Ten Weeks of Summer: #gradesmarter (Weeks 6 and 7)

Week 6: Last year I tried to lead a book group at my school around the book Grading Smarter Not Harder by Myron Dueck. Since all the teachers I know at my school are very busy, I decided to make it a virtual book group.  I had everything set up in Google classroom.  I had made prompts that would go live every 2 weeks and I was looking forward to having a lively discussion with my colleagues.  Did they have a no zero policy? Did they have a re-testing policy?  How did they view homework and grading of homework?  There were two colleagues that posted once or twice and after that nothing happened despite the fact that about 20 teachers had joined the Google classroom for the book.

Then at some point early this summer I noticed a few Twitter book chats by math teachers.  I tweeted that I really had wanted to discuss this book with my colleagues, but my colleagues had not been interested. And so, the twitter chat #gradesmarter was born.  Each week for the past 4 weeks, we have been discussing a chapter in this book.  Week 1 was Chapter 1: Grading (July 11th) , week 2 was Chapter 2: Homework (July 18th) and week 3 was Chapter 3: Unit Plans (slow chat over July 22 and July 23rd). This week is Chapter 4: Re-Testing (July 31) and next week (August 7th) is Chapter 5: Creativity.  I would encourage you to look up the hashtag #gradesmarter if you weren't able to join the chat to see what was discussed.

What are my takeaways so far?  First, I will not be giving a homework completion grade next year. Homework is practice.  I'll make note of who is practicing and who is not, but I won't be awarding a grade for that.  Grades should reflect the level of understanding of a student.  Giving one student an A because they got it and a C to another because they didn't get it is fine on a test or quiz, but not for homework.  Second, I hope to make my students more reflective about their own understading as they work through homework and after they get back assessments.  I have tried test corrections in the past, but it ends up being more grading for me and I am not totally convinced that the student is always doing their own corrections.  (It sometimes seems like the work of a friend/parent/tutor.) This year I will be starting a new job at Kent Place School and having the students be reflective learners is part of the culture of the school and math department.  So, I will be looking to them for advice and guidance.

Are other people getting something out of this book chat?  Here is what Kristen Fouss @fouss shared in the chat via a screenshot. One of the things I love about what she shared is that she has brief statements that are easy to implement.  For example, retests "must be completed within two weeks of tests being returned".  This is important to think about prior to the start of school and implementing a re-testing procedure or policy.  However, it is also a work in progress.  Notice the question mark at the end of 4.d.

I am so glad that I was encouraged my my math twitter friends (a.k.a. #MTBoS) to lead the book chat for Grading Smarter Not Harder on Twitter.  It has forced me to think and share and think some more. Plus @myrondueck (the author of the book) joined us during the chat!  Hopefully, what I have taken from the book and the chat will make me a "Smarter Grader" and have a positive impact on my students learning.

PostScript: Are you a new math teacher to twitter?  Here are links to some helpful resources.  They may be a little outdated, but can help you get started with your own Twitter Professional Learning Community.  Twitter Chats for Math Teachers and Math Teachers on Twitter

Ten Weeks of Summer: Prepping for the Fall (Week 5)

This week is a break between leading workshops for AP Statistics.  My workshop group at Cabrini University last week was amazing.  In addition to learning many ideas about teaching AP Statistics, the group collaborated and shared ideas related to teaching, grading, homework and classroom management.  They even formed a Google Classroom group for everyone to continue sharing after the workshop was over!

My next workshop will be in San Diego and there will be 30 people in attendance!  I typically have workshops that range from 12 - 15 participants and 30 will be challenging.  But if I always stayed in my comfort zone and never took on new challenges, I would never grow professionally.  Here is to taking on a new challenge, seeing some sights in San Diego and learning from the experience!!

In addition to prepping for my workshop for next week, I have been working on reviewing AP Calculus (AB) topics.  This will be a new course for me in the fall.  I know many of the topics in AP Calculus, because I have taught a non-AP calculus course over the past few years.  However, there are some topics that are not as familiar.  To help me prep for the course, I read the "Course and Exam Description" as found on the College Board's website.  I worked through the 20 multiple choice questions and got 3 wrong.  Two of them I was able to figure out what I did wrong, but the last one I had no idea how to approach the question.  Specifically, it is to be done with a graphing calculator.  Here is the question:

If anyone wants to steer me in the right direction with this, feel free to post in the comments.  However, I will likely be posting on the AP teacher community and will be posting to the AP Calculus Teacher facebook group, too.  Back to doing some more prep work for fall.  We are at the halfway point of summer this week!

Ten Weeks of Summer: To Teach It or Not To Teach It (Week 4)

"To teach it or not to teach it. That is the quesiton. Whether 'tis nobler in the mind..." Whoops, slipped into Shakespeare's Hamlet for a second.

I am part of an email group of math teachers and last week there was a question going around about should we teach and/or why don't we teach concepts about alternate exterior angles formed by two parallel lines and a transversal.  Some argued via email that it was important to teach that concept for future engineers.  Others explained that they did teach the concept and that they taught it through discovery.  I said that it is probably not seen in many textbooks, because interior angles have more importance, especially when considering quadrilaterals.  So, to teach it or not to teach it.  Here are two stories I shared with my email group.

Story #1: I got my master's degree at Iowa State and for one of my projects, I used a theorem about secants and tangents to circles.  It is a theorem based on similar triangles.  The professor (with a doctorate degree) questioned me on the use of the theorem.  Either he had never heard of it or he couldn't recall it.  However, he had enough understanding of geometry that when I explained why it was true, he understood.  

Story #2: Over the past 10 years as department chair, I have to speak to groups of prospective parents/students and describe what is offered in the mathematics department at my school.  Do I speak about specific theorems or concepts?  No - they assume that I am teaching the math content that is typical of a high school mathematics curriculum, and let's be honest, a list of topics would be yawn-inducing.  Instead, I say that in math class students make and test conjectures, combine concepts in new ways, form logical arguments and critique the reasoning of others (verbally and in writing), notice and describe patterns, and make connections between different ways to represent a concept.  What I have just described is something that ALL students need no matter what major or career they go into.

Of course there are big ideas that matter in the teaching of mathematics and we can't gloss over those - function, inverse, transformations, proportionality, and rate of change are just a few.  However, if we leave off some concepts, will our students be somehow lacking?  Think back to Story #1. Was the Ph.D. mathematician lacking?  Some might say yes and that he should have learned and remembered that concept.  I would argue no, because he had a firm understanding of the big ideas and the ability to reason and apply his understanding.  His ability to do this, and not recalling a specific theorem, is what makes him, and I hope my students, mathematicians.

Ten Weeks of Summer: Analyzing THE Exam (Week 3)

Right before school ended, AP teachers at my school got an email from the person in charge of our AP program saying that the AP exam books from 2017 were available.  They were put in my mailbox and I didn't have time to look at them at that point.  I remember thinking that it probably would have been more helpful to get them before the students took the AP exam on May 17th.  

At my most recent workshop, participants wondered how it worked to get AP exam books back.  Here is what I found.  It cost us about $300, because we got all the exam books back for all of our students for all our AP courses, and the exam books arrived at our school somewhere between October and December.  This makes me wonder where they were from December through May.  It is a bit frustrating, because I could have reviewed the material in the books and used what I learned with my current AP Stat students.

Today I finally had a chance to look at my exam books and I used the rubrics to determine each student's score.  I was happy to see that no student left a question blank and it appears that some students got the highest possible score for a few of the questions!  But what were some of the big things I noticed? Do I need to modify my instruction or emphasize certain things more?  Here is what I discovered.

1) From question #1, I noticed that many students interpreted slope correctly, but did not mention a predicted change in the response variable.  Using words the words on average, approximately or predicted, would have indicated the non-deterministic nature of a LSRL.

2) From question #2, almost all my students used their graphing calculator to do a one sample z-interval for a proportion.  However, not all students named the procedure or checked to see if the conditions for doing the procedure were met. A few students did not have the correct confidence interval procedure at all, but all students gave a correct interpretation of the interval they found.

3) From question #3, almost all of the students could do the normal distribution calculation correctly for part a.  However, to get full credit for this, they needed to show boundary and direction.  If the student had simply drawn a normal distribution and marked it appropriately, they would have received full credit for part a.

4) In general, I noticed that students weren't showing their work for probability calculations.  Students may get partial credit on probability calculations if you have a wrong answer, but the work must be shown.  The directions on the exam even state, "Show all your work.  Indicate clearly the methods you use, because you will be scored on the correctness of your methods as well as on the accuracy and completeness of your results and explanations."  I need to emphasize that more.   

5) From question #5, I had many students leaving off the expected counts condition entirely or comparing the sample size of 207 to 30.  But on the plus side, almost all students were able to draw the correct conclusion in context and included linkage between their p-value and a chose alpha level.

The Positives - Students are using context, making correct inference conclusions and correctly interpreting confidence intervals!

Areas to Work On - I need to model drawing a normal distribution and require students to draw a well labeled/shaded normal distribution for any normal distribution calculation.  We need to spend more time on mixed review of identifying inference procedures and their associated conditions.

Consider - I currently split up LSRL between the two semesters.  LSRL, residuals, standard error, correlation and coefficient of determination are in the first semester and inference for LSRL is in the second semester.  Interpreting slope (and y-intercept) with non-deterministic language can be challenging, because students don't really understand that one sample produced that one very specific LSRL and that it is not likely to be the true regression line for the population.  In addition, they don't understand the concept of sampling variability early in the first semester.  Perhaps moving all the LSRL topics to the second semester would make this better, I think. This is the approach used by some stats teachers I know and one that I may want to use myself.

The remainder of this week I will be working on reading the AB Calculus Course Description from the College Board and identifying my areas of weakness relative to AB topics.  For example, I remember learning about slope fields in differential equations in college, but that was in 1990 - twenty-eight years ago!!  Since I haven't seen that topic since then, it is safe to assume that I am rusty in that area.  Perhaps next week I'll blog about AB Calculus or I'll blog about meta-analysis of my teach 180 blog from last year. (Spoiler: I am about 1/3 of the way through and definite themes are emerging!!)