If In Search of Practice Problems…

I volunteer at the local middle school in a resource room for an hour every Tuesday and Thursday, and the last time I went, the teacher suggested that I help students prepare for the standardized testing they’ll be doing in a week. Coming up with a way to help them broadly study eighth grade mathematics without knowing what they know stressed me out a bit, but then the teacher asked if I’d ever used IXL. She showed me it, and I’d have to say, it’s an impressive tool for review. It basically gives problems for each concept you could teach in math, language arts, science, social studies, or Spanish. For example, the teacher who runs the resource room said I should work on real life examples of area and perimeter. There’s a section called “area and perimeter: word problems” that I could use. It gives problems that are exactly as described.

The way I used it was by just going through the problems up on the board, but it’s really set up for students to use on their own. It presents a problem that the students have to answer. If they get it right, it adds to their “SmartScore.” If they get it wrong, it takes away from their score and gives them an explanation for how to solve the problem. It also keeps track of how long they’ve been working. After students are done, a teacher can look and see what each student’s areas of need are, which can help the teacher differentiate for their students. IXL can present information in graphs to show “your students’ growth, trouble spots, and even their readiness for standardized testing.” IXL is built around content standards, so it’s great for preparing for standardized testing. I think that it can potentially be a great resource, especially because of this reason, but it can be easy to go overboard with it.

While it’s great to have so many problems available, they are pretty simple problems. They should be used for repetition, not teaching. I could see some of my own high school teachers delivering a quick lesson and then just letting us loose on IXL for the remainder of class, which doesn’t help the students much. The problems don’t encourage much deep thinking; they’re better for practice. This is fine, I’d just had for teachers to become too in love with it and use it constantly. To conclude, I think that IXL can be great for practice and review, and it can help teachers learn more about their class more quickly, but shouldn’t be overused.

IXL Home Page

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Tracking In The Mathematics Classroom

The article that I read was “Promoting Equity in Mathematics: One Teacher’s Journey” by Alan D. Tennison, published by NCTM (link: http://www.nctm.org/Publications/mathematics-teacher/2007/Vol101/Issue1/Promoting-Equity-in-Mathematics_-One-Teacher_s-Journey/). After searching for articles involving equity in the mathematics classroom, I stumbled upon this article when I began to look through the NCTM website. Throughout the article, Tennison describes his personal experience with equity in the mathematics classroom as a teacher. The specific topic of discussion in this article is tracking, or grouping students based on their abilities in different mathematics classrooms. He discusses that although tracking may be helpful to students who are high-achieving, it has proven to be detrimental to poor and minority students in the past. At the end of the article, Tennison describes his own experience with creating a heterogeneous classroom where there is a standards-based curriculum and students with differing mathematical abilities are put in the same classroom. The curriculum was split up into units where there would be a central problem relating to other areas of study that the students would investigate throughout the unit. Within Tennison’s school, he found that students who participated in this track were more likely to enroll in four-year mathematics courses in high school, and had a higher average ACT score by 3 points. The article overall begged the question about the value of tracking in high school, causing me to reflect on what I consider its value to be in the classroom, as I had always considered tracking a positive part of schools because it challenges the students that need more challenge, and gives the students who may need more support in their classes the support they need to be successful. However, there are more questionable aspects of tracking than meet the general onlookers eye.

Tracking is a controversial topic in education as often times the students who are in the “lower” track are often overlooked, and as Tennison writes in his article, they are trained to memorize formulas rather than problem solve. The problem there lies within the instruction itself, which is at the core of equity in schools. Teachers ask that students in “lower” tracks memorize formulas because do not believe that the students are capable of learning the material to the same standard that students in the “higher” track are. Tracking inherently predisposes teachers to have prejudices about students in the different tracks. While in general tracking may seem like it has benefits, the way in which it is too often carried out negates these benefits.

The information that Tennison provided can be used in the future when designing my own curriculum, especially if I am given the opportunity to teach students who consistently struggle in mathematics. A portion of the problem that he mentioned in the article is that students in tracks that are not advanced focus on drilling different formulas for memorization, not problem solving. Problem solving, critical thinking, and other skills that can be developed in the mathematics classroom are focused on in the higher-level tracks. Therefore, if working in a school where tracking is part of the curriculum, the students in “low” tracks may especially benefit from a curriculum that focuses on problem solving, and critical thinking. Thus, the modification I would then make is to implement the standards-based curriculum heavily into tracks where students more noticeably struggle in mathematics to promote equity in mathematics. Tracking in itself does not allow for full equity in the classroom because it separates students based on ability, but there are ways that teachers can work toward creating the most equity they can if working in a school where tracking is present. Tennison’s proposal for creating a heterogeneous classroom prompted me to:

  1. Ponder the value of tracking in the classroom
  2. What teachers can do to help students who have been placed in a lower track if a school does implement tracking
  3. What the underlying benefits are of having a heterogeneous classroom

Therefore, I found a chapter of a book that discusses tracking in schools, and its implications. This chapter addresses the concerns listed above about tracking, and discusses its strengths and weaknesses. The link to the chapter: https://www.google.com/urlsa=t&rct=j&q=&esrc=s&source=web&cd=5&cad=rja&uact=8&ved=0ahUKEwjbJbT49DYAhVL2oMKHb3SBqcQFghJMAQ&url=https%3A%2F%2Fwww.nctm.org%2FHandlers%2FAttachmentHandler.ashx%3FattachmentID%3DxjfHMap4gFw%253D&usg=AOvVaw03miqiCNC8UgoGsqh6nfsj.