Days 8-11: Starting (and Restarting) Discussions

I've been bad (and tired) this week, so the blog has been ignored. Here's my day-by-day recap...

Day 8: Starting Discussions

Monday the students were randomly selected for the groups of eight I'm planning to use for the year. I handed out a sheet with some discussion expectations and the group norms the class developed last week. I had the students read and briefly discuss the expectations/norms.

I explained that each student should take responsibility for one of the eight problems and lead a discussion of each problem. The students took the brand-new personal whiteboards and began...to doodle, chat, mess around. You know, act like kids.

Some groups claimed to have fully discussed all eight problems. Yeah, I didn't think so. Two groups discussed two or three problems, and I believe that.

I had this similar experience last year. Clearly I haven't explained my expectations well to the students -- or I don't clearly know my expectations. I'm being good to not blame the students, but to closely watch myself and figure out changes that I need to make. I've got an idea...

Day 9: Restarting Discussions

Today I put the students back in the same groups. I explained that I didn't do a good job describing my expectations.

I directed the groups members to put their own work on problem #1 on their whiteboard, and for the group to discuss their efforts. Once everyone in the group felt like the problem was thoroughly discussed, they were to call me over so I could ensure that they did as I requested.

This approach worked better. I could hear and see that the students better discussed the problems. The students need to work on their recording the results on paper, but as I questioned the groups, I feel like they are better understanding what I want.

In the end, the groups collectively were able to thoroughly discuss problems #1 and 2. One group again claimed to get through all eight problems, although they didn't have me check all eight problems.

Tomorrow we continue...

Day 10: Continuing to Make Progress

Wednesday I randomly re-seated the students. I want to avoid one group getting far ahead of the other groups. By re-arranging and having each group start at the collective stopping point, more discussion and better continuity should develop.

The groups continued discussions at problem #3. The conversations were better; groups called me over to verify their efforts; students still don't want to write their work down in a notebook. Despite my offer to allow the notebook to be used on assessments, the students don't yet get it. Perhaps when the first assessment occurs next week, they'll better understand the benefit of the student-created notes.

One group was rather off-task, in terms of too much chatting about non-math and loud laughter. I attribute this to the kids still learning to be serious about the effort and a particular collection of students being together. Re-seating will help this, but I'll watch that it's not particular students causing the off-task behavior.

The groups ended collectively at problem #6. Four problems talked through is the pace I'm wanting, so let's see if this continues. I passed out eight new problems, and asked that the students prepare up through #14.

Day 11: Fixed vs Growth Mindset Talk

As I'm taking the How to Learn Math course through Stanford's OpenEdX, I'm wanting to include what I'm learning in my classroom. A couple of weeks ago, someone posted a link to a blog wherein the creator took some of Jo Boaler's videos and designed some pages where students and parents could view and discuss elements of the course.

Since I needed to put my classroom desks in rows for the quizzes/exams in all my other classes, today was a good day to start the fixed vs growth mindset talk with my Algebra 1 kids.

I started class with a math inventory test I found on Math Hombre's blog, which allows students to rank what mode of learning they prefer -- Mastery, Interpersonal, Self-Expressive, or Understanding. I collected they tests so I can analyze the results.

Next I handed out a reflection sheet and spent a few minutes discussing fixed and growth mindsets. We watch each of the three videos and I had the students reflect and write responses to some questions based on the videos. The period ended sooner than I wanted, but a few students said that the videos were useful.

I need to continue to infuse the course teachings in my classroom. Well, I first need to finish the course this Labor Day weekend...

The Plan for Tomorrow...

Tomorrow the groups continue from problem #7. I need to continue to convince the students to record their work product. Hoping to continue to see improvement, in both the students and my own comfort level.

Day 7: Syllabus and the First Eight Problems

Day 7 marked the discussion of the syllabus and explaining just what the students are getting into. Going over rules and expectations is boring, but necessary. 

More importantly I distributed to the students the first eight problems for discussion. I hope that the students take the time over the weekend to attempt the problems. And a big THANK YOU to the math department at Phillips Exeter Academy for the curriculum -- I'm adding to it and modifying it for my purposes, but without their work, I wouldn't be doing this work this year.

The Plan for Tomorrow...

I'll collect the signed syllabus strip (here's hoping that the kiddos get-r-done), and hand out the group norms that the class developed, along with some group discussion expectations. I'll interrupt 'em a couple of times to assess how the discussions are going. The students will have their first time playing with using the personal white boards, so I'll watch for more art than math.

The one question I have yet to answer: when and how to give the answers to the problems. I'm gonna ask the students what they think on the issue...

Days 5 and 6: Group Norms and Graduation Requirements

Time got away from me yesterday, so I'll write about two days at once....

On Day 5: Group Norms

Having completed the New Planet Activity and writing some reflections, today the students spent about 10 minutes discussing their individual reflections in the same six groups from the past two days. I then asked the students to take out some paper, and during a quiet five minutes, I had each student brainstorm some rules/guidelines for behavior while working in groups. After this, the groups discusses the results of the brainstorming, and each group had to distill the results to their favorite six rules/guidelines.

I led a share-out of the favorites. I asked each group, in turn, to share one rule and explain their thinking. After all groups shared one rule, I asked for any other rules that anyone would like to have on the board. Four more rules were shared.

The list...

• Everybody participates.
• Respect each other.
• Be quiet when someone is talking.
• Consideration of other's ideas.
• No arguing with each other.
• Don't be shy. Share your thoughts.
• Take it seriously.
• Be open-minded.
• Stay on task.
• Ask questions.

Not a bad list for group norms! I appreciate that most of the students treated this activity seriously. So far, I have a great class!

Day 6: Graduation Requirements

I set the students in groups of four (OK, I had one group of five. With 37 students, one must be flexible) and gave my first lecture of the year on graduation requirements. I had groups of six groups of 9th graders, and three groups of 10th through 12th graders. After explaining the requirements and answering questions, I handed out four case-study transcripts of actual students currently enrolled (made anonymous) and asked the groups of determine how many credits of which required classes the students were missing. They also had to determine if the students were on pace to graduate on time, and to offer some advice to the case-study students.

The students had some trouble with my expectations. I will have to rewrite the record sheet provided for their answers. Students were analyzing the transcripts, and a couple of students expressed sympathy for the case-study sophomore who has 25 credits after his freshman year. This student failed seven of the 12 semester classes he had.

I believe that the students have a good idea what is required to graduate. I pushed my mantra: Pass your classes!

The Plan for Tomorrow...

Tomorrow I will hand out the syllabus and discuss rules of the class. More importantly I will explain the philosophy for the use of the Harkness method in class. We'll see the procedures and expectations, and the students will get their first eight problems to tackle.

Day 4: New Planet Presentations

Today the students presented their choices and reasoning for those choices on the New Planet Activity (see yesterday's post). After ten minutes of prep time, the groups went to board. I thought the groups would take about five minutes each; they averaged about 2.5 minutes each, so we were left with about 25 minutes of class.

I handed out the reflection and asked the students to write for about ten minutes quietly. They ended up taking about 15 minutes (good!) and chatted quietly for the last few minutes.

I wish that all the students participated in the presentations; a couple of groups had some students not talk. For the first presentation of the year, I was happy with the result. I certainly need to become more comfortable with groups and presentations, and the students will gain comfort with this style of learning as well.

I also need to learn how to handle my new-found "free time" -- since the groups discuss the tasks, I don't have my usual job lecturing. I feel lost just wandering the room, listening to discussions. It's weird! Once the Algebra starts, I believe that I'll find my footing.

The Plan for Tomorrow...

For the final day of the New Planet Activity, the class will debrief as a group, and the students will generate the norms for group discussion/interaction. Should be another good day.

Day 3: New Planet Activity

Today the students started a new group-building task, called the New Planet Activity. Newly organized groups of six or seven discussed which 10 of the 30 various persons described would be allowed on a rocket ship to repopulate a distant planet. Reasons for the choices must be provided as well. Students were told that they will have to present their work the next day.

With about 20 minutes left in the period, I gave an additional instruction: the chosen ten persons must be ranked in order of importance, in case that all ten persons are not allowed to go, due to budget issues.

The groups dove in, with only a couple of students not engaging. There were a few clarifying questions, but the groups seemed to get it. Overall the period went well. Hopefully the group presentations go well, as well.

Grading Commenting the Marshmallow Challenge Writing Prompt

Tonight I've almost finished commenting the prior writing prompt related to the Marshmallow Challenge. I asked the students to write for ten minutes on the prompt "How does the Marshmallow Challenge relate to doing Algebra?" As expected, I have received an array of responses.

Since I am not grading my Algebra students in the traditional fashion (more on this later this week), I am learning to put constructive comments on the responses. In fact, based on my research tonight on "effective feedback", I found and ordered (for under $6 including shipping) the book How to Give Effective Feedback to Your Students by Susan Brookhart. I also have learned from Grant Wiggins. I hope to see my students respond positively to the comments, and the lack of a grade.

The Plan for Tomorrow...

After giving the groups about ten minutes to prepare, the groups will present their choices and their thinking/reasoning. After all groups present I will hand out a reflection sheet, and set the thinking about how the groups worked. This will lead us to discuss group norms. More about this next time...

Day 2: Reflection on the Marshmallow Challenge

When class started, the groups from Day 1 reassembled and spent a few minutes talking about the reflections that they wrote. I stamped the reflection sheet, so that the students know that I was checking that they did the work. (OK, I didn't really check!)

After a few minutes, I asked each group to speak to the class about how the group functioned and how the students felt during the challenge. I also had the groups talk publicly about what didn't go right and how the mistakes helped them in building the structure. Lastly, they discussed how the time/competition elements affected their performances.

Overall I thought the discussions went well for the first time. Early on there were students talking or sneaking on their phones, but a quick statement about appropriate behavior seemed to fix the trouble.

One senior noted that the freshmen tend to have trouble talking in groups, while the older students have gotten over that issue. She was/is right! Fear of looking stupid is a concern that the students must overcome.

I believe the Marshmallow Challenge was a quality first-two-days activity.

The Plan for Tomorrow...

The next group-building project is the New Planet Activity. Groups of six (or so) will debate which 10 persons from a diverse list of 30 candidates should be allowed on a spaceship to travel to a new planet to colonize. The students will have to rank their choices in order of importance, and provide reasons for their choices. The next day they will present their choices and logic to the class. More info tomorrow...

Two days in, and the class seems into the (non-math) group work so far. When will the honeymoon period end??

Day 1: First Day and the Marshmallow Challenge

First day of school, and all's well. Nice classes, no surprises.

In Algebra 1 the students partook in the Marshmallow Challenge, which I described in yesterday's post. After stalling about 10 minutes to allow for late students and some group introductions, I explained the challenge...

Build the tallest freestanding structure which supports a marshmallow on top in 18 minutes. Provided materials are 20 sticks of spaghetti, 1 yard of masking tape, 1 yard of string, and 1 marshmallow.

After thoroughly explaining the rules and answering questions, the groups got going. Some fun appeared to be happening, some looks of boredom, but overall, most students were engaged.

After measuring the standing structures (6 groups of 9 had successful structures), I handed out the reflection sheet (link in yesterday's post). Shortly thereafter, the bell rang.

The Plan for Tomorrow's Class...

Tomorrow the groups will reconvene and we'll have a whole-class discussion of the reflection questions. Hopefully the students will begin to engage in questioning and reflection, and it'll go for the full hour.

The purpose of my giving the Marshmallow Challenge is to provide a first common experience in

• group dynamics and the effects on the group working
• how mistakes leads to learning
• how feelings affect performance
• how time pressure and competition can affect performance
• what good work did groups do

A good first day!

Day 0: Preparing Harkness in Algebra 1

During the Summer...

The day before school starts, and I think I'm ready. This year I have two IB Math HL classes, two AP Calculus AB classes, and one Algebra 1 class -- all classes I regularly teach, so no problem with preparing.

Well, OK, this year I'm using the Harkness method in my Algebra 1 class, so I've been learning about group work, teaching for deep understanding, modifying the Exeter curriculum. I spent a week working with the California State University, Sacramento Mathematics Project, which I enjoyed. The emphasis was on group work, and projects which lead to deep understanding of math. I was continue to participate in the CSUSMP this school year.

I am also taking the Stanford OpenEdX course How to Learn Math, taught by Jo Boaler. This course discusses fixed vs growth mindsets, and the results of such mindsets on students in math. Thus far I've finished about halfway through Session 5 (out of 8).

The Plan for Class Tomorrow...

Tomorrow is Day 1 of the new school year. In Algebra the students will have random group selection and will partake in an opening group activity. I found the Marshmallow Challenge, and I believe that the students will have fun while being to learn about my new philosophies concerning teaching and learning math.

I will describe the learning outcomes of the Marshmallow Challenge next time, but you can view the TED talk that inspired me...




and view the Reflection assignment to help the students prepare for the debriefing discussion the next day.

Here's to hoping the first day goes as well as I imagine that it will!

End of Experiment Thoughts

The end of the year has come, and I slacked on updating this blog. I will write a couple of concluding posts, and follow with thoughts and ideas as I prepare for the start of the school year with Harkness in Algebra 1.

The Test Brought...

The experiment ended with an exam in the Harkness style. For review I told the students to focus on 15 specific problems from the problem set that they had worked through. The students didn't seem to be interested in reviewing. I allowed them to use their homework/notes on the exam. The problems came partly from the Exeter exam materials (thank you, Richard Hardej of Exeter!), and partly from mimicking the focus problems. I included one problem that they didn't cover in the problem set...

A restaurant has 23 tables. Some tables seat 4 persons and the rest seat 2 persons. In all, 74 persons can be seated at once. How many tables of each kind are there? Show your work or justify your answer.

I hoped to see that the students would attempt draw out the tables, or guess and check, or actually write an equation or two (they had learned systems of equations last semester).

Disappointment...

Well, the exam was a mess, to put it nicely! Top score: 29.5 out of 39 (76%), with the expected distribution -- previous top-performing students scored at the top, and my usual weak students scoring weakly. I decided that the scores would unduly lower grades, so I didn't count the exam results in the overall grades. I did keep a number of the exams for analysis purposes.

Also, I was surprised how many students couldn't get the answer to the restaurant problem. More so, there were many students who didn't even attempt the problem. Frustrating...

But Hope

Interestingly, despite my (not unexpected) disappointment over the results, I still hold hope.

• I learned that the problem set was not at the correct level for my situation. If I had 12 students in one group with my attention, I believe my students could have handled the difficulty level. With four groups of seven, I could not be everywhere, so the students did not delve deeply enough to thoroughly learn the material. My fault!
• The two week experiment was too short a time period for the students to learn how to learn in the Harkness method. I believe that starting from day 1, instilling an investigative and discuss-based bent, will definitely provide better results.
• More so than usual, the students made errors on the exam. However, there seems to be more consistency in the errors. Perhaps it's wishful thinking, but just maybe, the students were learning, but the limited time limited their learning. The same error occurs on test after test. With more time and better problem sets, I believe that the students will learn better, and these errors won't occur.
• Students who did attempt the restaurant problem, did use varying methods to solve the problem. I found diagrams, guessing-and-checking, working backwards (starting from 74, decreasing by 4's and 2's), an attempt to write a system of equations... I'm happy to see the varying attempts. I need to coax students to use varying attempts in homework, and lead them to attempt on the assessments.

Throughout the two weeks of my Harkness experiment, I ran into frustrations. Each time, I tried to reflect and decide what I could do about the troubles, rather than blame the students. I'm happy about that!

With all of this, I have my work to do this summer. I'm energized to devote time and energy into Harkness-izing my Algebra 1 curriculum. But I'm scared that I'll mess up a group of students in the next year... I'm staying positive!

Smaller Groups, Day 2

Today was the second day with groups of 6-7 students, rather than the Harkness standard of 12-14 students. Today went very smoothly. Groups got together independently; they started up where they left off; and although I would like for them to get to the discussions more quickly, they are volunteering/assigning problems and working on them.

One example of the (re-)learning that's occurring: Although the students solved problems like this...

\[\frac{2x}{3}+\frac{3x+5}{2}\leq5\]

...in Chapter 3 (Solving One-Variable Linear Equations), Chapter 4 (Solving One-Variable Linear Inequalities), and Chapter 11 (Rational Expressions and Equations), on Monday the students acted like they had never seen such a problem. You know, fractions are scary!

Today, two days later, and students in every group is showing solutions to this problem, and discussions about errors were occurring. Marvelous!

Using the Harkness method (I need to figure out a name for my evolving method) and selected, appropriate problems from the Exeter Math 1 book has shown me that the student forgot more than I realize--more than they realize. The student-led discussions are bringing back forgotten knowledge--or maybe that the students are actually owning and gaining understanding of work that they have done.

I have also realized that I will have to work hard this summer to rework the problems for my Algebra 1 students for next year. I stole used the Exeter math questions for my students, but I see that my students need to be led more directly in finding connections between problems. They aren't naturally looking for how problems relate. At Exeter and other private schools with small class sizes (Catlin Gabel!), one teacher with 12 students means that the teacher can watch and comment on every problem. With my 25-27 students per class, I cannot hear everything nor participate with each group every moment. I'm sure that connections are being missed, which means reduced conceptual learning. I've got some ideas for next year...

Tomorrow I am gone from school for my District's next CCSS Workgroup. I hope that the students handle themselves while I'm gone. I left a couple of questions for my substitute to answer about his perceptions of the discussions; I can't wait to find out what he thinks.

Less frustration, more peace...almost!

Today's other Algebra 1 class responded to the smaller groups as positively as did the earlier class. They engaged as smaller groups (6 or 7 students), and made positive progress in their Harkness discussions. Well, almost...

I did have one group that featured a couple of girls almost came to blows. You see, student A was presenting a problem. Student B asked a question of Student C, which C began to answer, which caused Student D to say something like, "Hey, shut up! I'm trying to listen." Student C took umbrage to D's comment, and Students C and D started after each other.

I found out what occurred, ultimately deciding that Student B was the instigator of the side-conversation (although it was math-related, it was rude to talk when someone else was discussing), and apologies came without prompting.

I see this situation as a positive. Student D tends to be quiet and reserved; today, she stood up for herself and the process. Student C was trying to help another student. Excellent!

I also started having the groups track their own discussions. I slightly modified a sheet from Johnothon Sauer, which had each group track the problem number, the presenter of the problem, and which students made a useful contribution to the discussion of the problem. This group tracking seemed to help the groups, since they knew that they were responsible to each other more overtly.

I continue to find evidence of the value of the Harkness method -- the student-centered discussion; the natural ability of the students to find connections when they discuss; the growing comfort in discussing problems, even when the students are uncomfortable with the material.

The one big challenge continues to be that the students won't attempt the problems and record their attempts if they perceive the problems as hard. I'm realizing that my usual method of operation -- teaching by lecture, homework of my own worksheets, answers shown the next day and questions answered, worksheets collected once a week or so -- hid the fact the many students weren't doing homework. I knew that many weren't doing the homework daily; that many weren't turning in the homework packets regularly, or turning in partially done homework packets, but I didn't have to face that problem each day so obviously. With the Harkness method, it's clear when students haven't worked on the problems. My struggle: how to motivate the nightly work?

Frustration...and Peace

As I am in the middle of my experiment, I am experiencing the full range of emotions and issues expected of any change.

I started my Harkness experiment on Monday, May 6. The prior Friday I had given my 52 Algebra 1 students the first eight problems (mostly pilfered from Exeter's Book 1), along with some explanation to the intent of the method. I expected that the students would try the problems and come to class ready to discuss.

Yeah. 12 of the 52 students admitted to attempting the assignment. I called an audible and gave the students 15 minutes to independently work, and then the students began.

Fast forward to yesterday (Monday, May 13)... The students had a few problems to work over the weekend, and 14 of the 50 present students had tried the problems. Also, the groups of about 13 students each were just a mess. Lack of preparation and lack of interest came together in a bad way.

After (barely) surviving the day and blaming the students, I thought, "What can I do to improve this?" I took Johnothon Sauer's advice and created groups of about six today.

I had to write this now...my first Algebra class went great! I handed out a sheet detailing what a good group discussion should look like, and the smaller groups did it. I could sit down, engage the students, and the groups worked and were quiet about it. They discussed how to solve a challenging equation, and worked together.

Yesterday, I wanted to quit this experiment; today, I love Harkness!

More later...

My Harkness Experiment

I'm late in creating this blog, but here I go...

It was April 3, 2013, when I discovered the Harkness method. I am a member of my school district's Common Core Workgroup, and the group was having its second meeting. I was researching teaching approaches related to the new Mathematical Practices, and I found the math department website for Phillips Exeter Academy. Something just clicked, and I was smitten!

In just over a month, I have spent many an evening scouring the Internet, searching for information, materials and experiences related to the Harkness method. I have gone on an out-of-state classroom visitation to Catlin Gabel and spent the day with Jim Wysocki and his math department, learning about how they implement Harkness. I have had communication with Johnothon Sauer, author of Harkness for Thirty, his blog detailing his experience implementing Harkness in his Precalculus classes. And I have had my two Algebra 1 classes working in the Harkness style for a week.

During this next week, I will discuss my Harkness experiment: how I feel about it, how my students feel, what I've tried and what I need to do. Ultimately I have to decide whether I will commit to Harkness for the next school year. Right now, I believe so.

This whole experiment is exciting, but scary. The new Common Core Standards brings change; the new emphasis on the Mathematical Practices is a big change. My Harkness experiment is my personal attempt to find how and where I am able to change.