Tech Analysis

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The app that I chose for this analysis is called Factor Race.  It cost $0.99 through Apple’s App store and can is compatible with iPhones, iPads, and iPod Touch.

According to the app description “Factor Race is a game where the player must identify the binomial factors of trinomial equations.”  Students have to correctly factor different trinomial equations in order to make it around the track.  As students complete each level, they earn better race cars.

I really like the idea of this app.  It’s a fun, interactive way for students to practice factoring without it being another worksheet in class.  I actually stumbled upon this app when I was looking for engaging activities for my students to practice factoring.  However, I spent days trying to get the app to work.  Once it goes through the opening “credits”, you can only see half of the app.  Not being able to see the full screen makes it really difficult to even complete one factoring problem, let alone complete an entire level.  I would really have liked to use this with my students, but I didn’t feel comfortable expending class time with an app that I’m really unsure of how it works beyond its description.  I’m really hoping that the developers fix the bug because I think it would be a great app for algebra students.

Curriculum Analysis

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Kristen and I shared similar views on how each of three textbooks she looked at approached factoring.  We both agreed that having the repetition-style practice.  With something like factoring, having that kind of practice allows students plenty of familiarity with the process.

We also agreed that it was nice that the Core Connections book outlines in detail what teachers need to address, especially as first year teachers.  It’s easy to get lost in the details, and the CPM curriculum really aims to have an integrated story, so having a detail teachers guide is very beneficial.  We also agreed that it was nice that the Core Connections book had activities that broke up the direct instruction.  I think it’s beneficial, not just because factoring is something that students need to work at on their own to gain mastery, but also because it allows for avenues for students to connect and see the meaningful background for a concept like factoring.

We also agreed that the common errors alert was great.  It’s easy to forget what those errors are because you have so much experience with the concept, but that isn’t true for students.  Knowing where they might make mistakes can help both you and your students, both in terms of being less frustrated by the concept and in ensuring that the students are really understanding what they’re doing.

Dynamic Geometry

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There have been a number of studies that show that students have difficulty with mathematical reasoning.  I’ve seen it in my own classroom (both math and science).  Students can take an equation or formula, plug in the numbers, and get the correct answer, but they can’t explain why what they did was correct or have difficulty solving a slightly different type of problem using that same equation or formula.  The article points out that that “teaching approaches often tend to concentrate on verification and devalue or omit exploration and explanation.”  I try to incorporate different avenues to encourage students to explore and explain their work, but they are hesitant or resistant to doing anything but show you that they got the right answer.  They don’t think beyond “I’ve used the correct formula and gotten the right answer, I’m done.”  This was particularly prevalent with a unit in Chemistry about Gas Laws (a topic that is very heavy in algebraic manipulation).  As a class, we would walk through how to solve the problem and I would ask “How do I know my answer makes sense?”  The smart-aleck comment I got was “well you’re the teacher so of course it’s right”.  The point I was trying to make was to go back and look at the particular law and what the concept says.  The math should follow along from that and if they have done the work correctly, knowledge of the larger concept will allow them to check their own work (without having me there to say “yes” or “no”).

Interactive geometry software are computer programs that allow students to explore geometry concepts.  It allows them to see how the relationships in geometry work and how they all interrelate.  It allows students to see that we aren’t lying when we say that it’s all connected because the evidence to support that statement is right in front of them.  Students look at why the geometrical shapes and constructions are the way that the are, and what elements need to be there for the whole thing to work.  The main issue is with student interaction with the software.  Students have a hard time ensuring that the shape they use is correct for the program to recognize and for them to move on and actually work with the geometry.  I think if the interface was less finicky, along with clear instruction on how the program worked and its limitations, I think this could be a powerful tool in the classroom.

 

Student Thinking #2

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We recently started in on sequences and the book opens the chapter with problems that require students to create a table and come up with a pattern.  The first one was about multiplying bunnies.  The problem stated that we start off with two bunnies and, each month, each pair of bunnies has two babies.  The problem wanted students to figure out how many bunnies there would be at the end of 12 months, as well as to determine the pattern and what family of equations described the growth.

I had one student who fairly quickly completed the problem.  One of the extension questions that the textbook suggested was for students to attempt to write an equation that represented the situation.  This student, after he graphed the growth, recognized that it wasn’t a linear growth pattern.  When asked if the situation could be represented by a straight line, he said no, it was something else.  However, when he was set to the task of determining an equation for the situation, he always came up with a linear equation.  When I asked him what the graph of his equation would look like, he knew it would be a line.  When I showed him the basic exponential equation (y=b^x), he recognized that was the form he needed to use, but even by the end of class all of the equations he was creating were linear equations.

I didn’t expect him to come up with the correct equation, but it was interesting to me that he was constantly writing linear equations.  If I had been able to sit with him, he probably could have been guided to finding the correct equation.  It just wasn’t possible for me to do that.  I know that it is a topic covered later on in the chapter, and in another chapter in the textbook, so I know that he’ll eventually have the opportunity to work with the concept more.

Common Core State Standards – 6th Grade Math

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According to Common Core, instructional time should be spilt between four areas:

  1. Connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems;
  2. Completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers;
  3. Writing, interpreting, and using expressions and equations; and
  4. Developing understanding of statistical thinking.

In 6th grade, students will learn to:

  • describe and summarize numerical data sets
  • identify clusters, peaks, gaps, and symmetry
  • consider the context of collected data

They will also be building on their work with area in elementary school, teaching them the basic information to prepare them for 7th grade math, where they will work with scale drawings and constructions.