Iterations Improving the Proficiency of my 3-Act Math Delivery

NOTE:  This is a late post - supposed to have been published last month but I've only recently found time (during exams) to post it.

For today's lesson, we turned to Dan Meyer’s video question on which cup contained more juice.  Here's my powerpoint that goes with it:  

It is a splendid 3-act problem that inspired some interesting questions.  However, the quality of their questions has decreased since September; the questions had more depth, and their observations keen.  Now, they are just giving me the question that I am looking for.  Wasn’t the whole point to emphasize the questioning to clearly define problems a little more?  It looks like I’ve fallen hard into my habits and have prized THE answer as opposed to prizing the question and problem definition. 

Wow, blogging really forces me to reflect more than usual.  It just dawned on me that the reason why the question quality has been decreasing since September is that I don’t answer all of their questions.  There were so many quality math questions that were generated by the students from the videos in September but I ignored the most quality ones because they would probably take a day to answer. 

I have placed 100% more importance on following my scheduled spiral curriculum than their curiosity. 

Looking back, I should have made more of a compromise, and actually followed through with at least a few of their questions.

It would show a lot more teacher willingness to venture into the unknown and really value their questions.  Following through to try and answer their questions would actually demonstrate how I learn – one of the most important things to model.   Instead, I’ve trampled on their curiosity and lost that opportunity to be a role model of a real learner. I feel really badly now. 

But, can’t be ruminating now, can we?  I’ll just change it for next semester.

So I’ve digressed.  Going back to the 3-act question:

After receiving their questions, I specified the question that we were going to answer today.  Which cup has more, and by how much? 

Here are their guesses as a completion to act 1: 

It’s interesting to see how many of them chose that cup A and cup B had the same amount. 

Nevertheless, act 2 came along, and with those measurements and the conversion ratio the students went about to work. 

After about 15 minutes of discussion and hard work on large whiteboards, the students put their answers on at the front.  Only 10% of them got the right answer:

 The stumbling point for many students was the CONVERSION!  I have to find another way of teaching conversions as I have been repeating it throughout the year and it still hasn't sunk in. 

In truth, the fact that many of my students weren’t able to complete this question in pairs disappointments me. 

I made this question into an entrance card to repeat for tomorrow in hopes that the students will get it during their second try.

I will take it up and repeat a similar question as an assessment on the next Friday. 

Update:  They did very well on their assessment.  I wonder if they’ve gained any ‘permanent’ skills along the way in this process or if they've just memorized the process.  I will only find out later I guess especially with that EQAO coming up soon.  

Success! Students Create, Solve, and Assess Equations all on Their Own

I just marked the students' test on spiral #9 which included a) volume of pyramids and b) solving equations.

Volumes of Pyramids
16/22 members of this applied math class achieved level 4 or higher on this multi-step pyramid that involved using the pythagorean theorem first.  Since this is the third time spiraling through pythagorean theorem, this high success rate is not surprising.


Solving Equations
Regarding the solving of equations - take a look at what they produced on the test:

Needless to say, they aced the other questions where they had to solve my equations.  However, their formal LS and RS checks needed a little work, and during their reassessment next week, they hope to capture that portion of the test. 

It shows that the formative peer work they did the day before worked.  I didn't have to do any marking to provide the feedback that they needed.  This community that the students have created in the past 3 months have allowed them to embrace their mistakes.  The amount of learning was exponential as the students were making their own questions on their whiteboards and discussing with each other their own individual problems.  They found each others' mistakes and they would justify to each other why it was a mistake.

Some students thought that a decimal/fraction answer was a "mistake"; they went back and "corrected" the question that they created so that the solution was an integer.  The process of critical thinking necessary to justify and correct it was fun to watch; however, I have put in a mental note for the students' need that a real number (non-integer) is a number too.

I'm glad that none of my students have stated any racist or sexist or any other inappropriate comments; but they certainly are 'fractionists'.  I have to figure out a way to expand their thinking on this one.  

The whiteboards' non permanent surface is a boon for students as there is no eraser mark, white-out, or need for an official eraser.  It encourages students to just write out their thoughts, display their thinking, and promote discussion. 
 
I wish I had employed the spiral curriculum since my first year of teaching with these applied students, as this success rate has been absolutely unbelievable.

At the same time, I have a couple factors that are exaggerating the spiral curriculum's success:

1.  I have motivated kids.  My level of engagement is even higher than that of my academic classes.  Dan Meyer's 3 act math had something to do with that.

2.  I have students with extremely strong learning skills this year.  My classroom management micromanaging at the beginning has paid off continual dividends that the students reap every day.