I realize that this blog has been idle for a few months now. While there is always tons to write, work, home, and life take over, and there is no time left to write. Which is both good and bad. Good, because it helps you to see what you are prioritizing. Bad, because you have started this project, and should take responsibility for its continuity because you continue to feel passionate about the topic of learning, especially math learning for small children.
Lately, I have been reflecting on the processes used in learning and how a child engages with their learning. These observations have helped me to reflect on some of my (university) teaching I do in design, especially human centered ways of thinking and learning, and translations of this understanding to the design of interfaces. Here is the critical question: while the online world is now flooded with that next app, that next digital platform, that next interface to make learning easy and engaging, and your children can pick and choose digital forms of learning that you never dreamt of, is there an evaluation framework? How do we evaluate the claim that learning, especially math, through a digital environment actually leads to better learning outcomes and a more engaging way of learning (as claims go)?
An observation: It is certainly having a big effect in practical terms. The dissemination of weekly public school homework (at least where we live in Sydney) is online, on a "social network" where kids, parents and teachers can interact. All the homework activities themselves are online, in the form of multiple choice questions and reading text passages sourced from various learning environments. When we look at something that is present, we must also comment on what is absent. Writing (with a pencil or a pen) and the "doing" of math (where you read a problem, break it up into parts, work out the meaning of the problem through drawing, text, or symbols, figure out the steps to solve it, and verify your solutions). This was the more traditional way but is completely missing in the homework pattern of today.
I am being careful to not make value-based judgements here, but just noting the characteristics and attributes present or absent in these two different forms of learning. For example, one of the things my 8-year-old son is extremely fond of is making paper planes. He often comes up with intricate designs, which I know nothing about, and certainly won't be able to reproduce by observation unless he spends some time tutoring me. When he does, it is great fun because he becomes my "teacher". He claims that he has learnt it from a few You-tube videos on origami. There was a point in time when he stopped watching the videos and started to experiment himself with different designs, noting that if "I put a paper pin and increase weight on the nose, the airplane behaves differently" or "this plane is a model only and while it looks good it cannot fly very well". I think this has been one example, where people sharing their hobbies digitally on Youtube, has led to an extremely engaging form of learning for a child, which may or may not have been the original purpose of producing the video. Thus, I am not saying that digital learning is all bad, and the non-digital ways all good - just that the medium of interaction has a role to play in what and how we learn, and critical aspects of the non-digital forms of learning cannot be replaced by the digital environments of multiple choice questions that are currently all the rage in examinations, in worksheets, in homework.
More importantly, the question is, if more and more learning is shifting onto digital platforms, what lessons in interaction can we learn from observing how a child learns? This is a design question. So, here are three observations from the recent work my son, some of his friends, and I have engaged in:
- As they grow, children need to discover that most problems in math cannot be solved "in the head" and that the journey or process of solving a problem is more important than getting the right answer.
Since the screen presents them with 4 choices, and the questions are mostly straight off one-step questions, children tend to think this is what "normal" math is like. And if there is anything more challenging, that is just too hard for them. Taking them to a mental place where they will stop trying or give up soon if the problem you present them with requires them to think in multiple steps. More importantly, they don't come to appreciate that the same problem can be solved in different ways to get to the same answer, and the different ways in which "pleasure" or "reward" is realized in our brains (for example, solving a problem in three different ways and realizing that you have discovered a much faster or more elegant way the third time as compared to your first solution). They get pleasure from the clap sounds or "you're clever" statements on getting a "correct" answer, so the reward system in digital platforms rewards a correct answer, not the method that was used to get to the answer.
- As they grow, children need to develop mastery in moving between concepts and their symbolic representations in order to be faster, more proficient and creative in their problem solving.
By this is meant, knowing that there are multiple ways to represent the same concept or moving between different concepts via a representation. For example, fractions and division, the relationships between symbols, and discovering parallel relationships between proper and improper fractions, mixed fractions, converting between forms, leading to understanding ratios and then proportions, and then percentages, and then...it could go on. Working with them on pen and paper, one realization was that if they develop the flexibility of moving between representations (and in parallel concepts), they tend to master higher and higher topics with amazing speed and clarity. On the other hand, the digital environment does exactly the opposite. By having sections on "fractions" where kids only see 10 or 20 similar questions on pizza slices, and then a section on "division", where kids see 10 or 20 similar questions on dividing cakes or lollies equally between a certain number of children, makes them concretize exactly that: that "fractions" mean this one thing, to be visualized as pizza slices, and "division" means this other thing, to be visualized as dividing lollies. Pizza slices are a great introduction to fractions, but if it stops there, we do have a problem.
- Learning should not always be made "easy" for the child.
The joy of working on a difficult problem, failing a few times, and then finally solving a problem, is not just a math thing, it's a life thing. Trying to engage children in math by making it easy for them is a bad idea. It teaches them to take pleasure from the final reward (usually in the form of "points" they earn, that they can "spend" to play games within this learning environment). It teaches them that the reward for doing math is not just that - the doing of math and the creative joy you get from it, but an external reward that then gets you other things (e.g. video game time). And yet, almost all the digital environments do exactly that. But there are simpler ways to reward the correct form of learning and making kids internalize the joy and fun of solving something, i.e., doing the thing for its own sake is the reward. When I work with the 8-year-olds on a traditional white board with colored markers, I introduce a concept, then give simple problems to solve, usually, I don't "tell them how" but see if they can "discover" it, with gentle prodding in the right direction needed sometimes. I ask them to write out or draw each thought carefully. Even when they have drawn correctly, I ask them to then write the same using symbols, encouraging multiple representations for the same concept. Finally, I ask them to "make up problems" after they have worked with a concept for some time, and to give these problems to each other to solve. They do not find this borning or hard, they enjoy it, and one little girl made my day by asking her mom when they would be having the "math playdate" again.
To a person who does a lot of math, these observations would feel like "duh". However, I wrote these down because these are exactly the attributes I find missing in the current digital learning environments, that are often the primary mode of introduction to mathematics in primary school for both kids and parents (since there are no books anymore, and no "math notebook" in which to solve problems from a book). This implies that thousands of children (and parents helping with homework) are experiencing these environments as their only lasting introduction to mathematics, and therefore, they increasingly form the following impressions in their minds (opposites of the three observations above, and real statements made by real 8-year-olds when I began working with them, stemming from real confusions about concepts and their symbolic representation):
- "I should be able to solve this one in my head. If I am not able to, I am not really good at math."
- "I cannot understand what these symbols mean, if we are doing fractions, why can't you show it to me as a pizza slice?..."Why do I need to learn why fractions and division can mean the same thing, fractions is about pizza slices, while division is about dividing lollies between friends, they are not the same".
- "This problem is way too long and hard, I can't do it, I am not really any good with math".
So, while the multiple-choice model may be a great one for older kids (see the excellent Alcumus as example), when children have learnt the basic important lessons and know how to pull out pen and paper and work out problems, as an already internalized and natural way of working. But, a really bad idea for little ones who are, perhaps for their life, forming an impression of what math is at this age. I wouldn't mind digital tools being designed that respect the complex and deep mind-conceptualizing-hand-writing-visualizing-writing-solving connections so essential to math (it will be a super-hard design task though). But more than that, I think a lesson in design is, if a simpler tool (books, notebooks, pens, paper) gets good results, perhaps we should not be quick in discarding them by putting them into the category of "rote ways of learning" and replacing them with much more primitive digital tools that supposedly make learning more engaging but actually are introducing alarmingly simplistic and fragmented notions and learning in children. By labeling all traditional learning as rote, we routinely throw the baby out with the bathwater.
