Today, I went to my friend’s house to boil sap. If you’re not from New England, you might not know about boiling sap. Sap boiling is the amazing process that takes clear tree sap and transforms it into thick amber deliciousness. This process is amazing to me because of its simplicity. You collect the sap, boil the sap, put the maple syrup in jars. That is it. Well, to be fair, our friend had to periodically throw logs on the fire throughout the day. Oh, and it takes a really long time to go from sap to syrup. At this point, you might be wondering, why would you spend your whole day at someone’s house just to watch sap boil?

Because something magical happens while the sap is boiling. Conversations bubble up, residue gathers, extraneous details boil off, and I am left with a nugget of truth.

The conversation started when my friend and I were discussing how cool it would be to make a three act task for sap boiling. My friend’s fourteen year old daughter, I will call her “*x*“, was fascinated. She jumped right in to the conversations:

“What is a three act task?”, she wondered.

I started to explain, “It usually starts with a visual that inspires you to notice and wonder. For instance, what if we showed a short video of all the five gallon buckets that are filled with sap.”

Her mom said, “we should probably have a clip of one of the five gallon buckets attached to a tree tap so people know what they are looking at.”

Her daughter laughed, “of course they are going to know what they are looking at. We live in Maine.”

Her mother and I explained that, if we shared our three act task, people all over the country might use it.

“Oh,” She said, “That is cool. So they would want to know how much sap you need to make syrup. Would you need different units?”

“Tell me more.”

She went on to explain that it takes a lot of sap to make a little bit of syrup so you couldn’t measure the syrup with the 5 gallon bucket because the amount of syrup would probably be less than one gallon. She wondered:

- Would we use millilitres?
- Could we use fractions of a bucket as our unit?

She said, “I wish I could do this in my Algebra I class.” I asked her what she was currently studying and she said “graphing inequalities”. I asked her if she thought sap boiling had anything to do with graphing inequalities. She said, “I don’t know. Is it like if I knew I wanted *at least* so much syrup within a certain amount of time, I could figure out how much sap I would need to boil? Maybe the graph would show me all the possible amounts? I wish we could talk about this in my class.”

I asked her, “why can’t you? What do you do in math class?”

She said, “we do the textbook. I hate the textbook. I think we should burn the textbook.”

I asked her, “what would your teacher do without the book?”

This is what she said:

*When will the milfoil overtake the lake?*

*What if you brought this question to class?*

*She will probably dismiss it.*

*It requires too much work on her part.*

At this point, you might be tempted to think, “This kid has no idea how hard teachers work. Who does she think she is?”

Please don’t. This kid is thinking hard about what it means to do math. Give her a chance. Let it simmer.

She goes on to describe how she and her classmates designed their own study guide. She says, “Do you want to hear what our study guide was – for our exams – which are like 40% of our grades?”

I said, “of course.”

She elaborated, “One day, the teacher said, ‘okay, I need everybody to go into the book and pick out a problem from each of these three chapters’. So, we did it. We didn’t know what was going on. So, she took them all, copied them, stapled them together and that was our study guide.”

I wondered, “What didn’t you like about that?”

“It didn’t help,” she said, “I threw it away. I studied out of my book… because she has been teaching us out of the book. If she had been teaching us in different ways than I wouldn’t be able to study out of the book.”

I wanted to know more, “So, you know the test is going to cover the book. Am I correct that you didn’t find the study guide helpful because you knew you were going to have to go back to the book anyway? So you couldn’t trust that your peers had picked out the right problems?”

“Well they wouldn’t have chosen the most in-depth problems, because, obviously if your teacher says pick three problems, you are going to pick three easy problems that you can do within five minutes because you don’t know that she is stapling them and that is your study guide and it only covers a very small portion of the book and the answers are in the back.”

At this point, my friend and her daughter started discussing how grateful they are for the answers in the back of the book. My friend mentioned that having the answers is helpful when she is trying to help her daughter.

Then, *x *remembered problem 26. Listen:

She has been talking to me for 15 minutes about how much she hates the textbook and the study guides, and the forced group work. I have been listening to a cacophony of frustration, relief, and longing in her words. What could have made her remember problem 26? Was it that awful?

Actually, it was quite the opposite. Listen.

*We were working together.*

*We were communicating.*

*We were problem solving.*

So I asked her, “if your teacher could change three things about her math class starting tomorrow, what would they be?”

She thought for a while. Then, said this:

*If she could learn to love the why, that would be good.*

I asked, “It sounds like you think she gets uncomfortable when you ask why. Why is that?”

“Because when you are teaching out of the book, you don’t need it. The book gives you what you need to teach without the why.”

I was so fascinated by the clear articulation and reflection of this fourteen year old girl so I pushed, “If it doesn’t give you the why, what does it give you?”

“Formulas and specific situations. It is more helpful for me if I know why it works and how it works and I can see the inner workings of the problem because then I can apply it to different situations and different areas of math.”

After listening, I tried to rephrase what I heard. The three things you would want your teacher to do more of are:

*Talking and Discussing *

*Problem solving together *

*Loving the why.*

I said, “Those three things don’t include burning the book.”

“Well,” she said, “Then there needs to be four things.”