Like many issues, but particularly in Education, learning and teaching strategies come and go with fads and new technology and are rarely accompanied by new research. Often teachers are looking for the “killer application” that will enable them to get their learners over the line easier and yield deeper learning that lasts. However, in doing so, many of us throw out the baby with the bathwater as one group of learning theorists see it as an opportunity to gain more of a foothold with the foot-soldiers (teachers).
So what on earth am I talking about? Well firstly the benefit of drill and practice, not just in Mathematics but across the curriculum, and also other forms of instructional software. They all have their place and as long as teachers know when and where to use them in their teaching their students will have significant learning benefits.
Instructional software is an academic term for computer applications that are used to aide in the delivery of instruction on a topic. The five main categories of instructional software are:
- Drill and practice
- Instructional games; and
- Problem solving
However nowadays many of the latest online sites and digital tools available, particularly in Mathematics, use a combination of the above types which can make it hard to distinguish exactly what the program or application does best.
According to Roblyer (2016) each of the above categories do the following:
- Drill and practice – allows users to work problems or questions and get immediate feedback
- Tutorials – act most like a complete teacher by providing all the information and activities for learning in order to master a topic.
- Simulation – a model that is a real or imaginary system to help the user construct the knowledge by experience
- Game – a game based system (could be drill or simulation) but with game elements or levels and achievements
- Problem solving – specifically targets the steps involved in solving a problem, the teaching is via the problem itself and not separate.
Now I would add that if you’re NOT using any of the above in your classrooms then your learners are missing out and so are you. There are so many relative advantages of using instructional software that one could wax lyrical for hours, but given I don’t have that sort of time let’s keep it simple.
(1) Drill and practice software allows for immediate feedback to the learner. In Mathematics that is like having 25 teachers in the room each standing beside each student as they complete their work and saying “correct” or “incorrect/try again”. So in essence it ensures each student is getting feedback almost instantly, and depending on the tool it may even give direction as to what they did wrong and how to correct it when they make a mistake. It should also be obvious that this process is faster than you marking twenty drill questions off the whiteboard to the whole class so it effectively enables differentiation as each learner can operate at their own pace and proceed as far as possible. Gagne (1982) and Bloom (1986) labelled this type of skill practice automaticity, where the knowledge was so clear in the learners mind that they could almost recall it automatically (on auto-pilot).
The introductory screen of a Prodigi challenge on Managhigh.com
Example – Mathletics.com or MangaHigh.com where students can log in and either complete drills (called challenges) of 10 questions either set by the teacher or chosen by themselves. As with many of the latest online drill and practice tools, MangaHigh is adaptive, that means it is a “branching drill”, where the software advances the student to more challenging questions based on what they have gotten correct in order to stretch their learning further. This is a common differentiating element that is sought out by most Mathematics teachers when evaluating drill and practice software today.
(2) Tutorial software allows for a more complete learning package and is perhaps that one that scares teachers the most. It is the one that critics of technology standup and say “but you want to replace teachers with a program!”. Well yes… and no. I’ve always said that if you honestly believe a computer program can do a better job then you in front of a classroom then perhaps yes, it should be replacing you! But seriously, tutorial software is also probably one of the most misunderstood pieces of instructional software. In theory it is supposed to be the whole package, the instruction, the theory, the lesson plans, the assessment, the feedback and the marker as well. There are little to few systems that do this in Mathematics but plenty are trying.
KhanAcademy.org course overview
Example – The most advanced and probably most well know is KhanAcademy.org. It is famous for Salman Khan whose 2011 TED talk made Khan Academy synonymous with the Bill and Melinda Gates foundation and the “flipped classroom” approach. It has since expanded into a global education phenomenon of tutorial software. That is a structured series of lessons broken down into concepts and taught sequentially. It has instructional videos to deliver the theory and then immediate drill and skill questions with immediate feedback to assess your progress. It also has the more advanced branching tutorial components were it will give you credit for concepts you already understand based on a pre-test. The site itself continues to go from strength to strength as it is integrating touch handwriting recognition on tablet devices and teacher-student tracking so teachers can use it in their own classrooms. If you haven’t seen it I highly recommend it, it will blow your mind…. and it is FREE! Surprisingly, as Roblyer (2016) points out, given tutorials have considerable value and are popular in corporate and industrial training, “schools and colleges have never fully tapped their potential as a teaching resource”.
(3) Simulations are essentially computer models of real world actions, in order to demonstrate to the learner how something works without them physically having to complete the action. These are popular in science and engineering areas where it would be far too expensive or time consuming to actually complete the real world task for learning purposes. This is one of the first benefits of a simulation, you can speed up time and significantly reduce the cost. In addition you can allow students to “construct” their learning by letting them control the inputs and try to “break” the simulation and prove to themselves what does and doesn’t work. In Mathematics dynamic geometry software such as Geometer’s SketchPad or Geogebra are close proxies for simulation software that fall in to the “those that teach about something” category according to Alessi and Trollip (2001). Interestingly the research on simulations seems to agree that “simulation work best when combined with nonsimulation activities” (Roblyer, 2016).
Example – My own experience is that they need to be structured or integrated into a learning activity rather than stand alone and as such can really create the “ah-ha” moment. For example in Mathematics the concept of theoretical probability compared to experimental probability can be a difficult one to grasp. Running a simulation after using physical dice to calculate the probability of rolling a 6 really allows students to see the connections and prevent misconceptions forever.
(4) Games are essential to all classrooms and I agree wholeheartedly with Roblyer (2016) that “a classroom without elements of games and fun would be a dry, barren landscape for students to traverse.” They are also not new, great teachers have used games to inspire, engage and break up learning activities for decades. Games are the essence of how we as toddlers first learn through play. We test boundaries, we learn the rules of life and then test them to “stay alive”. However in terms of instructional games Roblyer (2016) referes to them as software products that bring game-like rules and competition to learning activities. Teachers who give merits and track sticker charts are using a form of gaming and points based competition to drive achievement or behaviour. It is that extrinsic reward to inspire an outcome that is ironically one a true behaviourist learning philosophical element and yet many behaviourists probably scoff at gaming as a waste of good learning time.
Example – in my own classrooms games are used regularly. Most recently MangaHigh.com has developed an algebra game for teaching the concepts and principles of algebraic expressions and solving equations through a game. The narrative is fascinating and I have seen lower performing students rise to the top of the class leader board for weeks and re-engage with Mathematics through this game. You can play for free here: Jabara. The creators have also considered the transfer of skills from the game to paper by creating a written booklet that goes alongside the game and providing lesson plans for its use. As Roblyer (2016) states, teachers must help students recognise the need to focus on the math rules outside of a game. Both Herold (2013) and Helms (2013) provide some brilliant insight in to this area and make compelling cases for using video games in schools to foster learning.
(5) Problem-solving digital tools are arguably the least understood of all of the above tools. The term problem solving is often used interchangeably with critical thinking, higher order thinking, logic skills, algebraic thinking and reasoning. Whilst these are all accurate to a point there is no “single process” for solving a problem. All teachers can do is try to model their approach and the approaches of other students to make their thinking visible. This itself is a whole movement in education at the moment called “visible thinking” which I believe has its roots out of Project Zero and Harvard (http://www.pz.harvard.edu/).
As such I don’t have an example of a digital or technological “problem solving” tool. As the STEM movement gains traction here in Australia there are signs of a swing towards algorithmic thinking and computer programming to teach problem solving. Which in turn made Roblyer’s (2016) comment:
In the 1970s and 1980s, for example, many schools taught programming in mathematics classes under the hypothesis that the planning and sequencing skills required for programming would transfer to problem-solving skills in math. Research results never supported this hypothesis.
So what is the summary? The takeaway? Put simply, all of the above have their time and place in your lesson design and classrooms. They SHOULD be used, to improve learning, to deepen understanding, to have fun, to build automaticity and even to teach (when you can’t be there!).
Alessi, S., & Trollip, S. (2001). Multimedia for learning: Methods and development. Needham Heights, MA: Allyn & Bacon
Bloom, B. (1986). Automaticity, Educational Leadership, 43(5), 70-77.
Gagne, R. (1982). Developments in learning psychology: Implications for instructional design. Educational Technology, 22(6), 11-15
Helms, A., (2013, January 7). Education and video games are no longer enemies. Charlotte Observer Online. Retrieved from http://ostrc.org/doclibrary/documents/EduandVideoGamesNoLongerEnemies.pdf
Herold, B., (2013, August 13). Video-game research delves into how children succeed. Education Week. Retrieved from http://blogs.edweek.org/edweek/DigitalEducation/2013/08/video-game-research-delves-into-how-children-succeed.html
Roblyer, M. D.. (2016). Integrating educational technology into teaching. (7th Ed). Allyn & Bacon