Tuesday, September 19, 2017

Teach 180: Plickers (Day 12)

Today in Calculus we did some review for our test on Probability by using Plickers.  I use it as a type
of formative assessment - a way for me to get a sense of what the class knows and doesn't know.  Plus it is a way for students themselves as individuals to see what they know and don't know.

There are several benefits to Plickers.  First,
students aren't on a computer with other tabs or windows open to distract them.  Second, it is easy to encourage them to work together.  When we use Kahoot, it is about competition and getting your answer in first, even if that means guessing and not really understanding the problem.

When I scan the class using the app on my phone, I can immediately see how students did.  Green means the student answered correctly and red means the student answered incorrectly.  I can say something like, "It looks like many of you understand what you are doing", or "We may need to review this one." as I scan the room.  If a student changes his or her answer, I can quickly scan that student's plicker card again.  A second chance to re-enter an answer can't happen in Kahoot.

Finally, I can print off individual student results based on the plicker number I have assigned to him or her.  And here is a partial summary of my results from today.  Notice that some students did very well (their names are cut off the left side of the screenshot, but you can see the scores) and some questions were easier for the class as a whole than others.

Tomorrow I'll give students their individual one page report that shows how they they did on each of the seven questions.  They can use these results as they study individually for the upcoming test.

Friday, September 15, 2017

Teach 180: Games Day (Day 13)

Today there is just one class.  It is D period and I don't teach D period.  So, today I have no classes.  What am I doing today?  Today is Red and Gold Games Day.  It is a tradition that started in 2000 as the Millennial Games.  The entire student body (grades 1 - 12) are split into two teams - red and gold.  We play field day type games, like sack races, tug-of-war and 100 yard dash.  First grade students are paired with twelfth grade students and the twelfth grade students cheer on their first grader buddies as they race and help them with getting lunch.

What happens after lunch?  This year I have mandatory child abuse recognition training from 1 PM to 4 PM.  (There is required training for teachers once every 5 years.) Students will be participating in various activities including sports practices, scholastic scrimmage, working in the community garden, coda red music rehearsal, working in the art studio and my favorite - Who Wants to be a Mathematician qualifying contest!

Teach 180: Dealing with Student Absences (Day 12)

One of the most challenging parts of teaching is handling student absences.  Although it can be challenging for a student to get caught up on new content that was missed, it is even more challenging to get them to make-up a missed assessment.  Students can be absent for a variety of reasons – a dental appointment, a college visit, being sick or an early sports dismissal.  

On Tuesday, I gave a quiz in PreCalculus on solving quadratic equations.  All of the content onthe quiz was review from Algebra 2.  There were 3 students who were dismissed early for sports.  One student took the quiz early, one student took the quiz during a free period the next day and a third student did not have any free periods to take the quiz.  Rather than have him wait another day to take the quiz, I had him take it during class on Thursday.  (Note: With our new bell schedule this year, we did not have the PreCalculus class on Wednesday.)  This was less than ideal.  The student missed going over a review of the content he missed after the Tuesday quiz.  In addition, he did not do well on the quiz despite the fact that I told him that the most commonly missed question was the one on solving a quadratic equation by completing the square.  He earned 1 of 5 points on that question, because he got the right answer by factoring, but he showed no understanding of how to complete the square to solve the equation. 

After 25 years of teaching, you would think I would have developed a way to effectively deal with absences for tests and quizzes.  But the truth is that I usually have a list of three or four students that need to make up assessments at the end of a grading period.  Often these students have waited over a month to make-up the assessment.  At that point, they have forgotten much of the material that is on the quiz or test and usually don't do well.  Our school has a make-up policy that allows me to give them a grade of "0", but that doesn't sit well with me either.

If anyone has suggestions on dealing with student absences, please post them in the comments below.  Thanks in advance.

Thursday, September 14, 2017

Teach 180: The Birthday Paradox (Day 11)

Due to our new schedule, I only taught two classes today – Probability/Statistics and Calculus.  In Calculus we are actually studying some elementary counting and probability ideas.  For about 25 minutes today, we explored the birthday paradox.  If you don’t know what that is, you can view it on this TED-Ed video.  I showed the first 30 seconds or so of this video and paused it when it got to the question.

The main question being “How many people do you need to have in a room for there to be more than a 50% chance that at least two people share the same birthday?”  This problem incorporates complementary events and independent events. 

I started by having each of the 16 students write two dates on a single slip of paper.  Their birthday and the birthday of someone they know.  This doesn’t quite match the scenario, because it is very unlikely for a student to have his or her two listed dates be the same.  However, in reality two people standing beside each other could actually share the same birthday.  We did this twice and both times we found a match, which students found surprising.

Next, we used technology (TI-84) to randomly generate a list of 32 integers from 1 to 365.  We stored these numbers in a list and then sorted the list to make it easier to identify if we had a match.  Unfortunately, only 10 people had calculators on them, but we had 80% have a match the first time we used the technology.  We had 80% with a match on our second trial and 100% match on our third trial.

To help students understand why this probability was so high, I played the remaining 4 minutes of the TED-Ed video.   So, how many people do you need to have in a room for there to be more than a 50% chance that at least two people share the same birthday?  The answer is about 23.

Tuesday, September 12, 2017

Teach 180: Why Randomization Matters (Day 10)

Today in Probability and Statistics we reviewed the article The Immediate Impact of Different Types of Television on Young Children's Executive Function from The American Academy of Pediatrics.  This article looked at four different tasks to measure executive function across the three treatment groups: fast-paced television, educational television and drawing.  Children were randomly assigned to one of the treatment groups and a table from the article (seen below) shows that the groups were fairly similar.  But does randomization always matter?  Will randomization tend to create groups that are similar?

To see if this was the case, we worked through an activity in the CollegeBoard's Curriculum Module on Random Sampling and Random Assignment.  There are 14 subjects listed on cards.  Each card has the subject's name, gender and IQ score.  Students shuffled the cards and split the cards into two piles of 7 cards.  Cards in the left pile represented the students that were randomly assigned to watch an episode of Sponge Bob Squarepants.  Cards in the right pile represented the students that were randomly assigned to the drawing group.

Next, students calculated the difference in the proportion of females in the two piles (Sponge Bob group - Drawing group) and the difference in the average IQ scores in the two piles (Sponge Bob group - Drawing group).  Each pair did this a total of five times and then we recorded our results on a dotplot.  Students noted that there was variability from sample to sample, but that the dots tended to center around 0 for both the difference in the proportions of females and the difference in the mean IQ.  Here you can see our class dotplot.
We finished the activity by watching a video done by Doug Tyson which uses Fathom to do the simulation.  If students weren't convinced by our dotplots that randomization matters, they were definitely convinced by the end of the video.

Monday, September 11, 2017

Teach 180: My First WODB (Day 9)

I have seen WODB posts and ideas on twitter and today I tried out my first one in class.  For those of you who are not familiar with the acronym, it stands for Which One Doesn't Belong.  We had just finished reviewing the discriminant on Friday and I used this WODB as my opener for class.

I asked students to think which one didn't belong and why.  Then, I called on Christian and he said the one in the top right.  I asked for a quick show of hands to see who else felt the top right was the one that didn't belong.  Almost all the hands went up.  When I asked why, Christian said, "It has no x-intercepts and that means it has a negative discriminant.  All the other ones have x-intercepts and discriminants that are not negative."  After that we had a brief discussion as to why the other graphs might be the ones that don't belong.  One student pointed out the the one on the top left was printed in red ink instead of blue ink.  (This was intentional on my part.)  This was definitely a fun opener, but next time I might assign each table one of the four graphs to create a justification for why it doesn't belong.  Note: Shout out to Desmos for the awesome graphs that made this WODB possible.

Friday, September 8, 2017

Teach 180: Did I Break Desmos? (Day 8)

We continued working with factorials and counting methods today in Calculus. Near the end of class a student asked what the graph of C(11,x) would look like?  Would it be like a parabola, going up and coming down? (Note: I love the students in my school for thinking like this and being willing to ask these questions.)  We quickly looked at a table of values and noted that the values went up and then back down as x changed from 0 to 11.  Then, I said "We have 2 minutes before the bell rings.  Let's look at the graph in Desmos."  Here is what we got.

Wait a minute!!!  What is going on here??? Why does this look like a step function???  Why is it plotting values for non-integer values of x???  Did I break Desmos???  At that point the bell rang and I told my students that I would ask Desmos what was going on here.  And I know that on Monday they won't forget to ask me what the folks at Desmos said.

Thursday, September 7, 2017

Teach 180: Building Bracelets (Day 7)

In my Calculus class, we do a unit on probability.  Today, I decided to teach circular permutations by talking about bracelets. Each student was given 4 beads (black, blue, white and gold) and a piece of string with the question "How many different bracelets can be constructed with 4 different color beads?"  I should have had students spend more time struggling with this a bit themselves, but for the sake of time I asked one table to give me an ordering and I wrote it on the board.

One possibility is shown at the left.  Then I asked if anyone had something different.  We gathered 3 different bracelet orderings on the board, and then I did too much talking.  Rather than having a student point out that flipping the bracelet over didn't really produce a different bracelet, I showed that to the students.  They could see that the colors were still in the same position relative to each other, but to name the colors in the same order, we would be going in the reverse order around the bracelet. (clockwise vs counterclockwise)  I should have had students work together to come to this conclusion.

It was also at this point that I realized that the bracelet was actually a step beyond a simple circular permutation and the moment for deriving the formula of n!/n  or (n - 1)! had passed.  Although the students may have enjoyed this activity, I will likely try something different next time.  Rather than work with bracelets, I'll divide the students into groups of 4 and see how many ways they can arrange themselves in a circle.  This would get all students actively involved, talking and thinking.  Plus, I think the physical movement of realizing that rotating one spot doesn't change the order of the people (or beads) relative to each other would be more apparent.

Wednesday, September 6, 2017

Teach 180: Teaching in Longer Class Periods (Day 6)

We have moved to a dramatically different bell schedule this year.  Last year classes met for 40 minutes 4 days a week and 70 minutes one day a week.  Sounds pretty simple.

Now classes meet for 60 minutes 4 out of an 8 day rotation, 70 minutes one day out of an 8 day rotation and 50 minutes one day out of an 8 day rotation.  That means in an 8 day cycle a particular class that used to meet on a daily basis won't meet twice in the rotation.  Plus the periods rotate throughout the day.  So, sometimes I see students at 8 AM and sometimes I see those same students at 2:15 PM.  School started 6 days ago and at this point I think I have seen all my students 4 times in total.

Here is a graphic that may help you to understand the particulars of my teaching schedule.  You may want to click on it to enlarge it to see the details.

One of the adjustments I have had to make is knowing what can be reasonably accomplished in 60 minutes.  Reviewing a previous lesson, teaching a new lesson and having time for students to work on problems is not enough variety in 60 or 70 minutes.  Now instead of 2 or 3 changes in activities, there needs to be 3 or 4 changes in activities to keep students engaged for a longer period of time.  So, what do we do?

Here is what we did today in Probability and Statistics today:
1) Finish notes from a prior class - discussing sampling methods and problems that can happen with surveys.
2) Discuss all the homework problems.
3) Do a Plicker review activity to prepare for a quiz.
4) Video on Designing Experiments from Against All Odds Inside Statistics.

There was plenty of variety, classroom discourse and opportunities for participation to keep even the most attention-challenged students from zoning out.  But was it too much???  My one concern is that there may have been too much content for a one hour class.  Reviewing about a dozen ideas from previous lessons and introducing about five new ideas may not be optimal.  However, this course covers material that is on the AP Statistics exam.  In years past, I had just enough time to review (7 - 10 days of class time) prior to the AP exam.  With the new schedule, I am already concerned that I will be teaching new content up to the day of the exam.  By teaching old concepts and new concepts during the same class period, I hope I can at least salvage 4 days of review with my students in May.  Time will tell.

Tuesday, September 5, 2017

Teach 180: Reflecting on Reflecting (Day 5)

Reflecting on others reflections of my teaching sounds kind of meta, but that is what I am going to do in this blog post.  Reflecting on my teaching happens in several ways: notes to myself scribbled on the margins of papers, notes on my iphone, this blog, discussions with colleagues, and the more formal reflection that comes from National Board Certification application/renewal and applying for the Presidential Award for Excellence in Math and Science Teaching (PAEMST).  Today I received the following scores from three reviewers for my PAEMST application and was told that my application was not good enough to be a Presidential Awardee.

Reviewer 1
Reviewer 2
Reviewer 3
Dimension 1
Dimension 2
Dimension 3
Dimension 4
Dimension 5

Note that 1 = Fair, 2 = Good, 3 = Very Good and 4 = Excellent.

I was told in the email that came with my scores (direct quote) that, "If you reapply these comments may be helpful."   Note that Reviewer 1 gave a total score of 17, Reviewer 3 gave a total score of 18 and Reviewer 2 gave a total score of 9.  That's quite a bit of variability. Some of the scores are not even "adjacent".  (For example, 1 and 2 are adjacent scores, but 1 and 3 are not adjacent scores.)

At first I was very confused, if three different teachers gave these scores to the same assessment done by the same student, teachers and parents would have a right to be concerned.  When I score AP statistics exams, there is a rubric that needs to be consistently applied to be sure that similar papers receive similar scores.  Looking at discrepancies in these scores, I would conclude one of two things.  Either Reviewer 1 and Reviewer 3 followed their scoring notes, rubric and benchmarked examples (their scores are very comparable) or Reviewer 2 followed the scoring notes, rubric and benchmarked examples. Based on the table, it appears that reviewer 2 should have plenty to say regarding my areas of weakness.  So, I went to Reviewer 2's comments.

Here is what reviewer 2 had to say about Dimension One: Mastery of Content Appropriate for Grade Level Taught. "Perhaps all misconceptions could have been addressed before the students brought them up.  You did not address them until the students did."  I typically anticipate student misconceptions as I plan my lessons.  However, to purposefully mention misconceptions before students have a misconception robs students of an opportunity to learn from their mistakes.  Essentially this comment is telling me to wrap my students in bubble wrap and steer them away from anything that might harm their understanding of mathematics.  That will not happen in my classroom.

Moving on to Dimension Two: Use of Instructional Methods and Strategies that are Appropriate for the Students in the Classroom and that Support Student Learning.  Reviewer 2 states, "You are not discussing instructional methods, strategies or tools.  One strategy was indeed wait time and building on prior knowledge, but you used many others." Score: 1 = Fair  So, I used many strategies that were evident in my video, but I guess I didn't talk about them enough.  Since I had already maxed out on the number of words for this section, I guess I need to also learn to write more succinctly.  Writing more succinctly will make me better at "use of instructional methods".  Really?  (Head scratch.)

Now for Dimension Three: Effective Use of Student Assessments to Evaluate, Monitor and Improve Student Learning.  Here is where it gets confusing to me. (I should say more confusing. ) Reviewer 1 states "Teacher described a variety of appropriate formative and summative assessments."  Reviewer 2 states "You didn't discuss any forms of formative assessment or q & a. Very good."  "Variety" and "didn't discuss any" seem like opposites to me.  Do I need to improve in this area or not?

The comments by Reviewer 2 are even less helpful for Dimension Four: Reflective Practice and Life-long Learning to Improve Teaching and Student Learning. "good.  This is very good. You did not discuss professional development, per se." However, Reviewers 1 and 3 mention my blog and actions I have done related to professional development.  They also mention me helping other teachers to improve on their own teaching.  This leads me to wonder what Reviewer 2 had in mind as the definition of "professional development".

Finally, Reviewer 2 saves his sparsest comment for Dimension Five: Leadership in Education Outside the Classroom. Comment: "This section is very well done." Score = 3.  Then, Reviewer 2 states "Please note that the overall quality is poor.  It is often very difficult to hear. Also, the lesson starts in the middle so we don't see the explanation."  Neither reviewer made any comment on video quality being poor or difficult to hear.  This makes me wonder if this reviewer needed a better computer or speakers.  It also leads me to wonder if his analyses and scores were impacted by his frustration with the overall "poor" quality.

Let's summarize.  Overall, reviewers 1 and 3 indicate that I am doing a Very Good or Excellent job in each of the five dimensions of teaching and there are no comments from Reviewer 2 that "may be helpful".  Although the letter sent by Charlie Wayne, Educational Assessment Specialist, says "We invite you to reapply for the PAEMST Program in the future and look forward to hearing from you again," I do not plan to apply again.  Applying for this award four times and not receiving it has been enough for me.  I don't need to apply for an award to reflect on my teaching.  I just need time, space to write my ideas, and colleagues to share them with.