As mentioned in a previous post, I have been thinking lately about how to attack Functional Skills Mathematics to improve results. I have decided on a 4-pronged approach.
As functional skills is so focussed on long, involved questions. Students need to feel confortable deciding what steps they need to take and set out their work so that they can follow it and check for mistakes.
3-Act Maths - I find this way of working to be an ideal way to introduce problem-solving to students in a non-threatening way. Starting with just the actual question and no constraints, variables or other information means that problems don't even look mathematical at first and students feel free to take guesses, make assumptions and bring in outside knowledge. Getting students to work out 'the information they would like in order to work out the answer' means that, when you bring those variables in, they are no longer confusing and unclear, but are now the very tools the students were asking for. I've used 3Acts from Dan Meyer's list, problems over at Finding Ways to Nguyen, and picture and video prompts from 101qs. I also sometimes just take a book question, skip all the set-up to the question and just ask the actual question (e.g. How long would it take me to cycle to Edinburgh? Can we get enough rain-water from the college roof to have toilets that run on the recycled water? etc.).
Structuring of workings out - e.g. using the problem scaffolder from the previous post on literacy. The idea of this is to help students to think clearly about the steps they are making and what they are trying to calculcate from each step.
Discussion of problem-solving strategies - I made some posters last year which I have up on the wall. Before tackling a problem I ask "which strategy could we use here? Why will that help?", when students are stuck I ask "which strategies have you tried? which might you try next?", when they finish I ask "which strategies did you use? did anybody use a different strategy?" Getting students to a point where they're comfortable with using these strategies and are starting to get a feel for when each one is applicable can only help their confidence when faced with a difficult problem.
Problem Posing - I originally got this idea from Matt Ives (blog post about it here). Basically the idea is to move focus away from getting the answer and move it on to thinking about the steps you would take and what information you would need. Matt Ives' way of achieving this: don't have any numbers, so pupils can't work out the answer, instead rewarding students who work out the steps they would hypothetically take to find the solution. He has a whole raft of them here on scribd and they've worked very well in the past, once students get away from trying to find an answer.
Prong 3 - Improving mathematical skills
Regular lessons - In amongst the literacy and problem-focused lessons, I will also include regular skills lessons. These will come before more complicated problems that involve these skills (along with others) so that students get to see them in context.
Starters and Homework - I will also include general basic skill revision in lesson starters and homeworks.
Fill in the blanks on calculation tables are a great way to make repetitive practice of a skill more interesting. I wrote a post about it here.
Prong 4 - Putting it together (and improving clear working)
Exam questions - The previous prongs will then be put in to practice when we do past-paper questions in class and for homework. I will link the problems to the work we have done on literacy and problem solving and discuss the skills that will be needed to solve the question.
3-Act questions rewritten as past paper questions and vice-versa - After solving a 3-Act problem, I will show a version of how I think it would look like in an exam paper. Hopefully this should make students feel empowered that they've just solved such a difficult-looking question and will help them see the link between the problem-based lessons and the actual exams. After practicing an exam problem I will get students to try to imagine how it would look as a 3-act problem. Not only does this reinforce the link between the two, but help students decide which part is the question, the constraints, the variables, etc.
Peer marking - Will help students to see the importance of clear and methodical working as well as to think about different problem-solving strategies that others have used in their working.
Secret prong 5 - Improving Engagement
Overarching all of this is what I feel that I actually do best as a teacher, which is to show students that maths can be enjoyable and engaging. I achieve this in the following ways:
Improving accessibility - 3-Act maths are great for this, as are other rich tasks, and the fill-in-the-blanks calculation tables. This is because of the multiple entry points to the questions, and the lack of immediate reading and comprehension required. If students' literacy can be improved, then the more wordy questions will become less and less daunting.
Improving confidence - As students get more and more comfortable with multi-step problems they will see that there are things that they can achieve in maths. This never becomes obvious to students who only practice the basic, underlying skills, no matter how good they get at them.
Improving relevancy - By this I don't necessarily mean 'real' maths, but I mean maths that students can imagine themselves using in their lives. This is where are a focus on problem-solving strategies can be helpful, because even though the problem itself might not relate strongly to them, being able to use the strategies is applicable by anyone.
Of particular interest to me here are the recommendations for what is needed to create and foster a culture of participation (e.g. open-source software design). Would it be possible to create a culture of participation around learning Maths? What would it look like? Because I don't think it looks like khanacademy or any other website that I know of.
Quotes specific to education
Our current educational institutions often treat learners as consumers, fostering in students a mind-set of consumerism rather than of ownership of problems.
New models of teaching and learning, with an emphasis on learning communities, teachers as meta-designers, and courses-as-seeds.
A culture-of-participation perspective for learning and education is focused not on delivering predigested information to individuals, but on providing opportunities and resources for learners to engage in authentic activities, participate in social debates and discussions, create shared understanding among diverse stakeholders, and frame and solve personally meaningful problems.
Quotes on the required features of a Culture of Participation
A fundamental challenge for cultures of participation is to conceptualize, create, and evolve socio-technical environments that not only technically enable and support users’ participation, but also successfully encourage it.
Participation is often determined by an individual’s assessment of value/effort. The effort can be reduced by providing the right kind of tools with meta-design, and the value can be increased by making all voices heard by supporting social creativity.
Benefits must be perceived. Contributors have to believe that what they get in return justifies the investment they make. The benefits perceived may vary and can include professional benefits (helping for one’s own work), social benefits (increased status in a community, possibilities for jobs), and personal benefits (engaging in fun activities).
Low barriers must exist to sharing changes. Evolutionary growth is greatly accelerated in a system in which participants can share changes and keep track of multiple versions easily.
If sharing is difficult, it creates an unnecessary burden that participants are unwilling to overcome.
It creates technical and social conditions for broad participation in design activities by supporting “hackability” and “remixability.”
Boundary objects are needed to establish common ground and establish shared understanding for communities of interest.
Participants must be able to naturally express what they want to say.
Interaction mechanisms must have a low threshold for easy participation and a high ceiling for expressing sophisticated ideas.
Participants are more readily engaged if they perceive the design activities as personally meaningful by associating a purpose with their involvement
We act not only for material gain, but for psychological well-being, for social integration and connectedness, for social capital, for recognition, and for improving our standing in a reputation economy.
Cultures of participation rely on intrinsic motivation for participation by providing contributors with the sense and experience of joint creativity, by giving them a sense of common purpose and mutual support in achieving it, and, in many situations, by replacing common background or geographic proximity with a sense of well-defined purpose, shared concerns, and the successful common pursuit of these.
Broken link. Does anyone know where there is a mirror of this file?
Andrés Monroy-Hernández (2012): Designing for Remixing (excerpts -- Chapters 4 and 7)
Well worth a read, even if only for the anecdotes about 10-year-olds forming companies, media franchises and the like on Scratch.
Quotes
Also anecdotal evidence suggests that this form of remixing tends to be a useful way for newcomers to get started with Scratch,modifying an existing project instead of creating something completely new.
I argue for the value of using sociability to support creative engagement through basic mechanisms like remixing, which often facilitate more complex collaborative practices such as group work. Additionally, I argue for “participatory diversity,” that is the support for both “making” and “listening” or lurking.
Bootstraping a community works well through in-person gatherings, such as workshops, that help identify potential issues with the system and, more importantly, seed the community with the kind of content that is desired for the system.
