we watched online of teachers presenting mathematics lessons were useful to generate ideas on how one might possibly teach particular mathematics lessons. However, the teachers who were in the videos did not use technology at all in their lessons! They used the traditional paper and pencil types of methods instead. Therefore, I was highly disappointed after watching them. If I were to teach those lessons as did the teachers in the videos, I would not want to be a student in my classroom. They not only lacked the use of technology but student engagement and participation as well. The videos on that website need to be updated with teachers teaching fun, engaging, and authentic lessons.

Finally, we also researched math apps and applets in this class. I researched a map applet, a graph applet, and a counting app for middle school and grade school students. Out of these applications, I think the map applet would be the most useful because it can provide students with a great deal of statistical information in which they can use to perform a variety of calculations. The graph applet can be useful for helping early elementary students learn how to create basic graphs and the counting game can be a great reinforcement tool for young primary students learning to count as well.

Blog #17: Assessment in Math Reflection

Assessment in Math Reflection

                Teachers should take great care when creating assessments for their students. They should expect to make numerous revisions to their assessments. After each time a teacher gives students an assessment, the teacher should use student work to determine if there are any problems or bias within the assessment and revise it if necessary. Assessments should be as objective as possible. Additionally, teachers should make sure the directions to the assessments are written very clearly and are as specific as possible. The key to an effective assessment is continuous reflection on the part of the teacher.

                There is also the issue of asking students to evaluate the work of their peers. Can students be as objective as possible when evaluating the work of their peers, if students are not experts in the concepts they are assessing? The general consensus of teachers is that students cannot be objective and therefore should not be asked to evaluate the work of their peers. If the teacher believes students will gain insight by assessing the work of others, teachers should only ask students to critique the work of their classmates and the teacher should be responsible for providing the numerical score based upon student feedback.

Blog #16: Error Analysis Reflection

Error Analysis

            Student errors can be useful tools for teachers to determine how to tailor their curriculum and instruction to meet the needs of their students. Student errors reveal where previous instruction failed and where further instruction is needed for students to grasp important mathematical concepts. It is often the case that students understand the general premise of how to calculate particular problems but continuously make the same slight errors that cause them to get the wrong answers. For example, a student can multiply numbers correctly but position the products in the wrong place values and therefore get the wrong answers. Another example occurred when a student divides correctly but is dividing the wrong numbers and calculates the answer incorrectly. Teachers need to practice locating errors from student example problems and determining the necessary skills that need to be retaught in order to effectively aid students in learning mathematical skills.

Blog Post #15: Problem Project Reflection

Problem Project Reflection

 

The most difficult aspect of the problem project was integrating three separate content domains within a single project. As my group was brainstorming ideas, we each could come up with multiple projects to assess our particular content domains but found it difficult to create a project that incorporated all three domains. Once we decided upon a project idea, it was significantly easier to complete the remainder of the requirements for the assignment. My group members and I finished our assignment relatively quickly and it would definitely be a project that I would use in my future classroom. As a student, I loved assignments that enabled me to be creative and to create or build final products at their conclusion. This project will gain student attention and keep them engaged throughout its entirety. 

Blog Post #14: Content Standards

Supplemental Material Needed:

                The selected textbooks I reviewed for grades 6-8 are fairly standard textbooks. The information within the textbooks were generally more concrete, knowledge based questions with a so-called “application” section within each chapter. What these textbooks and those similar to them really need are more high order, open-ended types of questions that apply to students real lives. Many of the application sections discussed ideas that were not relevant to the lives of middle school students and typically included a short paragraph describing how a professional uses math in his or her everyday life. Additionally, the majority of the standards that addressed making connections between concepts were not covered in these textbooks. The textbooks included the concepts separately but did not attempt to build connections for students.

                The textbooks for the other grade levels assessed by my classmates, were similar to those I assessed for the middle grades. In general, the textbooks only included the skills of the content addressed in the standards but lacked application and review. In many circumstances, the standards were not addressed at all in the textbooks. This is further evidence that the textbooks that are currently in schools are outdated and do not correspond to the new Common Core standards.

 

Concept Development:

                There was very little differentiation within the textbooks themselves that showed the differences within the grade levels. All three textbooks had similar topics covered throughout the entire book. It can be assumed that each of the concepts covered gradually increase in difficulty as students’ progress from grade level to grade level. The standards, however, do not include a great deal of overlap as do the textbooks. Students will need to understand the 6^th grade content listed in the standards before moving onto the 7^th and 8^th grade standards of course, but there is not a whole lot of repetition of common geometry topics from one grade level to the next. The 6^th grade standards focus on area, surface area, and volume; the 7^th grade standards focus on three dimensional objects; and the 8^th grade standards focus on rotations, reflections, and translations. These concepts build upon one another rather than repeat one another.