*LfU: Learning for Use*

The LfU framework seems fairly “user-friendly” in that different educators can adopt the framework, yet still allow their own pedagogical styles be honoured. Using combinations of high tech, low tech, modern and traditional, as long as educators create an environment that creates opportunities for learners to be “mcr-ed” (“motivated”, “constructive” and “refiney”) with their knowledge, they are towing the LfU line! The key take away for myself was that LfU focuses on the *application* of knowledge as opposed to specific inquiry or learning models. (Edelson, 2000)

For those of us who have drank, er guzzled, the EdTech Kool-aid, technology use in combination with the LfU framework is unquestionably going to be a good time. Although prior to ETEC 533, I was utilizing LfU principles unknowingly, what is distinctly different now, is that I am choosing activities with more purpose, as opposed to simple hunches. It is not the first week during my MET experience that I have read about the affordances of constructivism, situated learning and reflection, however, what the LfU framework does, is it packages these principles up in a clear, understandable way. (Similar to Newton’s Three Laws! At least for me…)

So, the topic that I would like to touch on is one that I have taught for my entire career of 18 years—linear equations. I haven’t taught it the same way in all of these years; as technology has evolved, my approach has definitely evolved! Once we have already reviewed the concept of Cartesian Coordinate System, graphing with a table of values, domain/range and a bit of slope, I then move towards equations of lines beginning with horizontal and vertical.

- Motivate — Experience Demand and Curiosity
- Desmos Faces: Through an inquiry process, students eventually construct a simple face using horizontal and vertical lines. There is a collaborative component to the pre-made, online activity, as well.

- Construct — Observe and Receive Communication
- Not gonna lie— I utilize “Direct Instruction” to introduce slope-Intercept Form. In combination with Desmos simulations, my students practice from textbook questions. I show them how to use Desmos to their advantage, when completing their work.

- Refine — Apply and Reflect
- Desmos Art Project: Students recreate a graphic of their choice using a minimum of 75 equations. Students may choose to use higher order functions (curves), but linear equations can also be used entirely. 10% of their mark is based from their Reflection that is publicly posted on the Class Blog. I will say that the Reflections have been better quality when I have provided students with topics to discuss.

Dana,

I liked your application of LfU and technology to math, as I find that it is with math that most students find difficulty in connecting the concepts to real like applications. In particular, as they progress through the grades, they tend to view math as simply a means to an end (ie- grades) rather than as a way to model and define shapes or relationships in life. This disconnect is often voiced as “when will I need to know this?” and seems to keep at least certain students from engaging with the math.

Your idea to use Desmos to create drawings is a neat way to show students how math can be used to model shapes. I like that users can save a variety of Desmos drawings for others to see, along with the equations that generated them. In your “Construct” section, you said that you primarily used direct instruction to introduce slope-point form of linear equations. Desmos could be of use here as well as entering a variable for slope and y-intercept (ie- y = ax+c )allows students to use a slider to adjust the variable. Then they can slide the bar around and note how the line changes as a result, and then come up with their own explanation for what each of the value controls.

The only difficulty with this is that while the slope is easily seen as “steepness” of the line, changing the y-intercept results in a line that can be perceived as moving up/down or left/right. When I demo this on Desmos, sometimes setting the window to be narrow helps to isolate the line’s movement so that they focus on the vertical component. Of course, this is when the direct instruction would be useful to follow up and clarify the demo.

Lastly, I enjoy the idea of the art project, especially as the cross-topic nature provides students an opportunity to show other skills that the have.

Hi Lawrence, It seems as though many of us have been Des-dosed in our approach to mathematics! I am really looking forward to not being a Masters student one day, so that I can invest more time into the program– ideally creating my own activities. I cannot take credit for the art project as I adapted it from another teacher, after looking at the Desmos Art Projects on the Desmos site. Admittedly, I have only done the Art Project with my Gifted class so far. I am thinking that I could adapt the requirements for a Regular class, however. The Gifted students often run away with things, teaching themselves how to approximate curves and such. It is truly wonderful to witness your students digging their teeth into a project that in vastly done on their own time. Cheers, Dana

Dana,

I enjoyed reading your post {as usual!}.

I also appreciate the intentional focus of LfU in explaining not just the “how” of learning, but also the “why” of the how of learning. Particularly, I appreciate the reasoning given on the choosing to incorporate technology. Although the knowledge construction could be completed without technology, the accessibility to information, data analysis and visualization, the record keeping and reflection are all substantially enhanced through technology use.

In your example, the “Use” aspect of your student’s knowledge construction is highly evident which is also a defining aspect of the LfU model and not always present in other frameworks.

Well done, teacher Dana!

Many thanks, Jessica! 🙂

The Art Project is probably one of the best (if not the best) activities that I do in my classes. It really ticks all of the boxes on LfU, and more. The students help each other with tricky curve approximations, and the level of difficulty is challenging for every student, as more adept students tend to take on more difficult pieces (the curvier, the trickier!). The project for the majority of students becomes a “labour of love”, so the goal of reaching 75+ unique equations is often doubled or tripled AND completed outside of class time, for the most part. Once I introduce the project, I will give two full classes to work on it, but thereafter, students may work on it during work time instead of working on nightly practice work, should they choose. Although you didn’t request it, here are some links to my requirements— maybe someone else will be interested in rolling this one out? Cheers, Dana

Project: https://drive.google.com/open?id=1nA1JKLuJXAeNM25w6loSiyE282nTWyacLi6dw9RPnsk

Reflection Guide: https://drive.google.com/open?id=1ey_pHIg402HbGALk8nb8EdqAQdyDCD7W60yTg5QJWxs

Rubric: https://docs.google.com/spreadsheets/d/1qBAk53OX4DjhcXMa9-GF5Pj2Wi9DktgzcuK099jjgIg/edit?usp=sharing