Overall Use of Technology in the Math Classroom

Using a wide variety of technologies throughout this course has helped open my eyes to the many ways that technology can assist in teaching and learning math. That said, it has also made me more critical of the use of technology in the classroom. It is my personal belief that everything should be done in moderation, especially when trying something new. New technologies should be used in conjunction with old methods that have proven to be effective teaching tools. Students should be learning using math applets, calculators, SMART boards, and other new technologies, as well as more conventional learning tools such as paper and pencil, base ten blocks (physical blocks to pick up in your hands, not on the computer), unifix cubes, and pattern blocks. Using many different learning tools that are both high and low tech is one way in which a teacher can teach to a variety of learning styles and preferences. For many students, the use of technology is motivating, while for others it is frustrating.

More specifically, I think that the SMART board can be a positive teaching tool, though I can think of very few applications of the SMART board that can not be done with other technologies that are more commonly found in classrooms (i.e. projector, overhead, dry erase board, computer). One application that I do see the SMART board as uniquely useful for is the ability to project a graph, make notes on it, and then save the page. One of my main frustrations in using the SMART board is the inaccuracy of writing with the pen. I think it is important to model good handwriting to students, and I can not do this with the SMART board pen.

Making Techonology Work

In this article, 3 authors from Croatia explain why technology is necessary to incorporate into math education and how it can enhance the math curriculum. In summary, technology is beneficial because it enables students to work on more complex, often real-life, tasks, motivates students, and helps students visualize math concepts. However, technology is only useful in teaching when it's use has been thoughtfully evaluated and planned out. The authors described several specific programs and tools and their suggested uses in the classroom. The Geometer's Sketchpad is particularly liked by students and teachers because it allows students to focus more on overall concepts, rather than spending too much time on measuring and computations. Also, the article described a game in which students learn to differentiate when they should and should not use a calculator. Finally, the authors describe various real-life problems that students are able to analyze using various computer programs. Without these programs assistance, these problems would often be too advanced or too time consuming to implement.

I really enjoyed reading this article, as it has brought me one step closer to embracing more forms of technology for use in the math classroom. The article was extremely well written and concise, yet included excellent points and provided useful examples. I particularly liked the game in which students race to see if a computation can be solved faster by using a calculator or by doing mental math. I think that this is an excellent way to show students, rather than tell them, when they should choose to use a calculator as opposed to mental math. However, the idea of racing bothers me, especially the idea of having two students race against each other. What if one student is simply faster than another? This would skew results not to mention likely be the cause of hurt feelings. To alleviate this I may consider having students time themselves with a stop watch doing the problem first mentally, then using the calculator. This would not eliminate being timed, but at least it would minimize competition.

Soucie T., Radovic N. and Svedrec R. (2010). Making Technology Work. Mathematics Teaching in the Middle School, 15 (8), 467-471.

Smorgasbord of Assessment Options

In this article a fifth grade teacher from Virginia explains the importance of student centered assessments which match the "target achievement" or goal. She uses a Virginia Standard of Geometry to focus her example assessments on. Assessment should produce useful information for both the students and the teachers and should influence future teaching. Student centered assessment means that the assessment centers around the concepts which have been learned, instead of what has been taught. Similarly, learning is a process which is scaffolded, and assessment should reflect this by assessing what has already been learned and pointing towards the "next step". Lastly, teachers must carefully choose assessment that provide the most valuable information in the least amount of time invested in assessing.

I most definitely agree with all of the main points of the article. I particularly identified with the point the author made on page 467 that thought the process and products may vary from classroom to classroom or student to student, the content should still remain the same in accordance with the standards. Likewise on page 468 the author outlines how student centered assessment is extremely beneficial in meeting the needs of all students, including those with special needs, those who are bilingual, and those who are gifted. As a special education major, I can see how creating student centered assessment is vital to gaining information which is useful to both the teacher and the student.

Bacon, K. A. (2010). Smorgasbord of Assessment Options. Teaching Children Mathematics.
458-469.

Portfolio Assessment

This article details how two middle school teachers began using portfolios as a way to enhance communication between parents, students, and teachers. The two teachers were looking for a way to emphasize student learning and growth, rather than letter grades. To do so, they designed two lessons on triangles using the "backward" design approach, and approach in which the teacher begins the lesson planning process by determining what they would like their students to gain from the lesson and which standards they will be meeting. The teacher then goes on to determine how they will assess the student and finally creates a procedure in which to teach students the material. After the two lessons on triangles were completed, students created portfolios, showcasing their work. The portfolios included a letter to their parents explaining their learning, examples of their work and assessments with commentary from students, a letter from the teacher, and a student/parent reflection sheet. Overall, both teachers felt that the portfolios and "backward" design was very beneficial. The portfolios increased parent understanding of what their children were learning as well as increased communication between parents and students. Another benefit is that students feel pride and ownership of their work when using portfolios. Also, the authors emphasized the fact that portfolios demonstrate whether or not students have met state and national standards more completely than some other methods assessment.

Britton, K. L. and Johannes, J. L. (2003). Portfolios and a Backward Approach to Assessment. Mathematics Teaching in the Middle School 9(2), 70-76.

My Bar Graph Tells a Story: Teaching Children Mathematics

The article "My Bar Graph Tells a Story" detailed a five day lesson in which a class of diverse second graders explored the relationship between qualitative and quantitative bar graphs. For the first three days of the lesson the teacher guides the students through various activities introducing the relationship between qualitative and quantitative bar graphs. Students fill in pre-made blank graphs and measure them using unifix cubes in corresponding colors. During the final two days the culminating activity was for students to match common nursery rhymes and stories to qualitative bar graphs.

I thought that this article was extremely detailed and specific in the manner in which they presented the idea of the lesson. The authors seemed to ramble on with the specifics, which I find not to be very useful to teachers. I think that most teachers would adopt the basic idea of this lesson, but then alter it to fit the needs of their students. The general idea, objectives, and methods of the lesson are of a high quality. This lesson would definitely help students to strengthen their ability to communicate using mathematical language, and to interpret graphs with and without labels.

Poematics: Exploring Math Through Poetry. Mathematics Teaching in the Middle School

The article "Poematics: Exploring Math through Poetry" details a lesson in which fifth and seventh graders write their own poems about math topics. First, teachers explained two types of poems, haikus and limericks, and showed examples of these two types of poems. Then, students created their own poetry, choosing any mathematical concept they found interesting to write about in the format of either a haiku or a limerick. Some students had difficulty thinking of topics to write on or getting started writing; however, in the end all students were engaged in writing. The authors suggested having students peer edit each others' poetry to improve the level of accuracy in the future. Using writing, especially poetry, in math class allows students to use their creativity to express their ideas more freely.

I thought that this article provided a very new and innovative idea that could be relatively easily implemented in mathematics classes of a variety of levels. This activity does not require any special materials or supplies, or any extensive preparation, which makes it easy to implement. Also, the activity could be done at a range of grade levels, because it does not focus on any one particular mathematics topic. The activity does not take up a large amount of time, and can be incorporated into any mathematics unit. I think that students could benefit from this lesson as soon as they have a basic understanding of poetry and can write poetry on their own. Finally, this lesson is beneficial because it forces students to reflect on what they have learned and think creatively and conceptually.

Video Analysis 2: 7th grade graphing

The main purpose of the activities in this lesson was for students to identify and demonstrate the relationship between two variables in an equation. Also, students learned how equations, ordered pairs, tables, and graphs are related and how they are used. Lastly, students developed their abilities to identify patterns and formulate equations or "rules" from patterns based on real life scenarios.

1. How do you determine whether group work is appropriate and effective?

I believe that group work is effective if students are actively learning and working together to do so. I think it is important that all students within the group are learning and benefiting from the group work. Group work can be very effective in lessons that involve investigation of a new concept. In a small group, students are able to bounce ideas off of one another so that they hit fewer dead ends. Also, in instances where it is beneficial for students to explain the process in which they found their answer, or why their answer is what it is, group work can be very effective.

2. What criteria do you use to determine whether or not to use a particular task with your class?

First and foremost I consider what the task is teaching the students. In other words, what will my students come away with after doing this task? Then I ask myself, does this align with the state and NCTM standards for this grade level? I also consider the level at which my students are at and the concepts that they have mastered, are still learning, and have not yet been exposed to. Where would this task fit into those categories? Is it logical to do this task now, or at another time during the year? Also, it is important to me that my students do tasks that are directly related to the real world. I will consider this when evaluating a task.

3. Describe how you generally deal with student mistakes and misconceptions that arise during a lesson?

This topic is discussed during one of the videos in which Ms. Allen was being interviewed after the lesson. One of the interviewers offers a compliment to Ms. Allen on how she deals with "errors" by bringing them to the attention of the class and having students talk about the error. I think that this is an extremely effective strategy; however, it must be used with caution as not to embarrass students. Ms. Allen explains that this is common practice in her classroom and students are accustomed to it. It is clear through watching her video that she has a good rapport with the children and an encouraging classroom environment, two things that are vital for this strategy to be effective. Allowing students to really understand why the mistake they made was incorrect will prevent them from making similar errors in the future. Bringing this to the attention of the entire class will help all of the students to also avoid the same error.

It is clear to me why NCTM has chosen this lesson as an exemplary one to place on their website. What first strikes me as most different from how I was taught, yet most like how I am currently being taught to teach is the emphasis on students talking about math. Since I have not been taught in this way, it is helpful for me to view videos of this style of teaching to better understand how it is actually done in the classroom. I also liked the fact that all of the problems the students did were connected to real life scenarios that the children could relate to. For example, starting with ten dollars and earning three dollars each week is something most seventh graders could easily do by doing household chores or helping a neighbor. Real world connections to math were also evident during the first part of the lesson in which students worked in groups to develop stories to premade graphs. I thought this was an excellent start to the lesson and helped make graphs meaningful to students.