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.