Education ∪ Math ∪ Technology

Tag: classroom practices (page 3 of 4)

What is The Effect of Technology Training for Teachers on Student Achievement?


This paper discusses the importance of teacher training in technology.  One important question is looked at, specifically; does training in technology lead to increased student achievement?  Following a review of current literature in this area, we look at possible answers to this question and reasons why teachers often receive less technology training than they require.


One thing my colleagues are always complaining about when it comes to technology is a lack of adequate training in how to use technology.  A common complaint at every school I have worked at has been about how teachers are given technology to use, some of it very expensive, and not given enough training to use the technology effectively.  This is a complaint that many people in our class discussions have brought up.  A useful question to ask then is, how much of a difference does training teachers to use technology make on the performance of their students?  Assuming that student performance, however it is measured, is linked to teacher preparation, we can hypothesize that there is a relationship between training teachers how to use technology effectively, and student achievement.

Review of Current Literature

An important part of answering this question is addressing the issue of how well educational research is done in the area of technology since we need to know how good the tools are that will be used to answer this question.  Kozma (2000) discusses this issue and decides that much work needs to be done improving our current educational research practices.  He emphasizes that "Perhaps it is the paradigm rather than the researchers or the user community that needs to change."   This suggests that we need to look at how we do educational research differently but the existing ways in which we collaborate are functional.

According to Cradler, J., Freeman, M., Cradler, R., McNabb, M. (2002),"A careful review of studies shows that more than the specific technology or software used, the context in which technology is applied is critical to the educator."  The authors suggest that when training teachers to use technology in the classroom, one should focus on how the technology is useful, rather than which technology is most useful.  This seems to me to be true, except that the typical level of comfort with technology that teachers have is low enough that theory will be of no use to teachers without specific examples to draw upon and learn about.  Therefore, training sessions should be used for a balance between practical hands-on examples and the theory behind the use of technology.

To paraphrase Brand, G. A. (1997) teacher training, in the area of technology especially, should:

"be flexible, take into account various needs, [provide] provisional support, be developed collaboratively,  include remuneration and teacher recognition, be sustained, be linked to educational objectives, provide intellectual and professional stimulation with a clear administrative message."

These traits seem to be true of any professional development but especially so for technology training given that only "20% of teachers feel comfortable using technology" (Cradler et al. 2002).

One way to help ensure the successful implementation of a technology training plan, as suggested by Williams, L. A.; Atkinson, L. C.; Cate, J. M. & OHair, M. J. (2008), is to operate within a learning community environment.  Rather than operate with "top-down leadership that hinders collaboration and professional learning" schools should "creat[e] technology enriched learning communities, where technology was used as an effective tool that is tightly linked to content standards and seamlessly integrated into ongoing classroom instruction." (Williams et al 2008).  In such a learning community members work collaboratively to decide on technology policy and learn how to implement it.

Another important thread that came up in our discussions was the amount of time devoted to technology training for teachers.  According to a study by Swan, B., & Dixon, J. (2006) "mathematics teachers need continuous and relevant training and support, especially when teachers are teaching out-of-field or are new to the profession."   This is true of any teacher, especially new teachers.

Now that we have established what is necessary in order to make the necessary teacher training work, we need to look at how this training affects student learning.  A high school principal mentions in Williams et al. (2008) that with "her low socioeconomic status students … She observed increases in attendance and decreases in discipline problems in classrooms in which teachers were integrating technology with authentic teaching and learning."  Such anecdotal evidence, while heart warming, should be examined next to an analysis of data. 

In a contextually limited study, Brush, T.A. (1997) discovered that when cooperative learning is used with integrated learning systems modest gains are made in student comprehension.  He also noticed that "[i]n the cooperative group, 85% responded that they believed the computer math lessons helped them with their math classwork" suggesting a link between the social use of technology and higher self-evaluation of one’s work.

When examining the factors influencing the use and implementation of technology related to student success, Baylor, A. L. & Ritchie, D. (2002) discovered "…a strong positive relationship between teachers who had a higher degree of openness to change and the impact of technology on students’ higher-order thinking skills."  In other words, having a teacher who was willing to experiment with technology was a strong indicator of positive student learning.  This is interesting because it is unclear whether technology training would either reduce or increase experimentation.

Experimentation with technology might be increased because of improved self-confidence of the teachers related to training (Cradler et al. 2002).  It could also be decreased because technology training is almost always done by presenting different tools to the user and the teacher may end up limiting their choices to the options presented.  In this case technology training might actually be a hindrance to student success.

After discussing this issue of technology use in the classroom with my classmates in ETEC 533, a common thread has emerged.  Technology use in the classroom should be supported by sound pedagogical techniques and planning.  This view is supported by Schacter, J., and Fagnano, C. (1999) who make the same assertion.  They add "…that teachers, administrators, policymakers, and parents need to understand the learning theories and principles around which the technology is designed in order to select and implement appropriate technologies that will have a significant impact on student achievement."  So in order to make sound decisions about how and why one should use technology in the classroom, one must be trained. 

Schacter, J., and Fagnano, C. (1999) analyzed meta studies of different ways technology could be incorporated into student learning and discovered that computer based instruction has been shown to "moderately improve student learning."  Using computer support collaborative learning, Schacter, J., and Fagnano, C. (1999) discovered through their meta-analysis shows "…significant improvement in the inquiry cycle…" of student learning.  Since this is a higher order skill, one would expect this is a result of increased comprehension.

However Lesgold (2000) notes that "[technology use] may fail either because the new possibility afforded by technology is not realized in classroom practice or because the infrastructure of the school does not allow the technology to facilitate improvements."  So just because a school attempts to use technology does not guarantee that they will see improvement in student learning.  Lesgold (2000) recognizes that places which already have strong technology support are often where studies showing improved student scores are done, and may not be indicative of the typical school environment.

Lesgold (2000) makes another important observation which is relevant to our discussion.  He points out that standardized tests are often used to measure student learning, and that valuable technology experiences may not be represented by this form of assessment.  He uses the ability to "write a really good report, which may take several days" as an example of a skill not easily captured by a standardized test.  In order to therefore justify our assertion that student understanding has been improved, we need to look at a variety of assessments.  Lesgold (2000) also suggests using expert analysis of school performance factors as an alternative to standardized testing.

We would also like to show that the use of technology has a positive effect on students’ ability to think critically.  Newman,D.R., Johnson,C., Webb,B. Cochrane, C. (1995) measured levels of critical thinking demonstrated by students using educational technology by using student questionnaires and a sophisticated content-analysis technique. 

The questionnaires were useful as a self-evaluation of the students’ critical thinking skills.  The content-analysis method seemed a bit subjective in the sense that the researchers interpreted statements made by the students as either exhibiting evidence of critical thinking or not.  However it seems like one of the only ways to measure this difficult to capture skill. 

Both of these techniques, according to Newman,D.R et al. (1995) "showed evidence of similar amounts of critical thinking in both face-to-face seminars and computer conference discussions" and the content analysis showed that "…overall learn depth of critical thinking was higher when learning took place [using technology]."


So to summarize, we can see that in order for technology training to be successful, we have to provide ample time for sustainment of the training, and plan our training to meet the needs of the diverse group of educators present in schools.  We also need to be considering the environment in which the technology is to used and tailor the approach depending on a variety of factors, including previous levels of adoption of technology and the likelihood of continued support for the new technology.

However if this falls into place, and technology is used in a sensible, pedagogically sound way, numerous studies suggest that it can help with improving student retention and understanding of material.  A variety of reasons exist why this happens, with some studies reviewed pointing to increased student engagement, improved collaboration between students, and more effective tools for demonstrating information.


Antonijevic, R. (2007), Usage of Computers and Calculators and Students Achievement: Results from TIMSS 2003, Online Submission.

Baylor, A. L. & Ritchie, D. (2002), What factors facilitate teacher skill, teacher morale, and perceived student learning in technology-using classrooms?, Computers & Education 39(4), 395–414.

Brand, G. A. (1997), What Research Says: Training Teachers for Using Technology, Journal of Staff Development 19(1).

Brush, T.A. (1997), The Effects on Student Achievement and Attitudes When Using Integrated Learning Systems with Cooperative Pairs, Educational Technology Research and Development, 45(1)

Cradler, J. & Bridgeforth, E. (2005), Recent Research on the Effects of Technology on Teaching and Learning,

Cradler, J., Freeman, M., Cradler, R., McNabb, M. (2002), Research Implications for Preparing Teachers to Use Technology, Learning & Leading with Technology 30(1)

Cradler, J.; Mcnabb, M.; Freeman, M. & Burchett, R. (2002), How does technology influence student learning?, Learning and Leading 29(8), 46–49.

Daugherty, M. K. (1993), Mathematics, Science, and Technology Teachers Perceptions of Technology Education, Journal of Technology Education 4(2).

Erminia Pedretti, J. M. (1998). Technology, text, and talk: Students’ perspectives on teaching and learning in a technology-enhanced secondary science classroom. Science Education, 82(5), 569-589.

Glenn, A. D. (1997), ‘Technology and the Continuing Education of Classroom Teachers’, Peabody Journal of Education 72(1), 122–128.

Gonen, S.; Kocakaya, S. & Inan, C. (2006), The Effects of the Computer Assisted Teaching and 7E Model of the Constructivist Learning Methods on the Achievements and Attitudes     of High School Students, Online Submission.

Kozma, R. (2000), Reflections on the state of educational technology research and development, Educational Technology Research and Development 48(1), 5–15.

Lesgold, A. (2000), Determining the effects of technology in complex school environments, SRI International, Menlo Park, CA, 34–39.

Li, Q. (2005), Infusing technology into a mathematics methods course: any impact?, Educational Research Vol. 47(Issue 2), p217–p233.

Li, Q. E. (2005), Mathematics and At-Risk Adult Learners: Would Technology Help?, Journal of Research on Technology in Education 38(2), 143–166.

Maninger, R. M. (20061001), Successful Technology Integration: Student Test Scores Improved in an English Literature Course through the Use of Supportive Devices, TechTrends: Linking Research and Practice to Improve Learning 50(5), p37 – 45.

Mitchell, B.; Bailey, J. L. & Monroe, E. (2007), Integrating Technology and a Standards-Based Pedagogy in a Geometry Classroom: A Mature Teacher Deals with the Reality of Multiple Demands and Paradigm Shifts, Computers in the Schools 24, p75 – 91.

Newman,D.R., Johnson,C., Webb,B. Cochrane, C. (1995), Evaluating the Quality of Learning in Computer Supported Co-Operative Learning, Journal of the American Society for Information Science. 48(6):484–495

Quellmalz, E. S. & Kozma, R. (2003), Designing assessments of learning with technology., Assessment in Education 10(3), 389–405.

Reznichenko, N. (2007), Learning with Graphing Calculator (GC): GC as a Cognitive Tool, Online Submission.

Schacter, J., & Fagnano, C. (1999). Does Computer Technology Improve Student Learning and Achievement? How, When, and under What Conditions?. Journal of Educational Computing Research, 20(4), 329-43. (ERIC Document Reproduction Service No. EJ603784) Retrieved February 13, 2009, from ERIC database.

Shacter, J. & Fagnano, C. (1999), EBSCOhost: Does Computer Technology Improve Student Learning and Achievement? How, When and under What Conditions?, Journal of Educational Computing Research 20(4), 329–343.

Swan, B., & Dixon, J. (2006). The effects of mentor-supported technology professional development on middle school mathematics teachers’ attitudes and practice. Contemporary Issues in Technology and Teacher Education [Online serial], 6(1).

Williams, L. A.; Atkinson, L. C.; Cate, J. M. & OHair, M. J. (2008), Mutual Support Between Learning Community Development and Technology Integration: Impact on School     Practices and Student Achievement, Theory Into Practice 47(4), 294–302.

Zhiting, Z. (2003), Teachers Professional Development in Technology-Pedagogy Integration: Experiences and Suggestions from China.




What would be an ideal pedagogical design of a technology enhanced learning experience for math and/or science?

Assignment as follows:

In response to Kozma (example article) and the above questions, create your own personal, short statement on an ideal pedagogical design of a technology-enhanced learning experience for math and/or science.

As I think about this problem, I am considering the following variables which influence my ideal design.

  • Students are social creatures.  Learning that happens within a social context is much more likely to be lasting and valuable. Students should therefore be working together.
  • Technology is a valuable tool we can use to help us with our lessons.  It is not a replacement for well designed lessons.  Therefore our lesson must have a back-up plan in case the technology fails, and the technology should not be the exclusive focus of the lesson.
  • Knowledge is generally constructed within a context.  In other words, students add new things they learn within the context of what they know.   We can use technology to help with this process, for example students could include what they work on as part of an e-portfolio, which would help them keep track of what they have learned.  If they also tag each item they add to their electronic portfolio, then they can be simultaneous categorizing their discoveries as well as cementing the connections each topic has with what they already know.
  • At the end of the day, we want the students to have learned something about mathematics or science, and what they learn about technology should not be the focus of the lesson.  The mathematical or scientific concept to be learned should be one that is condusive to learning through technology.
  • Like most good lessons, the focus of the lesson should be on what the students can do, and not what the teacher can say.  So an ideal lesson would involve the teacher avoiding the ‘sage on the stage’ role and become more of a resource manager.

An example of an technology-enhanced lesson would be the following:

  1. Before the students enter the room, the teacher has used some simple network tools (like Remote Desktop for example) to set up all of the computers in the room so they are ready to go.
  2. Student enter the room and sit in their assigned seats, and are quickly briefed, either in electronic form or by the teacher, on what the objectives are for the day.  During the lesson, students keep track of bookmarks to things they discovered and/or created during the lesson.
  3. Students self gather into small groups and begin to digest the information given to them.  Basically they read and reread the problem they are presented so that they understand it.
  4. Using tools they have learned in previous classes and any other suggested tools presented by the teacher, students begin to plan an investigation into a mathematical or scientific phenomena.  While this is going on, both students record notes while chatting with other about what their plan of action will be.  The teacher circulates around the room at this stage and gives advice on what might work, and what might not.
  5. Students try out their chosen plan of action, and the teacher supports each plan and provides assistance where necessary.  Students make sure to electronically record their observations.
  6. Students discuss with each other using an online public forum what they discovered.  Teacher joins and guides the discussion.  Each student logs their participation in the discussion.
  7. Students write a quick summary of what they have learned, and use the bookmarks to their various resources they have gathered to create a mash-up of what they learned in class that day.
  8. Once the students leave, the teacher examines what each student has produced (using an RSS feed or similar technology) and writes down his/her own observations on the class, and decides how he/she will either refocus the next lesson, or move onto new material.
  9. At the end of the semester, each student’s e-Portfolio is used as a primary assessment of what the student has learned.


List of resources for my ETEC 533 writing assignment

For my ETEC 533 class, I am planning on writing a short essay analyzing some current research on the effect of technology training for teachers on student achievement.  I’m interested in this because it combines two things I’m currently working on improving in my own professional practice, effective use of technology and leading professional development.

Here are some research links I’m planning on looking into in more detail:

Most of these links approach the idea from the perspective that if using technology shows no improvement on student scores, then teaching teachers how to use it will not have an effect either.  Assuming we can clarify that hurdle the next step is to show if there is a relationship between the amount of teacher training in a technology and its effectiveness in increasing student achievement.



Reflection of our course discussion about the use of technology in the classroom

Part of any useful activity is to make sure you reflect upon the outcome of that activity afterward.  This reflection helps you improve your practice and retain the connections you have developed through the course of the activity for a longer period of time.  Sustainable practice is only possible through careful reflection.

We just finished a week long exercise where we were to interview a person in our school or workplace and find out what their use of technology is, and what they think about the use of technology in a classroom.  After transcribing and analyzing the interview, we were supposed to post our observations to our class forum.  Once we finish our discussion, the last step is to write down what we got out of doing the activity.  My answers to the guiding questions are below.

How is your understanding of this issue changing? 

Well first I realized that there were some common threads between all of the interviews.  I had not thought that everyone had the same considerations about how to use technology, so it was encouraging to see some agreement between some very different people.  Pretty much everyone agreed that technology was most useful (or would lack use if this isn’t present) when it is carefully included as part of a repetoire of tools.  Technology should not be used for technology’s sake alone.

I was also surprised by how many people indicated an almost complete lack of support for training in their workplace for the use of technology.  In fact, I sent off a suggestion to my Alma Mater for a technology training course at my university and received a well reasoned out negative response.  It seems that even some teacher training programs are reluctant to take on the role of helping teachers come to grips with their technology woes.

What more would you like to learn or know?

I’d like to have more data.  Our anecdotal evidence was pretty convincing but there are definitely some sampling errors introduced by our biases when selecting interviewees.  It is unlikely that any Luddites would have consented to being interviewed for example, so most of us probably selected people who had some opinion about technology, one way or another.  A nationwide survey of teachers, where we find out what technology they use, where they want additional support, and what technology would they like to be able to use, would be a really useful tool. 

In what ways was your interview unique or similar to others?

Well my interview felt unique in the sense that the person being interviewed didn’t complain about the cost of the technology.  This is probably because we both currently work in a private school where the per student expenditures are higher than in a typical public school.  As well, our labour costs are incredibly cheap because of our location (Thailand) so the school has a much stronger budget for technology.

I’ve already mentioned a major similarity between my interview and other interviews, which was that technology as a tool  needs to be implemented carefully and not haphazardly.  Without this, it lacks purpose and can end up getting in the way of student understanding.

What does this say about the context/place or the issue?

It seems to me that, in terms of context, the use of technology is very similar in a wide variety of situations, but specific issues that arise can be quite location dependent.  In my school we have excellent physical resources, but lack strong internet connectivity.  Many of the videos and simulations we’d like to be able to use, for example, are much too bandwidth intensive to be useful in our part of the world.  However, unlike other schools we have all of the hardware that we need.  Instead of debating the cost of LCD projectors in classrooms, we have LCD projectors in every classroom in my school.  The context of the discussion that occurs is therefore very important as different observations can be made in different schools.  What seemed to be contextless however was the realization of all the participants in our discussion that technology, when used wisely, is a powerful educational tool.

Which issue do you want to explore further and why?

I’d like to have more of a  discussion about different types of technology.  I’d also like to be able to contact some of the people who were interviewed (which of course we cannot do because of privacy concerns) and get some more ideas from them.  Many of the teachers were mathematics teachers who had some very interesting ideas on how to use technology.

Analysis of video interview of a fellow teacher describing their views toward technology

Again, as part of my ETEC 533 class, we are supposed to interview someone who teachers mathematics or science and find out from them what their opinion and perspective is on the use of technology in a mathematics or science classroom.  The table below includes a partial transcription on the left of an interview with a senior science teacher at my school.  It is clear from the interview that the teacher makes pretty extensive use of various types of technology as part of their teaching practice.

Transcribed from interview Analysis


How do you incorporate technology into your teaching?


"… technology becomes another tool to use to help the students understand the objectives…"

"…if using a technology becomes a valuable way of doing this, then that’s what we do…"

"…students can investigate and learn without having to listen to me doing my ‘sage on the stage’."

This discussion seemed very familiar to me.  I realized pretty quickly that it was exactly the same discussion I had just had with my colleagues in my MET class.  Apparently, among people who use technology a lot in their teaching, it is just another tool.

My obvious question is, what would the response be among people who technology infrequently?  Is it clear that the reasons for the lack of technology use are things like "it’s too difficult", "it takes too much time", etc… However are there people who do not use technology simply because they haven’t found an effective way to use it?

I liked the the ‘sage on the stage’ mention in this person’s interview, especially since that is one of my primary uses of technology.  I like being able to direct the action, but I also like being able to have students make discoveries without my intervention.  Anything that leads to an ‘aha’ moment is what I want to be using.


Given unlimited resources, what other technologies would you consider introducing into your classroom?


"… the thing we need to improve upon the most is quality simulations where the students are either given simulations to do, or are given the tools to create the simulations…"

"…could definitely use more of the higher order thinking type tools."

What was interesting to me about the interviewee’s answer to this question was that he wanted tools to help him with higher order thinking problems, just like every other teacher I know.  In other words, there is a great similarity between teachers, regardless of use of technology, we want to make our jobs of teaching abstract thought and reasoning easier.  Some of us just turn to technology to try and help with this difficult task.

As I expected, this teacher wanted access to more simulations.  I didn’t find out why specifically, that was probably part of my poor interview style, but it seems this teacher was making a link between using simulations and being able to develop higher order thinking skills.  I’d like to have seen his reasoning flushed out a bit more there.


How has technology, and your perception of technology, changed over the years?


"… initially it was a fun thing to do and I was one of the few teachers at my school who got into doing the stuff …"

"It was a new way to explore learning on my part and the students’ part.  It then became clear to me, or clearer to me, that technology is a way to engage more than just the easiest of the senses."

"Technology is a way to engage the brain at the same time the hands and the mouth are moving.  I find that has been the best part of using technology."

"As technology has become all pervasive in our society it is pretty hard to amaze students anymore."

"Technology has done what it always wanted to do.  It has become the toaster.  It is now so pervasive everywhere that people just use it."

I was mostly curious about the answer to this question because of my own belief that although the technologies have changed over the years, our attitude toward them has not changed very much.  However this interviewee seems to refute this claim, and provided some excellent examples of why our view toward technology has changed.

At first it was a fun game, but as the technologies began to become more and more common, the ‘jee-whiz’ factor began to wear off.   Now students are less impressed with new technology, although I have personally noticed that when you use existing technology in unique ways, the students notice.

I’m not sure about the ‘technology becoming the toaster’ yet, as in my job I frequently have to give advice on using and trouble-shooting technology.  Every educator I know always has a back-up plan to a technology based lesson, not everyone I know has a back-up to their toaster.  Maybe we are getting there.



Would you say that technology increases student achievement, the use of technology I mean?


"The use of technology increases student achievement in a round-about fashion.  It gets kids more engaged in the learning and since they are more engaged in [the learning] there’s actually some learning going on, so as a result scores or knowledge increase.  Whether or not technology is the sole arbitrator of that success is almost impossible to determine."

This is a really key question and answer in my opinion.  The use of technology is only appropriate if it serves the ultimate teacher need, that of instructing students and having them understand your course objectives.  If the technology helps the teacher meet this need, then it is worth using.  The interviewee agrees with me, and provides an explanation why, which I think I can expand upon.

First he says that technology helps with student engagement and that helps with learning because of the increased attention being paid during the lesson.  I also would argue that technology, if used in certain ways, helps a lot with student empowerment and with ownership of the material.  Students who through technology make their own discoveries and write down their own opinions are much more likely to remember what they have learned.


Would you say that including technology in your teaching makes more or less work for you?


"’s just as another tool that I pick and choose to use."

"Sometimes technology is your friend, and then sometimes technology bites you. So on the days that it bites you, you definitely spend more time using it and trouble shooting it and trying to get things to work."

"…on balance using technology isn’t anymore time intensive than finding references in a textbook, or creating a worksheet, or giving kids something else to do."

As this teacher stated before, since technology is a tool, he chooses to use it when it is appropriate.  So this means that an approach where you use non-technological solutions mixed with technological approach is worth investigating.  It seems obvious to me, technology can’t solve every problem, and not every lesson has an easy way to incorporate technology.

He makes a good point about the ability of technology to be a chimera.  It is possible that everything runs smoothly with no difficulties, and it is possible that some key component of the technology you want to use fails at a critical moment, leaving you ‘high and dry’.  This is why any experienced users of technology always have a back-up plan for the mission critical situations, and why I argue, technology has not yet reached the status of the toaster.  More work needs to be put into the reliability of technology, and then a greater percentage of people will rely on it.


Can you describe an experience you had recently using technology which had an impact upon your teaching?


"The best thing that I’ve done recently…is developed a website for students to access…putting everything on the website…has allowed me to then to simply say to the students here is the stuff now we are going to work together to get through it.  Then I become somewhat less of a paper pusher and more of a resource manager…"

What was interesting about this answer, is that I completely agree. This is also the best thing I’ve done recently, and it has had the most impact on my teaching.  I’ve gone beyond using a website (a manifestation of technology) as a source of information for the students however and am trying to empower them to contribute to the resource.

This I think is one of the ways we can help technophobic teachers the most, since it has the greatest level of reliability, and doesn’t require learning completely new skillsets in order to be able to master web technology.  The proliferation of ways to get involved and publish to the web also means the entry costs to using this technology are much lower. 

I foresee a time, in the not too distant future, where every teacher will have a website for use with their students.  Probably every student will have a webspace as well, although the social networking websites are trying their best to fulfill this driving need in our society to be as connected as possible.  Possibly our students’ generation will have less personal websites than our own generation.

In brief, I found that the answers the interviewee gave to the questions were very similar to my own and that there were great similarities in our approach to technology.  Given that my interviewee has much more experience using technology than I do, it leads me to believe that I am on the "right track" and that my time spent mastering technology is worth-while in my teaching practice.

Students also appreciate the effort that we put into trying to incorporate technology into their classes.  It makes their lives more interesting, and can brighten a sometimes dull experience of trudging between classes, where still somehow students are often spoon-fed material.

What kinds of mathematics SHOULD we be teaching in schools anyway?

I was surfing around when I found a really interesting post by Steve Yegge.  He makes the point:

I’m guessing the list was designed to prepare students for science and engineering professions. The math courses they teach in and high school don’t help ready you for a career in programming, and the simple fact is that the number of programming jobs is rapidly outpacing the demand for all other engineering roles. – Steve

He then proceeds to describe some processes for learning mathematics on your own from the perspective of a computer programmer, which are worth reading about since pretty much anyone with an analytical mind and some experience in mathematics could follow a similar approach quite successfully.

This one point I think needs a bit more in depth discussion though.  Are we teaching the right types of mathematics in high school?  Are there any topics which might better prepare our students for careers outside of school?

First let’s look at career opportunities, focussing on jobs which are growing the fastest.  I’ll compile a list here, see my references at the end for sources of this information.

If we look at the list of the 30 professions with the largest employment growth, as an absolute growth rather than a percentage growth we see can pretty much separate them into two basic categories: those which require specialized training in a university, and those which do not. 

The professions in the first category, according to this list, are registered nurses, postsecondary teachers, elementary school teachers, computer software engineers, accountants and auditors, management analysts, network systems and data communications analysts.  The professions in the second category include things like carpenters, security guards, home health aides, etc…

We can also look at the current job statistics, where we see that professional, service, administrative support positions are by far the most common occupations for people to have today.

So the obvious question becomes, what types of mathematics do you need to be successful at these jobs?

1.  Statistics

Everyone needs to know statistics.  We use it all over the place because our society has become driven by data.  We collect it, we sort it, we analyze and we use statistics to make all sorts of arguments as a result.  Not understanding some pretty complex ideas in statistics is a serious hindrance in many areas.

2.  Probability

In order to be able to make intelligent decisions, people need to understand that the outcomes of those decisions are all based in probabilities.  Decisions about what medication to give, etc.. are based on the probability that a given treatment will be successful so understanding probability helps care-givers make better decisions.

3.  Number theory

Having a good grasp of what is going on in the various computer algorithms out there isn’t a bad thing, and courses in number theory could help out a lot of people.  It might be hard to justify this mathematics for the typical profession, but for the computer related professions, number theory is almost vital to being able to do their jobs properly.  So some more advanced number theory should be part of the higher level mathematics courses at high school and a basic introduction to number theory should continue to be included for everyone.

4.  Algebra

We still need to teach algebra and everything related to it.  We should also include more linear algebra in school in the more advanced mathematics classes, as a deeper understanding of linear algebra is crucial to many computer related positions.  As well, linear algebra is useful for almost all of the engineering fields and sciences, which is why universities typically include an introduction to linear algebra in those programs.

5.  Geometry

A little bit of geometry is a good thing so let’s keep a small amount of important geometry.  However we are still hammering our kids with geometric proofs from 2 thousand years ago that have almost no relevance in the work-place.  Proving something true is good for developing analytical reasoning but let’s do that in number theory instead.  Let’s leave the chords and tangents to a circle for a university level course instead.

What’s important in these statistics is that of the technical jobs, we no longer see engineering (except possibly computer engineering) prominently placed, which was one of the professions for which the US originally developed the current mathematics programs.  Computer related fields have surpassed the design and engineering fields which suggests that more mathematics which is useful for computer scientists should be taught in school.

Curriculum needs to be chosen that reflects the trends in the workplace, rather than on an ad-hoc basis, or because we have always taught it.  If the US, and countries whose education systems emulate the US, are to be more successful in a global market, our high school students need to be better prepared for the real world.  Every day we are inundated with statistics and a typical member of society needs to understand these better, in order to make more informed choices.  It is our school’s job to supply this curriculum, and it is our job as educators to implement it.

US Department of Labour


My analysis of two different video case studies on the use of technology in a classroom

These two case studies refer to videos I have watched as part of my Masters course, ETEC 533 and the copyright on the videos is unclear, so I am unable to show them here.

Learning Environment 6 with Teacher G (Post-secondary Applied Science)

This case study is about the use of a “clicker” or instant feedback device in a post-secondary applied science classroom.  The basic idea is, students have a remote clicker which they use to wirelessly transmit their answer on a multiple choice question presented at the front of the class.
The first thing I noticed about this video was that the instructor’s approach to teaching and what kind of information he was collecting seemed to be similar to what a secondary teacher might want to collect.  In other words, the position of the instructor in a post-secondary institution was less important than the fact he is an instructor.  This suggests to me that his experience with the “clickers” might be applicable to where I teach, in a secondary school.

The second thing I noticed is that what he likes about the clickers is the apparent engagement it creates among the students and how this could be useful.  However this has to be taken with a grain of salt, since as one of the students put it “Everyone else is just using PowerPoint or overhead projectors, so this is much more interesting”.  So the WOW! Factor might be critical here and we might be seeing a skew in our results.

The clicker technology though has the advantage of immediate feedback, not only for the students, but more importantly for the instructor.  Once you know whether or not everyone gets an idea, you can move on.  It seems to me that the clickers only allow for multiple choice responses, so this could be a bit of a disadvantage because it can be quite difficult to frame a multiple-choice question so that all types of learners are able to process the question and apply their knowledge to it.

There is another newer technology this reminds me of, where you create polls on a website, and students send in their responses via text message, and you can view all of the responses live on the website.  Very similar to the clicker technology, but might be more useful in a distributed learning environment.

The benefit of this technology is obviously the immediate feedback it gives the students.  A major drawback is the cost, both in terms of time setting up the multiple choice questions during the class to which the students respond and the cost of purchases enough remote clickers for every student.

Learning Environment 7 with Teacher E (Science, Elementary Preservice Teacher Education)

This case study is about using stop-motion animation to help teach physics concepts.  The basic idea here is, create an animation for the students to help them understand a concept in science.  An example would be, showing the animals in a food-chain actually eating each other in an animation, instead of using a simple picture with arrows pointing between the animals.

First reaction is that it must take an enormous amount of time to create the stop-motion animation.  This reaction was born out by the responses of the participants, nearly all of whom complained about how much time the animations took to create.

My second reaction was that I couldn’t hear the interviewer’s questions in most cases, so it was difficult to follow along the various videos for this case study.

One of the participants mentions that the stop-motion animation allows a teacher to present their instruction in a medium that the students of today, immersed as they are in digital media, can understand and appreciate more deeply.  By using the same digital media to present an idea, it is more likely to be understood.

Another participant used the students to help create the backdrop and pieces used in the stop-motion animation which he suggested help the students be even more engaged in the process, since it was their work they were seeing.  The same group suggested using a narrative as a way of helping students follow the process along more easily.

The instructor’s main point about the exercise was that the use of technology should be integrated into all of the courses a student takes, rather than as a stand-alone course.  He also mentions that if a textbook is “good enough” for learning a particular concept, then the use of technology to present the same concept should be carefully examined. 

A benefit of this technology is clearly the enhanced student engagement by the use of media.  A serious disadvantage is the amount of time taken to go through the process, whether it is classroom time with students or preparation time for the teacher outside of class.

Further questions

How much do these two different technologies cost to implement?

How much time does it take to learn how to use the technology?

How much time does it take to prepare the use of technology for the classroom?

Are there other cheaper alternatives that can be used within a classroom with similar effects?

An ideal classroom in which technology is used to facilitate real student understanding could exist, here’s how

Here is a quote from my class.  This guy has it right on.

  • all students would have laptops with integrated cameras, microphones, speakers
  • all students would work through configurable simulations of key concepts
  • all students would have full-time access to all the knowledge (and cruft) on the internet
  • students would track their own learning in a public learning log, possibly using blog or wiki software
  • anything that students say is within their core competency, they can be tested on
  • tests are given one person at a time, whenever the students are ready
  • teachers are there to teach concepts, lead labs, and ensure students are roughly on track with a learning schedule that will ensure they learn all needed concepts for state/provincial standards
  • frequently, students who have learned a concept would take a turn explaining it to the class. Who could do this and how often would be loosely coordinated schoolwide, so that as much as possible all students get opportunities to present in areas of their strengths
  • students would interact with others in learning communities all over the world via Skype. Sometimes a distance or foreign student might lead a discussion on a certain concept. (Note: I’m in conversation almost daily with members of my team in Italy, Norway, Ukraine, China, the United States, and the United Arab Emirates.) The school would seek out 5-6 learning institutions at similar levels and timetables so there’s a baseline of collaborators to start with, but students could talk to anyone if they’re on-topic.
  • teachers would frequently bring in social media output of practicing scientists/mathemeticians who are web2.0 producers when appropriate, helping to show relevance

John Koetsier in ETEC 533.

This kind of classroom sounds fantastic to be in.  Instead of having to spoon feed a bunch of students who don’t really want to know what you are offering anyway, you as a teacher get to become a mentor and guide.  Students would be actively engaged and definitely interested in what they are doing.  Given that in our current system many students learn material which they never use again, and fail to learn even the most rudimentary of research skills, this kind of school would empower students to set their own goals and seek their own understandings of how things work.  The existance kind of school would be a sign that standardized testing would soon be getting a run for its money.

Obviously there are logistical things to work out.  How do we fund such a program, and how to we set graduation requirements so that a time-line for completing of high school still happens?

Questions like, "How do we make sure the students are being productive and not messing around all day?", "Can we make sure that some sort of basic curriculum gets covered in this scenario?", and "Will any students choose hard enough things to study that we will have people entering mathematics, physics and engineering at the university level?" are also a concern.

I think that the first two questions are legitimate, at least in our current paradigm.  I suspect that an open learning style like this would help save money that is spent on various classroom management initiatives (think study hall, detentions, jails…) and save society enough money to pay for these types of schools itself.  The second question is one where we can only answer it by realizing that suddenly, there is no need for a time-line to complete high school.  Students who are able to demonstrate competency in enough areas to attract interest in a university are free to go there.  Otherwise students will be trying to demonstrate their competencies to potential employers instead, and when they are ready, they can leave high school too.

Anyway, if anyone knows a place where education like this occurs at the high school level, or anything like it, let me know I’d love to visit.

What are the characteristics of properly used technology in a mathematics or science classroom?

Here is a question posed in my class this week.

What is a good use of technology in the math and science classroom? What would such a learning experience and environment look like? What would be some characteristics of what it is and what it isn’t?

Here are my thoughts in no particular order.

  • The technology is being used seamlessly in the lesson. Students do not need to spend 5 or more minutes learning the technology because they know how to use it already. This means that new technologies should be introduced separately from their use if possible, or be so easy to use that they require no special instructions
  • Technology should be used to provide simulations or examples which are either difficult to do in real life, or time-consuming. Its purpose should be to demonstrate an idea or help handle repetitive tasks as part of a bigger picture
  • If it is possible and easier to use a non-technological solution to presenting some information, this should be used as experiences grounded in what the children know are preferable (see constructivism).
  • Use of technology to facilitate communication that is above and beyond what is normally possible in the classroom is also an example of an acceptable use of technology. This can be used to extend instructional time outside of the classroom, by providing a classroom blog for instance for students to post questions, comments, and summaries of what they have learned.
  • The people implementing the technology (the teachers or instructional aides) need proper training first, no technology should be implemented by people who are not experts in the technology first. Otherwise, when problems occur, valuable instructional time will be lost when the teachers/aides cannot fix the problem quickly.
  • The technology needs to work without too many major bugs, it needs to be easy to use, and it should run quickly.

A good learning activity would have students using a web applet, for example, or a simple desktop application to run a simulation, and then analyze the data given by the simulation to come to some conclusions about what they have seen. Students would be engaged not by the technology, but by the simulation itself.

I guess that the use of technology should not be simple because it exists, but because it is much easier or less time-consuming than trying to make the same discovery using non-technological tools. I feel like under these circumstances, technology can actually be a useful replacement for a real-life experiment. It could also be useful if an experiment can be done under ideal circumstances in a simulation, and then confirmed in the less than ideal real world

One of my colleagues in the class, Tris says pretty much the same thing.  He gives some different examples though which are worth mentioning.  Specifically:

  • This could be by extending or enhancing a students understanding of an area of content (using a computer simulation or model)
  • speeding up a process (using a graphing calculator to graph functions rather than pen and paper)
  • improving a students grasp of basic concepts (using a computer game [to] memorize timestables)
  • increasing the number of learning styles or intelligences being addressed in the classroom, or reducing the cost of education (making content available online rather than purchasing textbooks – this being a hypothetical argument assuming no copyright issues)

– Tris (posted in the ETEC 533 discussion forums)

His ideas pretty much mirror mine, but I’m including his examples because it provides more ways of using technology in a thoughtful way. I particularly liked how refers implicitly to Howard Gartner’s multiple intelligences theory as a reason for using technology, which I think is excellent. Pretty much every teacher has noticed that students learn differently, and that providing multiple forms of representation of the material you are trying to cover is going to benefit your students. I’ve noticed that my use of daily classroom summaries seems to have helped reduce the gap in achievement between my ESL students and my other students. I should do some research to see if this actually the case, or if I am just imagining the gap closing.

Ian, another of my classmates agrees with me in one point, so I’m going to quote him here, since he says it better than me.

"Ironically, the use of technology in classroom teaching should endeavor to focus as little as possible on the technology as possible…" – Ian

A photocopier.This is a good observation to make since so often it seems technology is just used because it exists. If we think of older technologies, we can see that the ones that have been successful have followed this credo. I’m thinking of the overhead projector, a word processor running on a PC, the photocopier, etc… none of which people think of as "fancy technology" but which have made an enormous improvement on our profession. Can anyone imagine a school with no word processors, no photo-copiers and no overhead projectors?

 These old technologies are just seeing a resurgence in their development actually because of the green environmentalist wave that is sweeping across our society.  So maybe they aren’t so taken for granted as I think…

 What new technologies do we see in use today will become the norm for classrooms for the future?  Is every classroom going to have a smartboard?  Every student with a tablet PC?  Are wireless interfaces going to change the way we interact with technology?  I think the answer is that the same properties that made the older technologies (like a photocopier) so useful are going to be the properties which determine which technologies survive for the future.

Communication Online with Students Outside of Class

Once you’ve started working with creating and managing online resources for your students, it becomes natural that the ways the students communicate with you is going to change a little bit.  Here are some guidelines for ways you can communicate with your students, and some ways to protect yourself while doing so.

Last night a student of mine asked me a question while I was online through Google chat.  I didn’t mind answering it, and so we had a quick 5 minute discussion about her project.  This saved me a bunch of time the following day, because I didn’t need to repeat the same conversation with everyone else, I just posted the relevant information to my classroom Math blog and then all of the students had access to it.

Google chat has a very handy safety feature for teachers, it automatically records your chat history, which you have access from your Google mail account.  This means that you can easily protect yourself from any accusations of misconduct which might occur.  This process is very similar to a student calling you on your phone and so the same principles apply.  If you don’t want a student trying to contact you via Google chat, don’t give out your gmail address.

You can also communicate quite effectively with students via email.  This has the advantage of allowing multiple students to receive responses, being able to record your conversations for later, and finally being able to send responses when it is convenient for you.  I hate it when students come up to me immediately after a class and ask a bunch of detailed questions because I almost always need to go to the bathroom, or prepare for another course, or get a snack.  These are the times when being able to send an email later is very handy.

Google mail has two neat features that make email with students a bit easier to manage.  The first is that you can apply a label to any email message sent or received between you and a student, which is a handy way of finding messages from students in specific classes.  The other feature I like is called filtering, which can allow you to perform automatic actions on emails that you receive depending on the sender, the contents of the email, etc…  One of the things I like to do is automatically label student emails by class when I receive them.

Finally, never delete emails between you and a student.  They are proof that you have been trying to help the student, which can be useful for administrative reasons I won’t go into here.  You can keep them to help yourself remember what types of questions ask about particular topics.  Finally your record helps protect you from potential problems later.

An interesting and relatively new way to communicate with students is through a website called  This website basically acts as a place where you can post a quick (140 characters maximum) message to the world, and anyone who is "following" you gets a copy of the message.  Since you can forward messages sent to you to your cell phone, it allows you to receive messages from an online source quickly and easily to your mobile phone.  This can be an easy way to set up a one-way broadcast system between you and each of your students in a particular class.  As long as you don’t "follow" your students’ messages, you won’t get any messages from your students that you don’t want.

Emails and chats are good for 1 on 1 or 1 on a few types of communications, but by far the best tool I have used for communication with my students is my classroom blog, described in another post.  Basically, I post information, worksheets, assignments to my mathematics blog, and students can all come read it on their own time.  The information is totally public and always available to look at later.  I also have students do daily summaries of what happened in class, which means I have a record of all of my lessons.  Students are free to post comments, which gives me some idea of what the class understood, and what they had difficulty.  For some reason I find my students are a bit more honest when responding on the blog, or rather less likely to remain silent about difficulties.  In fact, I’ve enacted policy changes because of legitimate complaints students have brought up through the blog, so it has acted as a tool to empower students as well.

These are 4 ways you can communicate online with your face to face students on a day to day basis.  Although we all don’t want our professional life to creep into our personal life too much, we also want to make sure that we help our students learn effective modes of communication, and that they have the help they need to handle those difficult projects we seem to be throwing at them endlessly these days.  Stay tuned for a future article about how to use for communicating with up to 20 students simultaneously for free.