Tuesday, May 22, 2018


I'm not a big fan of review activities before a unit test or final exam; I'm also not a big fan of unit tests or final exams. But that's not what this post is about...

The fact of the matter is, it is the expectation of my department/school that I give some type of summative, comprehensive final 'thing' at the end of the year. Someday, the final 'thing' I give will be an authentic, socially relevant project that allows students to show intelligence in different ways. For now, however, the final 'thing' is just a final exam. And my students expect some type of in-class review to help them prepare for the final exam.

My first several years' teaching, my review activities were pretty standard. For example, we did a lot of station review where I there are different stations set up around the room--each with a different concept. Students choose the concept they want to work on and go to that station. I didn't like the station structure because it felt passive: how do students decide where to go or what to work on? Are students reflecting on what they know/don't know? Or are they just working? Probably my biggest dislike of passive review is the message it sends to students: we spent time in class 'studying' therefore you are better prepared for the test. However, I feel like this message neglects to acknowledge that action (being in a room where studying is happening) isn't always synonymous with accomplishment (greater understanding of a concept).


A few years ago, I came up with a review structure that I felt like it addressed some of the issues. I call the review structure TeachBack. I don't think it's a perfect structure, and it can be a lot of work to set up the right partners/groupings, but I think it is a step in the right direction.

Why do I love TeachBack? I thoughtfully group students, give students the tools they need to be an effective peer coach and then watch as the room FILLS with amazing conversations and learning. Also, I can focus on the few students that really need intense intervention since all other students are diligently working with their peer coach.
  1. Intentionality: I narrow down the review concepts so that we are only focusing on the essential concepts. There can be a lot of skills in a mathematics unit. My goal is to sift through all the skills to identify those skills that are most essential. In a linearity unit, this might mean focusing on the skills equation to graph, point and slope to equation, graph to equation, and identifying a linear function in a table or equation. In terms of being the most essential that is all subjective. The point is, rather than just reviewing everything from the unit, I am very intentional about WHAT skills I want students to work on.  
  2. Clarity: However I decide to tweak the structure, I am very, very clear to the students on what success looks like. This means I use sentence frames and word/phrase banks to model how I want students to talk to each other. I also do a fishbowl before the start of the activity. I usually sit with 1 or 2 students (depending on how I'm going to structure the activity), call everyone to gather around us, and the students and I model what the activity should look like. I also try to use positive praise in the first 10-ish minutes of the activity to shoutout groups that are demonstrating the body language and words I expect students to be using. 
  3.  Choice: Students can choose what skills to work on. And if they want to practice the same skills more than once, I try to have multiple versions of practice sets for each skill ready to go. 
  4. TeachBack Cycle: This is the 'TeachBack' part of the activity. The TeachBack process is three steps. First, the coach does an example problem for that skill. The coach needs to make their thinking visible by talking out loud while they do the problem. And the student(s) need to ask questions. Second, the coach and the student(s) do the problem together. Again, talking out loud, asking questions, and having discussions about mistakes or misconceptions. Third, the student does the problem on their own. The coach cannot answer questions at this point. The student is encouraged to try their best and the student and coach will discuss the work and any potential errors once the student is done with the problem. 

Over the years, I have modified this structure a lot. One thing I like about this structure is that it is easily modifiable. And I like that there are a million ways to modify this structure. To me, that 's one of the benefits. And, depending on the personality and/or needs of a certain class, I can easily tweak this structure to better meet the needs of those that class. Some modifications:
  • sometimes I offer an assessment at the beginning and end of the activity so students can think about what to work on and then see how they did
  • sometimes I do partners with no defined coach--the instructions are clear that partners take turns on coaching
  • sometimes I do triads with an assigned coach

Finally, I like this structure because it is about more than 'review'. Students are learning soft skills like how to reflect and how to coach. So I'm not just reviewing material that's already been learned, I'm also making space for students to develop higher-order skills.

an example of what a skill practice page looks like

the reflection that students/coaches complete after each skill

an example of a coaching phrase bank for this activity

Grouping Students

How I group students is key to this activity. On matter what modifications I make, how I group the students is an important part of this activity. I am not an expert on grouping students. There are other, blog posts on this from other teachers. There are also a lot of good books/articles on grouping students. However, my basic philosophy is this:

When I group students, I think about what combination of students will best put the students in that group into their ZPD. For example, I would partner the student most proficient in a skill with a student that is least proficient in that skill. Neither student will be in their ZPD. Rather, the most proficient student might be partners with a student that is doing well on foundations but is ready for a challenge. Similarly, I might partner the student that is least proficient with someone that has shown a lot of growth in the unit and is thus ready for the challenge of being a tutor. 

The other factor I consider when grouping students is their ZPD for coaching. Some students are not ready to be coaches and this has nothing to do with comfort in the content. They just aren't ready to be coaches (I image my college professor for Complex Analysis teaching my 9th-grade algebra class...he is an expert in content that is NOT ready to be a teacher for 9th grade). So I try to consider who is ready to coach and what students would make the most sense to put them in their ZPD for coaching. 

Finally, when grouping students I think about status. Classrooms are messy places where gender, race, socio-economic status, and other forms of status all intersect. Ideally, my groupings assign status or competency to the right students without reinforcing existing status that may or may not be healthy. For example, I don't make the male student that shouts out the answers first a tutor. That would be reinforcing the "male, fastest = smartest" status. I don't want to do that. (side note: if there are a lot of those types of students in a class, I tend to use the 'no assigned coach' model and make clear that students need to alternate coaching). 

Does TeachBack solve all my problems? No! Is it the easiest activity to facilitate/develop/implement? No! Is it worth it? To me, the answer is yes. The traditional review never felt satisfying. TeachBack addresses some of the things that made review feel unsatisfying to me while still honoring that my students want/need/expect some type of review to feel prepared for the final exam. And that feels like a step in the right direction. 

If you try it, let me know how it goes. I attached a pdf of the TeachBack for Linearity that I'm using this week. 

TeachBack Linearity PDF

Tuesday, April 10, 2018

Circles + Squares

I've been experimenting with Question Formulation Technique (QFT) in my math classes this year. I used QFT for the fourth time today. And I had a big ah-ha after the lesson.

The purpose of QFT is to shift the intellectual authority from the teacher to the students (or maybe from the teacher to the students AND the teacher...since I'm still part of it).  The result is student-centered, student driven lessons that appeals to students' curiosity while also meeting content standards. Easy, right?? Not really.

My first attempt was ok. I used QFT as a launch for a Project Based Learning Statistics unit.  As I look back, I think the QFT was great. My follow through was lacking (more on that in a minute).

My second attempt exceeded my expectations. But that was a perfect storm of a lesson. I also spent way too much time planning that lesson. And my follow through was on point.

My third attempt was ok.  We used QFT to launch the exponentials usit. Actually, after some reflection and a quick conversation with the amazing people from The Right Question Institute, I think the third attempt was decent. But my follow through was non-existent. And I think the achilles heel of QFT is the follow through.

I am not an expert in QFT, but my process for QFT tends to look like: 
  1. Have students participate in some event. Watch a video clip, or a lab demonstration, or read a provocative quote, see a startling statistic, etc. But the event needs to evoke the curiosity of students. 
  2. Give students the "QFT Rules". Again...I'm not an expert. Here are my rules. Mostly stolen ideas from others. 
  3. Let students ask as many questions as they can. (you def need to encourage them to keep questioning. 
  4. Go through some filtering. Have groups change close-ended questions to open-ended and have groups select their top 3 questions.
  5. Have a class share out. The goal is to make sure each groups top questions are represented. 
  6. Then...do something with the questions. This is the follow through. And, in my experience, the follow through is the tough part. 
As a participation structure, QFT is genius. One reason I like QFT is that it gives students an opportunity to show different ways to be smart in my class. Since I teach math, students with strong procedural fluency are sometimes assigned status by peers and labeled as smart. QFT helps address that. 

QFT also pushes students to be curious. Sometimes learning can feel prescriptive or rigid. While the structure of QFT is somewhat prescriptive, the process creates a safe, encouraging space that supports students in the process of taking intellectual risks and asking really good questions. 

Today, I used QFT to introduce the quadratics unit. I showed students a bingo chip and showed them a 23x23 inch square I had measured on the board. I asked them how many bingo chips fit into the big square. (This is borrowed from the Penny Circle task...the algebra 2 teachers at my school build most of the quadratics unit around the Penny Circle task and they kindly asked that I modify so that it isn't immediately recognizable to students. Hence, Circles + Squares Task.) The task is linked below...nothing special though. 

Then I gave each group a few squares and a lot of bingo chips. I had squares of side length 1, 2, 3, 4, 5, 6, 7 and 8 inches. Each group got 2 or 3 squares. Students collected the data. We put the data into a class data table (averaging the number of bingo chips for a given side length as needed). I then asked students to tell me what type of function would best model the data in the table. I gave them like 3 minutes to discuss this. The goal WAS NOT that they have a definitive answer. The goal was to get them to explore the data in the table or graph (some groups also graphed the data). 

Then, I stopped them and we started the QFT process. They had really good questions. I teach two classes of algebra 1. These are the QFT results from both classes. 

The QFT was great. But the follow through...sigh. The follow through. Here is what I realized today:

QFT is awesome, but QFT isn't really the goal. The goal is to make my classroom student-centered and to make learning student-driven. QFT doesn't do that. What I DO with the questions students come up with is where QFT really becomes a tool to make my classroom more student-centered. 

In my first attempt at QFT, the QFT went great. But we never really used the questions to drive the project or the learning. 

In my second attempt at QFT, the questions the students generated BECAME the students' projects. The questions drove the learning and the focus of our work. And that was powerful, student-centered and student driven. 

In my third attempt, the QFT was great, the questions were solid, but I got buried in other work and never really referenced back to their questions as we moved through the unit. 

Thus, the goal with quadratics is to explicitly connect our learning back to the questions generated for the QFT. This is my opening slide for the next lesson (there are two different slides because 2nd and 3rd block had different questions):

2nd block
3rd block

I also plan to revisit these slides at the end of that lesson as a debrief. 

Basically, I took the lesson I had planned, looked through their questions and then found the questions that matched the existing learning objectives (or learning goals...or standards...not sure on the right term).

I think it will be powerful to show them this tomorrow. I also am amazed that they came up with the questions that, more or less, align with the standards I have to teach. 

Each time I do QFT I learn a little more. Which is the motivation to keep doing QFT. 

But, as I am finding, the QFT can be phenomenal, but if I want to effect change in how I teach and how students learn, the crux of the work happens in the follow through. That is, what I do with the questions the students generated is essential to the process. 

My goal now it to keep referencing back to the students questions as we move through the quadratics unit. I'll let you know how it goes! 


Friday, March 23, 2018

Lesson Reflection (homework)

(there are links to my Lesson Reflection templates at the bottom of this post)

I've struggled with homework for many years. When I was a new teacher, I struggled with homework logistics: managing my time grading it; getting students to do it; having a coherent, enforceable, sustainable absent/late policy.

My third year teaching, I came up with a homework system I liked: I began letting students 'grade' their own homework and I graded the quality of their corrections. Here is a blogpost on this homework system. Many of my teacher friends use this system--and I still like it. And it addressed some of the logistics problems. But something still bothered me about homework.

This year I began to notice a few things. These things were always there in front of me, but I didn't really see them until this year.  First, I noticed that the handful of students that didn't do their homework in each class tended to share a few characteristics. They struggled in class; but they also struggled with 'doing school'. Which often meant struggling to complete homework.  And their grades suffered because of it (I changed my grading policy a long time ago so that no student could fail for not doing homework). But all the zeros still dragged their grade down.

I also noticed that in parent emails, IEP meetings, or conversations with AVID teachers (or teachers of other support classes), one of the first topics to come up when we discussed struggling students was homework. I feel like the assumption we were making is that if the student worked a little harder outside of school on their homework, the other problems would go away. Like, not doing homework was the cause rather an effect of a greater problem.

I also started noticing that I often said (and I often heard other teachers say) things like: if it's a review topic just assign it for homework. Or they can do it for homework and ask questions if they have them.

One reason I think these things were on my radar is because I read Mathematical Mindsets by Jo Boaler over the summer. It's a great book and the chapter on homework was a game changer for me. Boaler really helped me see the inequity in homework. Homework is a social justice issue. Homework is an equity issue. If you haven't read Mathematical Mindsets, I would definitely recommend the book!

At the start of this school year, I began to think about what it would mean to not give homework. And, one day in October, I got the courage to ask the teachers on the algebra team what they thought about me not giving homework anymore.

Then, during our winter break, I decided to change my homework policy for the coming second semester. I decided I would no longer give daily, content based homework. Instead, I would give students a weekly Lesson Reflection. I loved some of the reflection questions I saw in  Jo Boaler's book so I used those as a starting point.

Implementing a new routine midyear is always a challenge. So there was a lot of norm setting and communication that had to happen in January and February in order for the new Lesson Reflection system to actually work. One of the best things I did to help communicate my expectations to students was to scan student examples of "high quality" work and "low quality" work. In the first few weeks of rolling out the Lesson Reflection system, I would show these examples daily. It was a slow start, with lots of very basic answers from the students (example: "I learned how to do a new problem"). But, with fervent communication to the students around my expectations for this new system, the quality of the student's responses began to improve.

this is a slide I would show students at the start of each class to help communicate my expectation for quality of their work
We are now in late March and I'm happy with what I see in the students work. The quality of their responses have improved greatly. But, more importantly, the Lesson Reflections give students an opportunity to express their math identities in different ways. Homework isn't just procedural fluency. Students can share a point of confusion; students can ask interesting questions about the content; students can reflect on something that was difficult or something new they learned that is exciting to them.

I also invite students to keep their Lesson Reflection for the week on their desk during class. That way, if they come across an interesting problem or a point of confusion, they can make note of it during class.

Has this system solved all my problems? No. Absolutely not. There are students that still don't do homework (remember the students I mentioned earlier that have trouble 'doing school'...they still do not do homework). But I've taken the content out of homework. And that makes things feel different to me. I used to get frustrated because students that didn't do their homework seemed to be at a disadvantage compared to their peers that did the homework ("you didn't get the practice you need to be successful!"). Now I don't feel that frustration because what I teach isn't dependent on assumptions about what students having done something content related outside of class.

But grades haven't changed. Students that did well on tests still do well on tests. Students that struggle on tests still struggle on tests. So, the outcome hasn't changed (and i'm willing to admit that is a fault in my system). But that also means that the traditional homework I used to give also wasn't an important factor in understanding/not understanding math.

But what has changed is my relationship with the students: I don't nag them for homework because homework has become low stakes in my class. And when I talk to them about their grade (or I discuss their grade with parents or support teachers) we don't talk about homework. We talk about what the student does and does not understand IN CLASS. And what behavior/habits the student needs to change IN CLASS to be successful. And this feels more powerful to me.

Moreover, I'm not making students that struggle with school do content work OUTSIDE of class. Which is how I think homework becomes an equity issue. Why have I been asking students to do math outside of class for the last 6 years?? I don't want kids doing math in isolation, at home, without support. I want them doing math with me and their peers. Celebrating new findings and puzzling over challenges together. Supporting each other in our learning. Math is social. Homework is anti-social.

Also, this is all new to me. So I can acknowledge it is not a perfect system. And it is a new undertaking during a year when I'm doing a lot of new undertakings (Stats Immigration Project, Social Media Stats Project). So this system isn't perfect. Ideally, I would have a rubric to help guide the quality of students work--and I will make a rubric for next year.  I do grade the Lesson Reflection, but each one is only worth 5 points. And the impact on the overall grade is negligible.

For now, reimagining my homework system was more about me: my willingness to take a risk and challenge a school tradition that has never felt compatible with my teacher identity. And Jo Boaler helped me understand why homework felt incompatible with my teacher identity. And the Lesson Reflection is a baby step in addressing that feeling of incompatibility.

Lesson Reflection (basic version)

Lesson Reflection (upcoming test version)

Lesson Reflection (lots of new vocab version)

Wednesday, February 21, 2018

Immigration Project: A Thank You Letter to my Students

Dear Students,

On Friday you shared your Immigration Statistics Project with staff, administrators and district personnel. All of you presented your work at least 10 times on Friday. And each time you presented with passion and with confidence. And you did it in a language that is not your first language. Some of you just arrived to the United States in November! I am so proud; so proud.

There are many impressive things that happened on Friday. But the best thing was seeing you all share your expertise as immigrants and help educate our school community about immigration issues in the United States. Of course, I’m a math teacher, so I love that you used statistics to help support your work. But I’m even more impressed that you bravely told your story to help the statistics come to life. And you helped us better understand immigration issues in the United States like the economic implications of ending DACA, the proposed border wall, and the assumptions politicians and the media make about the relationship between immigrants and drugs/crime. Our staff is more knowledge about immigration because of the work you all did! I am so proud of you; so proud.

I’ve never seen students work with the purpose and focus that you all had on this project. And, while I know I’m biased, I’ve never seen an entire class deliver such consistently high quality work. Like, every single one of you showed tremendous growth in your ability to talk about statistics with precision and present your findings to the public. I’m so proud of you; so proud.

As I think back to some of the things I heard you all say on Friday as part of your presentations, I get tears in my eyes—tears of pride.

When I heard one of you say, “when we hear people talk about the wall, we feel sad, homesick and angry,” I feel proud of your honesty.

When I heard one of you say, “we think the border wall is racist because the majority of undocumented immigrants overstay a visa and come from Asia or Europe, they do not cross the southern border,” I feel inspired by your willingness to educate others using facts and statistical representations.

When I heard one of you say, “when we hear people say immigrants cause crime, this implies we cause crime and this is not true. We came to this country to study and for a better life,” I had to fight back tears because you inspired me with your courage, honesty and passion. I’m fighting tears as I write this paragraph.

And, Marvin*, when I heard an administrator ask you about a specific graph that was part of your groups presentation, I’ll admit, I listened with a bit of apprehension. I know the last few weeks have been difficult for you—to be honest, if I were you, I don’t think I would even have the resilience to be at school that week. I know you face challenges in your life that make school seem insignificant. But you responded to the question with precision and confidence. As you pointed to the graph you said, with such authority and such perfect English that, “as you can see in the graph, as the years are increasing, the amount of illegal drugs seized at the Mexican border are decreasing” I was beaming. You were constructing knowledge and sharing that knowledge as you explained the graph to the administrator. I am so proud of you; so proud.

I’m proud of all of you for having the courage to speak your truth and tell your story about immigration. And, while I think I could improve a lot on this project for next year, I couldn’t be happier with the results of your work. It would be an understatement to say I’m in awe of the work you did. And I’m grateful for what you taught me and the other teachers and staff members about immigration issues in the United States. Students, you were the experts on Friday. You rightfully owned the day and I’m so proud of you; so proud.

With admiration, love and tremendous respect,

Your Math Teacher

*Marvin is not his real name

Monday, February 19, 2018

Immigration Project Days 7-13

Most of days 7-13 were work days because students had a lot of work to do! And a lot of English to learn so they would be ready to present to the public. Students worked incredibly hard over the course of these 7 days (for the most part). And all students showed tremendous growth. I also worked incredibly hard over these 7 days and I showed a fair amount of growth as well--I also learned A LOT for next year! Here are a few of my learnings:

Structuring Work Time

Probably my biggest ah-ha during days 7-13 was the power of setting clear daily goals and using a system to help me and the students check progress against those daily goals. To be honest, I don't think I did a great job of setting clear goals and checking students progress towards the goals on most days, but I learned a lot for next year.

After a few rough days of inconsistent results across groups, I did something simple that worked really well. First, I CLEARLY explained that there were three goals for the day. Then, I put those goals on the front board as Goals #1, #2, and #3. Finally, I wrote each group on the front board with a 1, 2 and 3 under their names and I asked groups to check off a particular goal once I had seen evidence that it was completed. 

While each group got some work done on days 7-13, ALL groups finished all three goals on the day I used the checklist system on the front board. And this is noted prominently in my "change/add for next year" list! 

Leading By Example

I did a PBL Statistics Unit with my mainstream algebra class a few weeks ago. The topic was teen health and social media. One big ah-ha from this unit was the power and importance of the doing the project myself "as a student". And that was the case with the Immigration Stats Project as well. 

The first benefit to doing the project as a student is that it helps inform my teaching. With the mainstream class's social media project, the big ah-ha for Ms. D (my student teacher) and I was that we developed our claim AFTER looking at the evidence. But we were expecting students to develop a claim first and then find the evidence. Discovering that helped inform our teaching and how we structured the project. 

The other benefit to doing the project as students was that we had an example to show the students. Especially since I haven't taught this before, I don't have exemplary student work to show. Thus, doing the project means I have something to help guide students. Though, I am very clear with the students that my work was only an example and that I expect them to add their own voice, creativity, and extend beyond what I did in my example. 

Misleading Quote

One goal of this project was to have students present an alternative narrative to what the media/politicians tells about immigration. To accomplish this, I created a warmup structure called "The President Says...". We did this on day 9.


I gave students a set of 4 graphs (shown above). I projected one quote and asked students to look through the graphs I gave them and decide which graph is the best counter evidence to his statement. 

This was fantastic! The students did such a great job. It was so gratifying to project a quote, ask students to talk to their partner about which graph presented the best counter evidence, and then see 7-10 hands go up! I was very happy! 

I then let students know they would be adding this to their project. I gave them quotes (I found the quotes that best fit to the claim--it was really hard to find the right quote). 

I'm glad I added this to the project. I think analyzing the misleading quote gave the students agency--it was so powerful to see them use their expertise as immigrants along with the statistics they found to challenge a statement from the President. 

Feedback Rotations

The most powerful part of PBL for me as a teacher is that I am able to assess students, give feedback and then provide opportunities for students to apply that feedback and then be reassessed. 

What I did well for this project was feedback and assessment on soft skills like presenting. I didn't do so well with feedback and assessment on content assessment, but that's an opportunity for next year!

I started by teaching specific speaking skills back in November with mini presentations (well before we started the project). I taught students about eye contact, posture and voice during these minilessons. I would assign them a specific goal for that weeks presentation (eye contact, for example), give them a week to work on it, and then have a mini quiz with feedback. The following week, I would add a new goal (posture, for example) and include the goal from the previous week. This worked great!  

Once we started the project, I also gave them a lot of feedback. Even before their posters were done and their presentations were ready, my student teacher and I were checking in on the presentations and giving them feedback. Here is the feedback form I used for the presentations. Over the course of days 7-13, each group was given 7-10 rounds of feedback. That's a lot of feedback! And it showed in their final presentations. Every staff member that saw the final presentations came up to me to comment on the awe of the quality and professionalism of the final presentations (many staff members didn't realize they had just heard a student brand new to this country present!). 

The final class before the presentations, I set up a structure where 3 groups would present and I assigned non-presenting students to a particular group to give feedback. Then we would switch and the non-presenting students would present and the students that just presented would act as audience members and give feedback. We did 5 or 6 rounds like that. Then, after we did all the feedback rounds, I gave groups about 20 minutes to practice their presentation. This was perfect because they had just received SO MUCH feedback from their peers and then had a chance to immediately apply that feedback. 

Something that surprised me was that the students were kind but critical in their feedback. Clearly, they understood the expectations and they were willing to give each other critical but kind feedback.  I heard SO MUCH peer-to-peer coaching (you had good posture, but you need better eye contact). As we were doing the rotations, I could clearly see that the students cared about the quality of each other's work and they wanted to help each other improve. 

Learning How to Present

During one lesson, I showed the students a video of Hans Rosling's Ted Talk. Hans was a famous stats guy that was well known for his enthusiastic, passionate, and engaging presentations using stats. I showed the video because I wanted them to see an example of how one might interact with a graph when presenting. 

If you've never seen Hans or this video, the magic starts at around minute 4. 

Quick funny story: my student teacher, Ms. D, actually taught the lesson where we showed the Hans Rosling video to the students. AND our principal (a great guy and great principal) dropped in to observe. So Ms. D showed the video and ask the students, "why did I show this video to you?"

Lots of hands go up. Ms. D calls on a student. Student says, "you showed us this because he doesn't make good eye contact." True. But not why we showed it. 

She calls on another student. "You showed us this video because he has bad posture." I had to suppress my laughter....the kids clearly knew what we expected in terms of eye contact, posture, etc and they didn't see that in Hans's video. AND Ms. D had a bit of internal pressure because the principal was observing. It took Ms. D a few more tries before a student observed that Hans did a great job interacting with the graph. And Ms. D did a great job facilitating that conversation! 

The Power of PBL

Looking back, these lessons feel like a blur. But now that presentations are over and kids exceeded my wildest dreams in terms of executing their presentations, I know that the lessons were effective. 

I think the biggest learning for me is the power of backward planning for PBL. I imaged what I wanted their final presentations to look and sound like. Then I backwards planned each of those skills (speaking skills, interacting with graphs, talking about statistical representations in a meaningful way) and created a lesson to teach that skills. Sometimes it was a mini lesson (the Hans Rosling video) and sometimes it was an intense series of lessons (statistics academic language production or speaking skills). But I TAUGHT the skills I expected them to be proficient in--whether those skills were content skills or soft skills. And then I ASSESSED those skills and gave students immediate feedback. Then, gave students another opportunity to be assessed on that skill so that the student and I could see the growth. This is the power of PBL. 

Stay tuned for my next post which summarizes the final presentations. Spoiler: the student presentations were so beyond amazing there isn't even a word for it!

Tuesday, January 30, 2018

Immigration Project Days 5 and 6

My initial thought was that day 5 wasn't what I expected. But Ms. D, my student teacher, helped me see the silver lining, which I appreciate. The project goal was to find another piece of statistical evidence for their claim and most groups accomplished that. The content goal was a quiz and that went ok. So what didn't meet my expectation?

Honestly, I think the problem is my own internal critic. The project launch went really well--like my favorite lesson from 6 years of teaching well. And that set a high standard. Now that I look back on it, Day 5 was really just a 'work day'. It wasn't sexy; it wasn't epic; it was just a day when (most) groups were using their time to look through the data portfolios I gave them and determine which statistical representations best supported their claim.

The quiz was a 4 question quiz on some of the statistics content. There was a histogram question, a question on using a trendline equation to make a prediction. Another question on finding mean, median and range. And a final question on describing the trend in a scatterplot. I struggled with whether to give this quiz or not. However, I needed some way to check individual understanding. I've have feedback cycles built into the unit, but that feedback is for the group and the product. I'll do one more 4 question quiz before the unit is over. The first one helped me see what students need to practice (and I've designed My Favorite Mistake problems as a reteach).

Also, it was a rally schedule on day 5. Which means nothing to you, but is total chaos at my school. We had a rally that day, which meant a special schedule to accommodate a mid-school day rally. The biggest impact for me and students: lunch is at 1pm instead of 11:15am. This is a big deal. Thus, when the students started sputtering and goofing around the last 25 minutes of the class during project work time (right before the very late lunch), I could understand why. They were hungry. So was I.

Day 5 was just a normal day. Work got done. Assessments were taken. High school students were being goofy. And that is ok!

For the day 6 lesson, I was stuck on where to go after day 5.  Groups have claims and most groups found at least two pieces of evidence for their claim. I thought a lot about what to do next (there was a weekend between days 5 and 6). I realized I needed to present a clear picture of next steps to students. And I needed to build in more support for the presentations.

For day 6, I started with a project overview. I showed them a calendar of the next 3 weeks and what I had planned for each lesson in terms of project goals and work time. I also highlighted the presentation date.

I then told students my goal is that they have a high quality product (including the presentation) ready to present to their audience (other teachers, staff, and district admin). I also shared with them the scripts I came up with.

As I was thinking and planning this weekend, I realized students need scaffolding to help them structure their presentation. And my big ah-ha was to use groups roles as the scaffolding.  One group member does the introduction and has a script for that, another group member explains the first evidence (evidence #1) and has a script for that, same for the second evidence and the conclusion. I like this because it adds scaffolding without taking away student choice.

Then, I gave each group member their script. I'm a little embarrassed sharing these scripts on my blog because they are a rough draft. I think this material will look better (and better clarify expectations) next year. This year I am truly making things up as I go along!

I like these scripts (with the caveat that they will be 100x better next year). Again, they provide support while maintaining student choice. Also, the students really liked these and they were actively using them right away. Success!

For day 7, I am going to have mini-workshops for each role. So I'll call all the introduction students from each group over. We will spend about 10 minutes (probably less) on questions, advice, and feedback for their intro. Then, I'll call all the evidence #1 students from each group over for a mini-workshop, etc.

I also let students know there are two individual checkins this week. Rather than check in on content as I did with the 4 question quiz, I am going to check in on presentation skills. On day 7, after we do the mini-workshops, my student teacher and I will each take about half the class and have the students read us their part. This will be for feedback only (and only feedback for presentation skills).  We are going to use the following form:

Finally, I let the students know they will present again on Friday. This time for feedback and a grade (like a quiz). I've been clear that I don't expect perfect English and they can read from the script, but they must make eye contact, speak audibly, have good posture (mostly no fidgeting) and show evidence of practice. I think it is important that I'm assessing soft skills as well as content skills. So much feedback for the students! 

Wednesday, January 24, 2018

Immigration Project Days 3 and 4

I just finished Day 4 of the Immigration Statistics Project in my algerbra class for English Language Learners.

The project launch on Day 1 was amazing.

Day 2 was solid for students, but left me with a lot of questions about next steps. Especially how to minimize the amount of help I provide in order to preserve student choice and autonomy.

Days 3 and 4 Goals

The content goals for days 3 and 4 were spiraling back to the previous week's lessons: mean, median and the effect of outliers as well as correlation, causation and lurking variables. 

The project goal for day 3 was for students to revise their draft claims from Friday. The project goal for day 4 was to finalize one piece of statistical evidence for their claim AND explain how that evidence supports their claim (hopefully using vocabulary and phrase from class). 

Overall, the work continues to be awesome. Here are my three big takeaways after days 3 and 4.

Forgetting the Obvious

I didn't notice this as an issue on day 3, but there were definitely problems on day 4. I had to step in and mediate for a group that wasn't working well together. The female student felt she was contributing more than the two male students. The two male students felt she was being overly directive with them...and the 4th student was just really, really quiet. 

This seems like an obvious problem that I should have thought about ahead of time. When I did my first PBL stats unit a few weeks ago with my mainstream algebra class, I had a simple rubric for group behavior and students gave their group mates evaluations. However, I didn't do that with this class because of the language barriers. I didn't want students to misinterpret subtle evaluation questions and unknowingly give bad feedback to someone. 

As I was reflecting on the lesson today, the obvious hit me. I've experimented with complex instruction in my classes. And one of my favorite components of CI is the idea of "actionable norms". On Friday I will reintroduce the actionable norms stamp card as well as start giving student shout outs. 

A quick explaination:
  • For the actionable norm stamp card: I basically circulate as students work. When I see students displaying one of the norms from the stamp card, I thank them (being very specific for why I'm thanking them) and I give them a stamp. (by the way...I learned all this from Laura Evans--an amazing teacher and complex instruction expert) 
  • For student shout outs: about 10 minutes into project work time, I will stop everyone. Pencils/pens down and eyes on me. I communicate the importance of my message with body language and tone. I then publicly acknowledge (shout out) students that had demonstrated the positive behaviors from the stamp card. I try to be thoughtful in assigning competence to students. If a student that struggles in math or group work took meaningful risk, I acknowledge that to the class. If a group work persistently and collaboratively, but might not have found the answer, I would acknowledge that to the class. I probably do 3 or 4 shout outs every 30 minutes or so. 

The Idol of the Marketplace

Ha! I knew my love for Sir Francis Bacon would come in handy someday...

As I was looking at the students' claims with a colleague, we came to a realization: the word immigrant is vague and often poorly defined by the politicians that use the word. Also, in much of the statistical evidence I am finding, the word immigrant is poorly defined. The word immigrant can be vague because we don't know if the immigrant being referred to is document or undocumented. Or if a data set contains information for documented immigrants, undocumented immigrants or both. 

I am fortunate this year to have an amazing student teacher--Ms. D. She is studying to be a teacher on a student visa from Africa. Thus, her voice, her moral support and her classroom presence has been helpful as we venture into the Immigration Project. 

I asked Ms. D to facilitate a discussion on the word immigrant with the class. And she did amazing. First, she reminded them of her story and that she is an immigrant. Then, she asked them to talk to their partner: what do they think when the hear the word immigrant? I recorded some of the student's responses on the board as they shared. 

The students (who are all immigrants) mostly said immigrants are undocumented people living in the United States. A few students pointed out that those people with documentation and legal status living in the United States are also immigrants. One student pointed out that any person that moves to a country that is not their birth country is an immigrant. 

The big take away we wanted for them was to be precise in using the word immigrant in their work and to critically examine the graphs they are using as evidence. A few groups modified or clarified their claim after this discussion. 

The Best Question Ever

One group was looking for evidence to support their claim. They were looking at a graph about the total drugs seized at borders (both north and south) for the years 2011 to 2015. The graph clearly shows a decrease in the amount of drugs seized at the border. And one of the girls in the group asked the best question ever: why are drugs seized at the border decreasing? Are there less drugs being used or are less people crossing the border with drugs? Why is it going down?

I loved this because she was thinking about lurking variables!! By asking what else might be affecting the trend we see in the graph, she was going deeper than just "let me use this as evidence". She was thinking critically about the graph and asking great questions. Really, this makes the many, many, many hours I've spent planning this unit (and many more to come) all worth it. And I mean that. If my students walk away with a critical lens for statistical representations and if they feel empowered to ask the questions that come up from critique, then I'm a happy guy. 

I am definitely looking forward to day 5 when students will get a new set of graphs to examine and they will start putting their claim and evidence together to form reasoning. Students will also take a quiz...sigh. More on that later.  


I'm not a big fan of review activities before a unit test or final exam; I'm also not a big fan of unit tests or final exams. But th...