MEDU 2010 - Technology in Mathematics Education

Fall 2016 - Professor Kate Poirier

New robot article

Hi everyone! I hope you are all doing well, especially with the chaos going on right now. An article came across my feed this week and I wanted to share it with you. In your responses to the article we read last semester about robots taking over teachers’ jobs, many of you emphasized the need for human interaction for learning. This article expands on that idea and applies it in a more generalized setting. I thought most of you might like to read it.

 

I’m on campus on Tuesdays and Thursdays this semester. Stop by my office if you’d like. I’d love to catch up with you all!

Final grades

Final grades have been submitted. Blackboard is down for maintenance for a few days, but once it’s back up, I’ll upload the grades for the final exam, projects, and portfolio, so you’ll be able to see where you final grade came from.

I hope you are all having a  relaxing break and happy holiday so far and I hope to see you in the new year!

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Perceptual Learning Modules in Mathematics: Enhancing Students’ Pattern Recognition, Structure Extraction, and Fluency – Luis and Gary

Title: Perceptual Learning Modules in Mathematics: Enhancing Students’ Pattern Recognition, Structure Extraction, and Fluency

Summary:

The article that we choose is about perceptual learning software where the technology can help produce rapid and enduring advances in learning. In the article it talks about the positives about using perceptual learning software in the classroom with the different experiments conducted with students. In the first experiment 68 students (9th and 10th grade) participated in the study in which the students were broken up into 2 groups, a PLM and a control group. The PLM group used the computers while the control group didn’t use the computers. When the PLM group used the computers they were able to see in recognizing algebraic functions and to transfer of Perceptual Learning improvements in information extraction to algebra problem solving to help the students be able to see and know what the question were saying. The result of the experiment showed that the students that used the perceptual learning modules did better than the control group that were using paper and pencil. Then in the other experiments conducted using students from different grades and different topics. The results were the same as the first experiment that was conducted. Then the authors did another experiment comparing the students that used paper and pencil to the students using the perceptual learning module software. In the third experiment conducted the students had a ball on top of the ruler and a billiard cue poised to strike it. The students had to find the distance traveled and the endpoint. The perceptual learning modules software was a way to help the students to find the cues to help students be able to understand the problems easier. In conclusion using the perceptual learning module software can be a positive thing for students but what about college students.

Discussion:

Would the perceptual learning module software work well for college students taking high level mathematics courses?

When it is appropriate to use technology as a tool-what determines the need?

Research article – thoughts from today

I really enjoyed everyone’s presentations today! I wish we had more time to discuss each of the research articles in detail; they’re all fascinating!

I have not yet nailed down exactly what questions you’ll see on the research article component of your final exam yet, but I wanted to capture some themes and issues that we discussed in class today and that appear in your OpenLab posts. Feel free to add your own ideas/questions/comments in the comments on this post.

These are the themes that I will have in mind when putting together this component of the final exam. My goal is to develop questions about any of these themes, phrased so that each of you will be able to answer using supporting evidence from these articles. Ideally, you could use evidence from the article that you read in detail yourself, but evidence from another group’s article might be more appropriate. Be sure to read each group’s OpenLab post to remind yourself of their summary of the article, their question and answer about the important detail, and their discussion questions.

  • There are barriers to implementing technology in the classroom. These barriers are both personal (for example, teachers and students may be apprehensive about using unfamiliar tools) and logistical (for example, not all classrooms have computers for every student; not all students have internet access at home).
  • There are components of the role of technology in math learning and teaching. I’ll spell out the four that appeared in Jodel and Josiel’s article here, though we discussed how these appeared in other articles (and in our own experiences) too:
    • exploring
    • conjecturing
    • verifying
    • generalizing
  • There are levels of technology use from the educator perspective that vary from non-use (before learning how to use the tool) and renewal (after having become comfortable using the tool and reexamining how to use it).
  • Students struggle to connect the calculations they do in their math classes with real-world applications. We saw in Tyniqua and Armando’s presentation as well as in Mei and Majid’s that students struggle with proportion/ratios/fractions. Technology can be used in intervention activities that allow students to make this connection through exploration and discovery by beginning with something students are familiar with.
  • Technology can be used as a pedagogical tool in different ways. Jodel and Josiel’s article showed us that Korean textbook questions for junior high school students used technology to foster conceptual understanding while questions for senior high school students used technology mainly in a technical/mechanical/procedural way. From Evelin and Sonam’s article, we learned that more successful students gravitated to using a graphing tool when it was appropriate; we noted that these student already have a conceptual understanding of the problem and are using the tool to do the mechanical work for them. The less successful students didn’t necessarily see how the tool could be used to answer the question. On the other hand, from Tyniqua and Armando’s article, we learned that Google Maps can be used to exploit students familiarity with technology in their lives to help them grasp an abstract mathematical concept.
  • For technology used as a mechanical/procedural tool, it’s important that students have to think in order to solve a problem. There must be a balance between thinking/developing technical or procedural skills and relying on technology.
  • Students’ perception can be exploited using technology to help them recognize patterns and learn more quickly. From Luis and Gary’s presentation, we saw that this use of technology can be more effective than traditional pencil-and-paper work. This helps develop fluency in mathematical language, ideas, and content.
  • Technology can be used to assess students’ strengths and weaknesses  and to deliver instruction that is tailored to individual students’ needs.

 

How can computer-based learning help students learn fractions? [Mei] [Admajid]

  • Title: Conditions for Effective Use of Interactive On-line Learning Objectives: The case of a fraction computer-based learning sequence

Authors: Catherince D. Bruce & John Ross

Journal: The Electronic Journal of Mathematics and Technology

Year of publication: 2006

  • This paper focuses on the challenges of students’ understanding about fractions from students’ perspectives and teachers’ perspective. Not using factions daily is one of the factors that makes it difficult to embed the significance of learning fractions as part of students’ life. The success of supporting students’ understanding lies on the design of instructions. The traditional teaching methods lack the emphasis at students’ conceptual understanding with little connections to students’ existing knowledge. However, technology-assisted learning is introduced as a successful model in enhancing students’ understanding with challenging math concepts.

The paper takes a main point on a computer-based learning package named CLIPS-Critical Learning Instructional Paths Supports. The package consists of its own characteristics and learning tasks for students. Even though students make meaningful progress in understanding of fractions under CLIPS, there are limitations and exceptions that students would not benefit from the program. Through case studies, the paper concludes the importance of building the direct relationships between online learning tasks and in-class learning tasks. The necessity of having in-class activities that are within students’ zone of proximal development. The full participation or involvement in the CLIPS will make a difference, and the pair work between students will support each other in completing the CLIPS tasks. Last but not the least, since the CLIPS program is computer-based learning, students can keep their own pace and go back for checking their work. The educators believe that students go with the sequence order to understand the content better than those who were absent and chose the tasks randomly.

  • Why do you think learning fractions is challenging for middle grades students in your own opinion?

First of all, there are different ways to represent fractions: division sign, colon, and fraction bar. Fractions are divided into proper fraction, improper fraction, and mixed fractions. They will have questions involving mixed fractions, but what they need to do first it to convert them to improper fractions to make computation easier. If a teacher cannot make his or her students understand the meaning of proportionality, it is going to be extremely hard for students to complete a task associated with fractions or understanding the significance behind ratio. From the reading, I learned that a computer-based learning might be a possible way to assist students to have a better understanding of something that was not clear to them through vivid images and audio. At the same time, there are challenges to implement technology in a classroom. The learning objectives from the sites should be correlated to the lesson itself. Schools need financial support to provide students’ access to computers. There are also technical issues along with computers that might happen in the classroom, which will make it unsuccessful for students to keep a consistent attention during the tasks. In conclusion, I agree that students need some technology in their learning if students can use it wisely with their goals of learning in mind.

When students are learning fractions, they will be able to understand what a ratio is. How to complete a ratio table is considered one of the basic and important tasks for students when they learn fractions from my observation experience. Thus, there are a lot of definitions that students need to know in order to understand fractions.

Without access to the reading, I learned that students struggle to factions because they are familiar with whole numbers. They are good at simple operations with these numbers, but students will have difficulty with whole numbers with different signs. They are likely to make conceptual errors when they subtract negative whole numbers. It is going to be a higher level when students learn fractions.

  • What are the strategies that you think can help students build a good habit of using internet?

What are possible ways that we can negotiate with students’ parents’ involvement with students’ online assignments at home? (like sit there with the students for half-hour)

Slower Algebra Students Meet Faster Tools: Solving Algebra Word Problems With Graphing Software- Sonam and Evelin

Title: Slower Algebra Students Meet Faster Tools: Solving Algebra Word Problems With Graphing Software

Author(s): Michal Yerushalmy

Journal Name: Journal for Research in Mathematics Education

Published: 2006

In this journal article, they conducted a study on middle school students to see how each pair used the graphing tool to solve word problems.  In this study, they conducted three groups, three pairs of successful students (U25), three pairs of average students and three pairs of low successful students (L25). Each group was given the same word problems to complete. Both groups had access to the computer and graphing tool.  The graphing tool is a software with capabilities similar to a basic graphic calculator that presents two-dimensional graphs and numerical values for any single variable expression. As each pair completed the word problem, there were interviews being done as they worked. The interviewer was not allowed to give the answers only to assess their thinking process. The main goal of the interviews was to observe the processes by which the L25 constructed mathematical meaning while solving traditional word problems with the function graphing software. From this study, they noticed how each pair had a different approach when it came to using the graphing tool. Some students wanted to use the tool to get an answer, others use the tool to check if their answer was correct and others students just wanted a visual representation of the function. Overall, the tool was part of the students’ reasoning and argumentation and was used to reflect on conjectures.

Question: How can we guide students to use graphing tools properly to solve algebra problems?

Graphing tools were constantly used in classrooms, and students were encouraged to use them. The techniques involved in using the graphing tool were practiced routinely in the eighth and ninth grades, including values, reading linked representations of function, and reading the values at intersection of two function graphs. Graphing tools are very helpful when students are dealing with functions. But if a student does not use them properly or over rely on these graphing tools, it may cause them just use the graphing tools to get the answers of the problems instead of trying to reason and understand the concept behind the problem. So, in order to help student to use the graphing tools properly, we need to set rules that they can only use them when they complete difficult operations and to confirm conjectures. Also make the assessment “uncheatable,” students need to be able to understand the concept, validate it and apply it. That is goal of solving a problem.

Discussion questions:

  1. Should middle school students be allowed to use graphing tools in class?
  2. What kind of graphing tool are helpful for middle school students?
  3. What are the benefits for students to use graphing tool in the class?
  4. How do you know if your students are over relying on graphing tools?
  5. How does a graphing tool help a teacher teach her/his students understand algebra?
  6. Should you allow student use graphing tool during the test?

Research Article: Jodel & Josiel

Source: EBSCO Database from Citytech Library
Published: October 1st, 2014
Title: Key factors for Successful Integration of Technology into the Classroom: Textbooks and Teachers
Author(s): Hee-Chan Lew, Seo-Young Jeong

__________________________________________________________________________________

The article is about the use of technology in a classroom; however, the author accentuates the most in Korean secondary school mathematics. From the article the author states that Korean Mathematics teachers and Korean Mathematics textbooks are the two primary reasons why it is difficult to implement technology in Korean Mathematics education. Furthermore, she talks about the four main components of the role of technology in math learning and teaching as well as noting that the role of technology in mathematics education requires careful distinctions between two different types of mathematical activities.

In fact the author defines the levels of technology-use in mathematics classroom within eight types of level of use in sequence. In addition, the author shows that technology mainly plays a technical role in activities of Korean senior secondary mathematics textbooks. There are 193 exercises with technology in Korean senior secondary Mathematics textbooks. However, there are 124 activities with technology in junior secondary textbooks.

Does Mathematics education benefit without technology benefit the teachers?

Links to Research Articles – password

In a previous post, I’ve included links to the articles you’ll be presenting tomorrow in case you’d like to have them handy for your presentation. Since the articles shouldn’t be posted freely on the internet, I’ve protected the post with a password. Here is the password hint: the first word in the title of this course with the first letter capitalized.

Protected: Links to Research Articles

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