As a science teacher I can agree that real world does not equal automatic interest. Science is only about the real world, and yet science class is not instantly engaging because of it. I think the general problem science and math education have is that we put the answer before students have the question. Students aren’t supposed to wonder, “Why do the days get shorter in winter?” we are supposed to tell them why, whether they wonder it or not, because we are on that chapter.

“I don’t know what your class worships”

This hits the nail right on the head.

I’ve never read that quote by David Foster Wallace before, and I am glad you shared. Ultimately classroom culture is the most important factor. It impacts everything from instruction to learning to discussion to assessment. Everything.

few comments I wanted to make:

1. Developing a learning culture is important and difficult

Each student comes with their own prior experiences and values. At times it comes with parental pressures and impressions as well. But ultimately a classroom culture is the combined/integrated product of every student, parents, school, and teacher.

“If you say a prayer to the “real world” every time you sit down to plan your math lessons, you and your students will never have enough real world”

So true. This is part of what I struggled with (and still often mull over) here
http://intersectpai.blogspot.ca/2013/02/stuck-on-applying-mathematics.html

They are questions worth thinking about though. How exactly do we promote (since we can influence, but not create) these cultures within our classrooms?

As Matt E pointed out: students “have no patience for irresolution.” This would definitely influence how we choose to tackle the problem of changing existing classroom culture.

2. What we claim to worship, and what we actually worship

This may be self-explanatory. A while ago during a workshop we talked about whether our classroom environments actually reflect what we value as educators. Are your seats in rows? What does that say about what you value? Is there a board in the back displaying student products? What does that say about what you value? Are there lots of manipulatives in the room? What does that say? How much time do you spend talking versus how much time do students spend talking?… the list goes on. Intentionally or unintentionally – what we say we value may not completely reflect in how we have engineered our classroom environments. This applies to the notion of worship as well. After that workshop, I thought hard about how the environment can be used to work towards or against our values.

3. How much should we change or influence the culture?

This point actually slightly contradicts my first comment. How much should we change or influence the classroom culture?

A class loves mathematics that are applicable to the “real world.” Do we try our best to also convince them that the “fake world” is equally interesting? Actually, the quick answer is probably “yes.” But I guess a better question is how do we best approach this for students that jump away in horror every time anything “non-realistic” pops out at them? Alternatively, students that love the “fake world” and believes the “real world” is boring – we need to also expose them to the complexities of reality. How do we best do this? How often do we do this?

I do believe we should explore these types of questions on our own and arrive at our own answers for each different classes.

So yeah, here ends my short nonsensical ramble

Some thoughts: Perhaps the mindset that every concept, every lesson, every skill, needs a real-world application to be exciting and motivating is the pendulum swinging in the opposite direction from, “do pgs 34 and 35 in the workbook.” But release from that mindset is liberating, actually. The puzzling/unpuzzling paradigm can applied to many learning experiences, and real-world is only one of them. From an elementary perspective, our curriculum is full, at every level, with all kinds of math games. Many are written into the curriculum. One alternative to real-world may exist in doing more to explore and mine the games we play. (I’m currently working on a post about what a colleague and I did with “Factor Captor”.) Kids love playing games, and taking them apart and seeing how they work, thinking about how to redesign them and reuse them, can yield some exciting results.
For the review assignment, I see a nice tension between the novel and the familiar.
I love the Wallace quote. I came across that many years ago and have never forgotten it. It comes from a commencement speech he gave at Kenyon College in 2005, and I would encourage everyone to take the time and read the whole thing. Yes, what we worship in our classrooms is critical. I think this is related to the paper you referenced a few months ago, “Intellectual Need and Problem-Free Activity in the Mathematics Classroom”. I now cringe whenever I hear a teacher say, “You need to know this for the test.” As an aside, I might add that the overwrought worship of “data” by the educational establishment has, and continues to have, very corrosive effects, and not only in math classrooms.

Hello everyone,

I have been enjoying the many discussions through these posts and wanted to offer a solution to the systems and intersection with the real world question.

I begin with the questions “who owns a car” and “who wants to own a car.” These are followed up with” are you buying new or used? what was the price of the used car when it was new? Why did the value decrease? does it decrease over time and if so, by how much?” These are the stimulation of interest questions. Fortunately, car ownership is high interest. We then move to the real life example applying a few students’ personal experiences in car ownership.

The lesson moves to determining the purchase price, the estimated life of a car, with the theoretical zero value at the end of a specified number of years.

Graph the points as purchase price, y intercept and zero value number of years as x intercept.

Now students can see the transformation of Cartesian coordinates to category axis and real life numbers transform back to (x,y) point values.

Students apply the billions (ha,ha) of slope calculations they have practiced to achieve the loss of value per year, slope.

Now take them on the journey of purchasing a vehicle with the use of a down payment and a monthly loan. They will now attempt to create the expense function and graph to with the depreciation function.

Students will trip and fall on the mixed units for the time axis. The depreciation is in years ad the expense function is in months. I let this slide and actually hope it is the case. This creates a create investigation after the students have solved the system of equations, i.e. breakeven of payout versus value. When students a re asked to prove the system solution by substituting back in to the equations, the looks on their faces tells the story and the detective work begins. hey will figure out that the expense equation must be converted to yearly loan payback or the depreciation equation must be converted to monthly rather than yearly units for slope.

You can use this model of systems to also graph exponential depreciation against expense functions,

AS well, you can use a table of depreciated care values form a Kelly Blue Book search to have students construct the basis of the lesson. Have students choose a car they would like to purchase and investigate the historical values, plot the values, run a linear regression, and for advancing skills, quadratic regression to determine best fit functions.

In the end, the discussion of why people trade in one or two year old vehicles is a great lesson to go back to the graph and explore exactly what breakeven means as the two functions converge.

If you wan tot have a great anchor problem for an assessment, blend loan payments formulas for student driven monthly payments. To challenge the “need to be challenged” DI group, you may wan to supply a break even point and challenge them to solve for the monthly payment amount and then remove a variety of variable values from the payment formula, i.e. interest rate, or length of loan payback. You may also add complexity with cost of ownership data.

I have had very good success and high levels of engagement with this investigation. In the end, students tend to value the understanding of how to make decisions will data and arithmetic modeling (Quantitative Reasoning), as well as understanding why their parent of a friend’s parent trades in a one or two year old car for a new one.

cheers.

Dean

Here is a blog post of mine about systems that is rather popular. My students and I discussed if buying The Soda Stream is worth it.

http://simplifyingradicals2.blogspot.com/2013/05/soda-stream-vs-coca-cola.html

@Nora: I ask for their advice, should I buy this machine? Then, they turn the table on me? They want to know some things about my soda-drinking habits.

Just wanted to say this moment (out of your Soda Stream lesson) is beautiful.

You have successfully avoided answering a question by providing a false answer to a false question.

Classrooms do not always “worship” something. Even if they do, can’t it be both or if it’s the second, can’t they desire the first? Some people value purpose and you’re taking the purpose away from them and their desire to learn.

If you try and create an environment where your students needs are ignored because you’re pointing them in the direction you want them to go, you will soon find that they go in their own direction which does not follow your curriculum. Not everyone has a passion for math.

If there is no real world question, why not just say that.

@matthew Kennedy: “Some people value purpose and you’re taking the purpose away from them and their desire to learn.”

Game designers/developers (my former profession) would argue that a balance of challenge and skill — driven by even the simplest “puzzle” — IS a purpose, and one of the most compelling. Besides enabling the psychology of “optimal experience”, known as the Flow State, a balance of progressively increasing challenge and skill creates a reinforcing loop that drives the kind of motivation/engagement we all see in kids and adults playing games.

A look through the *themes* of most games — even the most addictive — we notice a dramatic absence of “real world” purpose. But brains are tuned to find even the most arbitrary puzzle challenges irresistible under the right circumstances.

We know from what kids do voluntarily *outside* of school that students do NOT need a “passion for math” OR a “real world purpose”. They just need a brain. But the key word is “voluntary”. The psychology of motivation (Self-Determination Theory, in particular — the leading theory of intrinsic motivation) finds a strong connection between motivation and autonomy. Feeling autonomous need not mean we have total independence, but that what we are doing is what we *wanted* to do, even if someone else asked us to do it.

Finding puzzling challenges that tickle the brain into responding, regardless of the theme/”purpose”, is not trivial, but certainly do-able. Finding a way to create a context of autonomy — the context where the intrinsic motivation of puzzle/challenges thrives — is (I think) an even tougher problem for teachers and parents.

Just one of the reasons I’ve always found Dan’s work so useful is that it combines what makes games compelling (balance of challenge and skill — “Flow”) with what sucks us into a movie or novel (including those with no obvious application to our “real life”). It all begins with a question for which your brain now can’t let it go. Of course students today do not by default view a classroom as a film or game, but that doesn’t mean the same principles don’t/can’t work.

I had students ask “when will we use this in the real world?” immediately following a unit where we did a project about budgets and bill paying where they were assigned given paycheck amounts and finding housing and paying bills based on their paycheck / life scenario.

Many kids will ask this question just to ask it regardless of how relevant the information is.

Culture is crucial.

This week I put a “puzzle” up for students to do during a break for which I didn’t have the answer – and I told them this. Some students, who usually ‘get it quickly’ got frustrated when they couldn’t work out the answer straight away, some stayed and some walked away. One student came the next day and said “Miss I spent 2 hours on that problem last night and I still haven’t got the answer” :) , another student spent the 2nd lesson of the double working it out on the whiteboard and still didn’t have an answer but you could see he thoroughly enjoyed the challenge of finding links in the maths that he knew to try and find the answer.

My statement during this was is it’s not the “answer” that is the most important but the journey of finding out what works and what doesn’t. Everyone can say ‘Oh I should have done this and that’ with hindsight.