Author Archives: Gary Ma

Adaptive, Misuse, Support

Interviewee J has been a teacher for close to 20 years in a mixture of Science and Math classes from the junior to senior levels. Interviewee D has been a teacher for 5 years, and has experience mostly in Physics and Mathematics at the senior level.

The interview was conducted over email, which allowed for asynchronous response and made the information easier to process by the interviewer.

Adaptive

The first of the three themes that I noticed with the two interviewees is their experience, or desire to use technology to adapt to different student needs in order to improve engagement and learning. J mentions using technology to show videos, run lab simulations, and the use of various quizzing websites such as Kahoot & Socrative. These different pieces of technology serve to create differentiated instruction to students. Using videos to demonstrate concepts allow students who are visually based learners to the optimal opportunity to learn, while quizzing websites allow for different forms of assessment that deviates from the traditional pencil and paper method.

D has experience with similar technology but discussed the need for more adaptive learning technology that can cater more to student needs.

Misuse

Both interviewees discuss the lack of discipline on the students end when it came to doing productive work on devices. Both interviewees mentioned the need to police students to ensure that they are on task while given opportunity to work. D mentions the need for the school to create policies to control bandwidth or block undesired web traffic to prevent inappropriate use of technology.

Support

Both teachers thought that the best way that a school or institute could provide support for teachers is to increase the number of professional development opportunities and to increase the monetary investment to class sets of equipment. Both interviewees also mentioned that the improving the resources and technology available to teachers will improve the teacher’s effectiveness to use technology in their pedagogy.

Case 2: Graphing calculators in the classroom

I decided to analyze Case 2. To summarize, case 2 described a classroom in which the teacher suggested the use of graphing calculators as a way of engaging students in a grade 11 math class. The videos showed different ways the teacher used the calculators, and also gave some insight into the students’ experiences with the devices.

What are the underlying issues and why are they issues?

The first issue that always arises with the use of graphing calculators are their prohibitive cost. Texas Instrument has held a monopoly over the graphing calculator industry for the better part of 2 decades now and have charged a premium for a device that is outdated, and in today’s smartphone proliferated classroom environment, quite unnecessary. Desmos calculator for example, is an app that is available on smartphones that performs the same graphing functions as a TI 84, but is also free. Cost is an issue because it acts as a barrier of entry for students who cannot afford the devices. Although the summary of the case suggested that a number of calculators were purchased by the district and the school, how would these calculators help students outside of the classroom?

One other issues exist that prevent programmable calculators from being used in post secondary settings: How do you stop students from programming the calculator with information or programs that allow for academically dishonest activities? Short of checking everyone’s calculators before the test, this is pretty much impossible. That is why graphing calculators are typically outlawed in post secondary exams.

Some other issues described by the videos suggested that some students preferred to use traditional pencil and paper to problem solve before diving into the calculator because they thought it helped them better understand the concepts that needed to be learned, which could lead to problems for some students as some would move right onto the calculator before attempting to conceptualize the ideas that needed to be learned. Another issue that I have seen in the videos, and from my own experiences working with graphing calculators are their ease of use. In many cases, the number of buttons and functions that needed to be used for some students could prove to be a challenge.

What further questions does the video raise for you?

The videos were not dated in this case, but I am thinking they are likely from 2000-2010. Would the teacher have a different opinion of graphing calculators today with the abundance of smartphones that most students own? Furthermore, given Desmos calculator (an app available on their smartphone), would they choose this over a TI 84?

How would I explore a response to this issue?

I have explored the alternatives to the graphing calculator in my own classrooms by essentially eliminating all problems that required the use of a graphing calculator on tests. While there is value in using graphing technology in the math classroom, I have instead allowed students to use Desmos to solve problems in various assignments as another way of assessing their ability to use graphs to problem solve.

How might the issue that is raised exacerbate or ameliorate a conceptual challenge held by students?

As with the use of any calculator, giving students free reign to use technology before they have understood the fundamental concepts would allow students to solve problems without understanding the concepts, as a result, the graphing calculator has the potentially to exacerbate ANY numerical, or graphical misconception by giving students a free pass to avoid spending time learning the concepts at a high level. For example, adding numbers like 1/2 + 3/4 is very easily on a calculator, and giving students these devices at an early age allows them to bypass the need to understand how to add fractions, by giving them a way to solve the addition problem that does not require an understanding of fractions.

On the other hand, by simplifying the process of graphing, students have greater access to visual information that could be useful in unlocking concepts that are best understood with visuals. For example, graphing a straight line on a graphing device may help bridge the concepts of intercepts and why one would need to substitute 0s into an equation to determine their values.

Good use of digital technology in a math classroom

The following are what I personally consider to be worthy pursuits when it comes to incorporating technology in the classroom. In fact, below are some of the things I want to incorporate into my pedagogy over the next year or so.

Digital assessment in class, or at home.

One of the biggest benefits to technology that I am looking forward to developing is a way for me to assess students, and also for students to self-assess using technology. One of the things I want to be able to do is to have an automated test management system that will allow me to assign questions for students to complete as an exit slip at the end of a lesson. I find that if students, (especially the younger high school students), are set to a task that they have to complete by the end of class, it helps with classroom management as it gives students time to practice, and to explore their knowledge about what was taught that day. I personally also have an opportunity to determine student’s strengths and weaknesses. I know of different LMSes that could possibly allow this to be done (I want to look into setting up Moodle for the next school year), and I am looking for suggestions. It would be nice if someone with experience can comment on this.

Using videos to help students learn away from the classroom.

Some students cannot learn math in a traditional classroom effectively no matter what strategies a teacher tries. One can cite academia ad nauseum, or suggest strategies for different struggling students, but I still believe that at the end of the day, some students learn math better independently or by working with people 1 on 1 (as many students in my school do). Instead of forcing these kids to learn how to learn in a classroom, I think one of the things digital technology can do is to allow different avenues for learning. There are videos found online that would allow students to learn pretty much anything that I teach in my classes. I want to one day build a site, or find some way to host a central location where there could be videos given for every single topic I intend to teach. The goal being that this resource could be something I give to parents as an alternative to spending massive amounts of money on tutors. Building this site is a task that I may entrust to certain peer tutors in the future, if I am given an opportunity to work with one closely.

Using technology to give students alternative experiences with math

Despite the abundance of technology available today for teaching math, I still find that I have yet to “make a leap” in terms of how I deliver information. It feels like at the end of the day, students find it most effective when I stand in front of the class and work through different examples as a way of learning the concept, especially at the senior math level. After all, most of my senior students are result driven and want me to show them examples they wish to see on a test. With technology, I don’t think this needs to be. As time progresses, I want to find different activities that can be done on a device that could help kids learn a bit more independently, especially at the senior level. I have already explored using the different activities on Desmos (teacher.desmos.com for anyone that is interested), and I think similar types of learning activities would give students a chance to learn things a different way and maybe help avoid building up misconceptions along the way.

As a follow up to these types of learning activities, it would also be interesting to develop assessments that weren’t necessarily the traditional math test where students are given a set amount of time to solve a number of different questions. With technology, is it possible to assess students on their ability to complete a mathematical task as opposed to answering a question on a piece of paper to show their knowledge? I am interested in seeing what is out there.

I am open to suggestions on any of the things I have listed here. I look forward to your responses.

A common misconception in the application of exponents

Watching the video provided this week and seeing some of the common misconceptions that even the most educated students have about the solar system reminded me of a recent misconception that was shared among my grade 8 students about the concept of repeated multiplication. In the video, Heather’s misconceptions of the videos stem from misinterpretations of common illustrations used in textbooks, and a misconstrued view of the solar system and its planetary bodies. I find my own student’s misunderstanding to have similar causes.

The problem that my students struggled with this year had to do with an application of exponents, specifically with the number of bacteria in a population after it has undergone a period of exponential growth. The problem I pose to students is as follows:

“In the beginning of an experiment, there is 50 bacteria cells. The bacteria population grows when each bacteria splits in half. How many bacteria would there be after 4 divisions?”

A common solution given by my students is as follows: “50 * 50 * 50 * 50 = 6250000, so there are 62500000 bacteria after 4 divisions”

This calculation is incorrect because the concept of splitting in half cannot be captured directly by multiplying the initial population repeatedly. The correct solution would be that “50 * 2 * 2 * 2 * 2 = 800 bacteria”

One may classify this type of error as an error due to “rigidity of thinking leading to inadequate flexibility in decoding and encoding new information” (Comfrey, 1990) When students are first introduced to exponents, they are usually taught the “fact” that for a given number n, n^m = n * n * n * n m times, usually without any accompanying illustrations or physical models, thus it could become very difficult to come up with different ways of using that rule. As constructivists would have it, the individual mental construction of the concept is largely incomplete. (Cobb, 2004)

In order to better integrate this knowledge and apply it to bacteria growth, students need time to reflect on their solution in different ways (Davis, 2000). The students should be encouraged to ask themselves, “Is it plausible for 50 bacteria to turn into 62500000 bacteria just after 4 divisions?”, “If the same pattern was consistent, would 3125000000 bacteria after 5 divisions make sense?” Students should be asked not only to reflect on this through thinking, but also through illustration. How would one draw a bacteria population of 62500000? How does this drawing compare to that of 50 bacteria?

In order to solve the given problem, different strategies should be taught in addition to the rule. Some of which include drawing pictures depicting the number of bacteria after each split, or constructing a table to record the number of bacteria after each split. Other strategies involving digital technology would be showing videos or animations of bacteria growth in order to further help students in developing their understanding of exponential growth. I believe these are all strategies that will assist in helping students develop a more accurate model of knowledge.

Cobb, P. (1994). Where is the mind? Constructivist and sociocultural perspectives on mathematical development. Educational researcher, 23(7), 13-20.

Confrey, J. (1990). A review of the research on student conceptions in mathematics, science, and programming. Review of research in education, 16, 3-56.

Davis, E. A. (2000). Scaffolding students’ knowledge integration: Prompts for reflection in KIE. International Journal of Science Education, 22(8), 819-837.

Cisco Heat and “grinding” for personal bests

One of my first interactions with a computer was playing on a computer my mom brought home from work. The computer ran on DOS, and one of the first games I remember playing was Cisco Heat. Here is a YouTube video of the game: https://www.youtube.com/watch?v=nXUUf5qNATU

This was when I was 4-5 years old, and the first time I was exposed to a computer and computer games in general. Around this time, I was also introduced to the GameBoy, so really in general, my first interaction with technology was through games. One of the biggest impact that these devices had on me was that it taught me the importance of practice and perseverance. If I couldn’t beat a level in a game, I learned not to give up on it, and that if I kept trying, I would eventually succeed. I remember struggling in Cisco heat for a very long time before I managed to beat the first level, before I managed to get past it, after much repetition, and moved on.

Greetings from Vancouver, BC

Hello all,

I am glad to see many familiar names in the introduction so far. I live in Vancouver, Canada and this is currently my 7th course in the MET program. I have taken all the core courses and a few electives including ETEC 522, and ETEC 565M. I hope to learn about better ways to utilize technology in my Mathematics classroom so that I can give students new ways to learn, as well as new ways to make my job easier.

Outside of the MET program, I am a high school Math teacher in the West Vancouver school district.