Tuesday, October 31, 2017

A Group Test Makeover

Occasionally I give group tests. I usually give a group test with the intention of helping students prepare for the Unit test--kind of like a group review. I'll give each group a test that has problems similar to what they will see on the individual Unit Test. Students will take the test with their group, and I randomly select and grade one test from teach group. But I've never been totally happy with this structure.

I've experimented with other ways to structure group tests (sentence frames, each group member has a different color), but the group tests still felt like they were reinforcing a fixed mindset: the "test" part of the group test pushed students into their danger zone. Students that tend to opt out because of math anxiety were quiet in their group and dutifully copied the answers of other students.  Students that have to get an "A" on a test dictated what others students in their group should write on their test. My review structure was reinforcing existing inequities and student's own fixed mindset about themselves! And there wasn't much thinking going on! Argh!

Thus, while I like the idea of giving a group test to help prepare students for the unit test, I wondered if there could there be another structure for group tests? Could I give group tests a growth mindset makeover? I couldn't think of anything, but fortunately I went to the Carnegie Math Pathways National Forum to learn more about some cool new courses they are developing.

Group Tests for Growth Mindset

At this conference, I heard a teacher explain a group test process he used. I can't remember the specifics of how that teacher structured his group test, but I do remember he talked about using this fascinating individual/group/individual structure. Here is my version of what he suggested:
  1. Give students a "group test". However, students will work on the test individually and are sitting individually (not in groups). Basically like an individual test. I let them work for a set amount of time (10-ish minutes) individually on this test. At this point, I haven't said the words "group test" to the students. So they don't know what's next. 
  2. Students have a graphic organizer to record points of confusion they have. As they take the individual test, they record questions they have as well as what the student does know about the problem. 
  3. I collect the individual tests from the students. I tell the students they will work on the SAME TEST with their groups. I have students move into groups. Then, I give each group a blank test (the same test they were working on before) and let them work on this test together. Let students work for a set amount of time (10-ish minutes).
  4. Groups CANNOT have any pens, pencils, etc out. But each group has a group whiteboard and they can "do the math" on the whiteboard as they discuss the problems. 
  5. I collect the group test from groups and have students move back to their original seat so they are ready to finish the test individually. I return the individual tests to the students. However, they should finish their test IN ANOTHER COLOR!

Here is the graphic organizer I give students to record questions they have while they work individually. 

Then, after I collect their individual tests, students will have a reference of their questions or points of confusion that they can then share with their group.  Here are two examples of how students used this graphic organizer to keep track of their questions.

Here are some examples of student's individual tests looked like before and after the group work time. You can see what the added/changed with the different color! (I know there are still errors on these tests)

Problems with this Structure

Students want to do well on a test. I understand that. It is part of the culture of tests. And this drive to do well creates an issue with this group test structure: while working with their group, students will ask what the answer to #5 is, they will memorize that (or write it down) and then, when they get their individual test back, they will write down the answer to #5 without any supporting work. I think there is an example of this in the second student work sample from above. On question #4, a student has written that the y-intercept of the line is eight, yet they have no work to support that answer. 

The only way I can think of to address this is by making clear that the answer is the least important part of the problem and no work = no credit. But this doesn't feel like the best solution. :/

One other potential issue with this test structure is that it has to be with the right type of questions. I've used this group test structure with a stats test--that did not go well. Things to consider:
  • Are the questions group worthy? Asking students to graph the line y=3x+4 doesn't feel group worthy to me. This type of question isn't going to elicit conversation besides asking "how do I graph this?" (You can see I used a problem like this on problem #1 in the photo of the test I shared) 
  • Is there more than one answer, but still a limited number of potential answers? I used this group test structure with a stats test. One of the questions on that stats test was VERY open-ended and, with the right supporting work, there are an unlimited number of responses to the question. This was not a good question for this test structure because the open-endedness of the question elicited confusion, not conversation. I think the best conversations about a problem like that would be about how to write a convincing answer--whatever the answer may be. But neither I nor my students were at that level!

A Growth Mindset Makeover

This is an example of how I modified an existing routine that I wasn't happy with. I took something that felt fixed mindset and modified the structure to promote a growth mindset.

The growth mindset component of this activity is the opportunity students have to go back to the individual work. Often, tests have a feeling of finality--once a student finishes the test, that is it. They are done. This structure gives students a space to try, record points of confusion, talk with their peers about their questions, then come back to the individual test.

This structure certainly isn't perfect. If you try it and add any modifications, please let me know!

Sunday, October 22, 2017

Coaching Cards

I teach algebra 1. Some units in algebra 1 are very skill heavy. The linearity unit, for example, has a lot of 'skills'. Same with quadratics. 

As I've been teaching, I've noticed that different students learn certain skills at different rates. For a particular skill, some students 'get it' relatively quickly while other students need more time. However, for a different skill, the groups can switch and students that previously 'got it' need more time while others can master the skill in less time.

If you're a teacher, you know this. And the solution is differentiation. But I've always struggled with differentiation. Like, I have to plan the entire lesson and then plan another lesson for the kids that finish early?? Some lessons or activities lend themselves well to differentiation, and in those cases I do it.

A couple years ago I came up with a participation structure that helps me differentiate. I don't use this participation structure the time, but for certain skill-y lessons (like the linear skills I'm teaching right now) this structure works great.

I call it a coaching card. The basic idea is that as students finish a practice set of problems, they call me over to check their work. If their works looks good, I give them a card with coaching sentence frames. However, more important than the card, is the quick one-on-one conversation I have with the student. I make clear: their job IS NOT to give answers; their job is to ask good questions. I suggest they do not carry their correct work around with them because it will make it feel like an answer key. And being a coach is not about giving answers. It is about asking good questions.

However, that can be a lot for a 9th grader to take on. So I provide the card with sentence frames for students to use when they coach other students.

Coaching Card for graphing linear functions. 

Coaching Card for graphing exponential functions. 
Coaching Card for sketching parabolas.


I really only use this for specific times when I want students to practice a skill like graphing linear functions, factoring quadratics, or graphing exponential functions.  Other times, I will do activities where students work in groups and the goal is conceptual understanding. However, for those times when I want students to practice a skill, and I'm not sure what to do with the students that finish early, the Coaching Card is the right tool.

Timing and Structure

The skill activity is usually 4 or 5 questions. The activity, including the coaching, doesn't take more than 20 minutes. I"m not using students to teach the lesson! The shelf-life for the coach structure is about 7-10 minutes. At least in my class. After that, students crack the code and the quality of the coaching drops pretty quick.

As students finish the activity, I give them a card, have a quick coaching conversation where I stress they are to ask questions not give answers, and I tell them to wait until I direct them to get up. Once I have about 4-5 coaches, and the entire class has worked for at least 5 minutes without help, I direct the coaches to get up and I let the class know that there are students available to help them.

How I Make a Coaching Card

I like to use Coach Cards for short, focused skill based lesson segments. Like a warm-up on writing linear functions from different representations. Or a practice problem set of 5 problems on rewriting standard form linear functions in slope-intercept form. 

I like to make the sentence frames specific to the activity. So the activity has to be focused in terms of skills so that the sentence frames can be focused. I create the card with the assumption that a 9th grader has never coached before and needs a 'script' of what to say in this situation. Because, to me, in a coach/coachee situation, informal, conversational language will not be helpful. Students need to use precise, consistent, and direct language in a coaching conversation. 


This activity definitely raises issues of status. While different students accel at different skills, there is always a handful of students that struggle with stills as well as a handful of students that tend to learn new skills quickly. Thus, a few students are always tutors and a few students are always tutees.

That being said, I only use this structure about once or twice a month. And the tutees seem to appreciate the peer coaching--otherwise it is tough for me to get to everyone that needs help.

In the photos from my classroom, you can identify the tutors as the person with the brightly colored paper--again, this becomes a token of status...not sure how I feel about that. 

Final Thoughts

Again, I only use this once or twice a month--so not very often. And I only use it for short, focused skill based lesson segments. 

A warm-up of 4 problems that asks students to graph linear functions. Great. Or a warm-up with a handful of problems that ask students to write linear functions from different representations--perfect for Coaching Card.  A worksheet of review questions from the linearity unit. I wouldn't use Coaching Card for that. The reason being is that I like to make sentence frames that are specific to the skill. If there are 5 different skills in the worksheet, I think it could feel overwhelming to a 9th grade student that is coaching for potentially the first time. 

Also, at least for me, students get informal with this structure pretty quickly. Really, for about the first 7 minutes, there is a magic feeling in the air. Students are earnestly helping other students by asking really good questions. They are not just giving answers. And, since these are 9th graders, that magic feeling wears off, reality kicks in, and I've got to remind Kevin not to argue with Aldo about which team won badminton in 1st period PE. But it's beautiful while it lasts!

Linear Functions Coaching Cards

Graphing Exponentials Coaching Cards

Tuesday, October 10, 2017

It's the Climb

I want to credit my colleague, Madison Miller @mathemadison , for creating the original task! Also thanks to my colleague Kristel Chew for helping format the task and for adding the debrief.

I've been attempting to implement tasks that use complex instruction (CI) into my teaching practice. And Madison's task seemed perfect for a CI makeover.

An important part of CI are group-worthy tasks. Group-worthy tasks require students to use higher-ordering thinking and engage students in non-routine mathematics, which creates a need for students to negotiate meaning with each other to complete the task.

Madison's task definitely had all of that going on!

Both the original and the complex instruction version of the task are linked in this post. For me, however, it is more than just the task. The participation structures I use are what make this task successful.

Supporting Students in Productive Struggle

I give groups about 40 minutes to complete the task. Then about 10 minutes to answer question 1 (minimum). If they can get further, that's great!

How do I get 9th graders to struggle productively for 40 minutes? After lunch. On a Tuesday in October. I use a lot of the ideas that were introduced to me by Laura Evans. Laura is an expert in CI and I was fortunate to attend a PD on CI facilitated by Laura. My big take away from Laura's PD is that I have to create a culture that supports students as they engage in productive struggle. What norms or shared values do I think will help students engage in productive struggle during this task? And how do I develop and maintain a classroom culture of norms that support productive struggle? 

There are a few actions I can take to support a culture of productive struggle:
  • To develop the culture, I use a positive behavior stamp card. Laura calls them actionable norms. I liked Laura's phrases of "Communicate Productively" "Take Risks" and "Work Persistently" so I used those.  As I circulate as students work, I give stamps when I observe or hear students and/or groups displaying that falls into one of those categories. Then I give them a stamp and I say something like "I appreciate you taking a risk when you asked your team to slow down" or "Thank you for drawing a sketch of the graph for your team...you are helping the team to communicate productively". 
  • Being really specific about what a group role entails and making group roles meaningful help maintain the culture. 
  • To develop the culture, about 5 minutes into the task, I stop the entire class. I ask for pencils down and all eyes on me...my tone and body language communicate that this is an important message.  I publicly acknowledge (shoutout) specific students that had demonstrated the positive behaviors I had given stamps for. I try to be thoughtful in assigning competence and status to my students. If a student that struggles took a meaningful risk, I acknowledge that publically to the class. If a group worked persistently on a part of the problem, but hadn't found the answer, I would acknowledge that publicly. I do three or four shoutouts. 
  • To maintain the culture, I call the Stick Together Police from each team up to see me. We do a team huddle and I explain that it is now their job to do shoutouts for their team. They must keep working, but also listen and look for productive behaviors. I let them know that in about 5 minutes, I will be calling on them to give a shoutout to someone on their team to the class. 

These actions help me develop and maintain a culture of productive struggle. This allows the students to fully engage in the task. It also helps support equitable participation. Because students have a specific role as well as a clear idea of the things they should be saying and doing, it takes away some of the "noisy" cognitive demand of socially fitting in that teenagers feel. They know what things to say and do to receive praise and positive acknowledgement.  They don't have to think about it--I've made it clear.

Choosing Group Roles

I let students know what traits make a particular role successful. For example, the Justify Police should be confident in how to find slope. And the Coach should not be afraid to ask someone to participate (not a role for someone quiet). The Resource Manager might be good if you like to move around a lot or fidget. I give groups 1 minute to decide which team member is doing which role. For this task, I also share a few specific things about their role. I show the following slide:

Doing the Task

Finally, I introduce the task on a slide. I start with a notice/wonder slide:

Students notice and wonder all kinds of things! But the difference in steepness always comes up. And this is my goal. To start them thinking about steepness. I have them rephrase what "steepness" is to their partner. Then I intro the task on a slide:

I don't say much else. I don't tell them they need to use slope. I call resource managers over for a team huddle, give them the first task card, tell them to go back to their group and start an 8-minute timer, and that they should announce to their team that they have 8 minutes for this task card. If it takes more than 8 minutes, that is ok, but if it goes past 10 min, they need to call me over. 

Resource managers go back, and groups start to work. I circulate to give stamps and make note of names for my first round of class shoutouts. The first task card is the most difficult and also the steepest climber. I intentionally give "Monifa" as the first task card. If groups only get through two climbers, that is ok, they will still find the steepest. If they get through all four climbers, that is great also! This is another way I build equity into the participation structure.  Completing all the parts of the task isn't necessary to understand the learning objective of the task. 

If in 10 minutes groups still haven't finished the first task card, I call the Justify Police over for a team huddle and give them a hint: 

We go over how to find the dimensions of the slope triangle together. Then I send them back to their groups. Usually about 1 or 2 groups can't figure Monifa out on their own. 

Groups then work on Toshie (students have great discussions about this climber), then Hazel and finally Rolando. About 35 minutes into the task, I stop all groups. All groups will have completed at minimum two task cards and most groups will finish all four. 

I move all groups to the It's the Climb Original Record worksheet. I let them know they have 10 minutes to work and all groups need to complete at least the first question. It's funny...no group has ever made the connection that they've been working for 40 minutes without looking for an 'answer' until now (no one remembers they are looking for the steepest climb...they get so into finding the slope for each climber). 

At 10 minutes I stop all groups. I show this slide. 

Groups go up to the classroom whiteboards and record their work. I give them 5 minutes to put everything on the board. 

I had planned for groups to give warm/cool feedback to at least two other groups, but we didn't have time for that so I had to cut it (next year). 

As a class, we discuss one incorrect example and one correct example (of course, I don't say which is which until the very end) response. The main goal is to get students to use the sentence frame "as the horizontal distance increases by 1, the vertical distance increases by..." to help compare the slopes.

After this, there is an individual debrief at the end of the Record worksheet. Students do this individually (i ran out of time so cut this...next year). 

All together, I take 60 minutes to implement this task, but I could have used more time. We probably could have used 80 minutes to do everything I wanted to with the task.

Monday, October 9, 2017

A Modest Proposal

Note: My school uses PLC as a teacher collaboration structure. PLC stands for professional learning community. I work on the algebra 1 PLC which is comprised of the algebra 1 teachers and the algebra support teacher. We meet once a week for about 90 minutes. 

1/11/18 Update

Today is the day I'm going to share the new homework structure with my students! I came up the following template for homework (now called Lesson Reflection).  I plan to give this once a week and let the students choose the lesson they want to reflect on. The reflection will be due the following Monday.

To be honest, I'm really nervous about changing to a lesson reflection from traditional homework. The reason I am nervous is because...well, I feel like I'm breaking a BIG rule. Math teachers give homework. Math students (should) do homework. What if the students stop taking my class seriously because there is no homework? What if the students don't remember anything because they didn't practice? What if there is a total break down of the system without homework?

I"m keeping Jo Boaler in the back of my mind today...I know the research supports this. But change and growth always feel scary.

I read Mathematical Mindsets by Jo Boaler this summer. I loved this book! I would recommend it for any teacher--not just math teachers. There are powerful messages about equity and mindset as well as strategies for effectively teaching a diverse population of students.

Mathematical Mindsets reminded me that some of the routines I do in my class aren't just things I like to do--these routines support students in seeing math as a space where learning happens via mistakes and productive struggle. My HW grading routine, my warmup routine of My Favorite Mistake and some of the group tasks I do give student space to make mistakes, reflect on the mistake, and try again (without being punitive in terms of grades).

My favorite poster in my room: "Mistakes Are the Gateway to Understanding"

Mathematical Mindsets also challenged my thinking about certain aspects of my teaching practice; especially around grading and homework. My algebra 1 classes already use an alternative grading scale that our came up with several years ago. I like this scale--we had to do a lot of work to calibrate our tests with this scale (as well as how we grade tests), but, after 3 years, we've worked out many of the kinks.

Algebra 1 Grading Scale (we do not give a grade of D)

Now, as I begin week 9 of this school year, I'm really thinking about homework. This sentence from Mathematical Mindsets is ringing in my ears: "when we assign homework to students, we provide barriers to the students who most need our support" (p. 107).

So this morning I shared a modest proposal with the algebra PLC leads: could we discuss homework at the PLC meeting this week? Specifically, I asked them "in the spirit of inquiry, could I not give homework to my algebra 1 students? Like, can we see if my students do better/worse/the same as the other teachers' students on the unit test if I don't give homework?"

I feel like asking the PLC to consider this is taking a risk. But I also think teacher leaders need to take risks. Again, I can hear Jo Boaler, in her lovely English accent, saying, "if as a teacher or school leader you want to promote equity and take the brave step of eradicating homework..." (p. 108). Yes! I want to promote equity! I can see, real time, that the biggest outcome from homework right now is amplifying existing inequities. Yes! I want to be a teacher leader. So I'm going to take the risk.

I'll let you know how it goes!

Wednesday, October 4, 2017

Teaching Students to Write Mathematical Reasoning

My Context

I teach algebra 1 for freshman. With respect to reading/writing, my classes are heterogeneous. Some students read/write at grade level, while others are significantly below grade level--some as low as elementary school level reading/writing. Thus, my lessons on teaching how to write mathematical reasoning have a lot of scaffolding built in. 

Also, this is all new for me this year! I'm sharing my baby-step lessons on teaching how to write mathematical reasoning. I don't think what I'm sharing is the ultimate way to teach writing mathematical reasoning--but there have been a lot of questions about student work and activities I've posted on Twitter so I wanted to share what I've done so far--imperfections and all! 

Update 11/6/17

I recently gave the second unit test (linearity) in algebra. This was a chance for me to see what students can produce in terms of writing mathematical reasoning with no peer or teacher support. The results were all over the place, which is expected (student work is below). I have a wide range of students with a wide range of reading/writing readiness. Some students are reading/writing at a 4th grade level, while others are at grade level. However, I saw some growth in almost every student's work.

I'm also going to use the student work to do a test re-engagement activity. I still firmly believe that students need opportunities to revise their writing in order how to learn to write mathematical reasoning.  So we will do some type of activity to give students a chance to revise some of this work in order to get a feel of how to improve their writing.

Big Ideas on Teaching Students to Write Mathematical Reasoning 

There are a few big ideas I keep in mind when I'm designing lessons or activities to teach students how to write mathematical reasoning.

  • I've made it crystal clear to the students (and myself) that writing mathematical reasoning is not a goal they will accomplish this week or this month. This is something we will work on TOGETHER all year. So we all need to be patient.
  • I need to build space for revisions into my lessons. In English class, students don't write a perfect essay in one shot. They draft, revise, rewrite. I need to honor that process in my lessons for teaching how to write mathematical reasoning. 
  • I need to write an ideal response to a prompt BEFORE I teach/plan the lesson. I need to write the ideal response because it helps me see the patterns in language I need to teach and it helps me inspect what I expect students to produce in terms of writing. 
  • For the initial lessons, it was helpful that the math was done for them (or very accessible math with multiple access points) and they just needed to interpret the math and write about it. Having to do math AND write mathematical reasoning in one activity doubles the cognitive load. If I want to focus on writing, I need to lower the math demand and give space for students to focus on writing mathematical reasoning.
  • Claim, Evidence, Reasoning (CER) is a powerful structure for argumentative writing that students are familiar with (science and ELA use CER). I'm not sure I want to teach CER explicitly, but I use CER as a rough framework when I write my ideal response and I use CER to help me backward plan my lessons on writing mathematical reasoning. I also use CER as a scaffold. 
  • Teaching how to write mathematical reasoning is hard for me and hard for the students. I need to have a growth mindset for myself and for my students. The students have been told for a few years to "write in math" but I not sure anyone has taught them HOW to write in math. Similarly, I've been hearing for years I need to teach students how to write in math, but no one has taught me how to teach writing mathematical reasoning. Yes, this is hard!

Sample Lessons

Lesson 1 (week 1)

Lesson Goal: Students will understand the drafting, feedback and making revisions are an important part of writing mathematical reasoning. The math part of this lesson was 30 minutes. The writing part was about 40 minutes (I broke up the writing over two days).

I used this fantastic, open-ended math task from Jo Boaler's youcubed.org Week of Inspirational Math for the math portion of this lesson. I used this task because the math was open-ended and had multiple access points. Again, the focus was the writing more than the math.

In planning this lesson, the other algebra teachers and I wanted to scaffold the task to help students differentiate between the patterns they used to see how the shape grows and how they used those patterns to predict what case 20 would look like.

I also wanted to acknowledge that students might not have been taught how to write mathematical reasoning in previous math classes. Thus, we provided "reasoning" sentence starters and a bank of transition words.

For the lesson, after students had time to work on the math individually and with a partner, I gave students about 10 minutes to write their reasoning. As students worked, I circulated to look for student work that had examples of what I was hoping to see based on the ideal response I had written.

After about 10 minutes, I stopped all students and showed a few examples of exemplar student work (these students had transition words, or did a good job in explaining HOW they used the patterns to predict case 20, rather than just explaining what case 20 looked like.

Then, I gave students a few more minutes to write. The idea of showing the exemplar work was to help students see examples of what they could do if they hadn't been able to get started yet.

Next, I had students stop writing. As a class we discussed how to give warm and cool feedback.

Slide from my lesson on how to give warm and cool feedback.
After we discussed how to give warm and cool feedback, I had students trade papers with a partner and give their partner feedback on mini-post-its. Students then traded with another partner and did more warm and cool feedback. This way, students recieved feedback from two other students.

Students got their own work back, read the feedback, and then made revisions to their writing USING ANOTHER COLOR PEN. I love using a different color because I can see their original work versus the edits they made.


Lesson 2 (week 4)

Lesson Goal: Students will write mathematical reasoning to interpret the result of math work. 30 minutes.

Slide from this lesson. 

We are in the solving unit at this point. The previous lesson had been about solving equations with infinite and no solutions. The goal of this lesson was to interpret the result of math work that had already been done.

For this lesson, the math was done so that students could focus on the writing.

Again, I let students just write for about 5 minutes. I emphasized that their first attempt was not a finished product and we would come back to edit their work.

As students wrote, I looked for student work that had elements of the ideal responses that I wrote. For this lesson, I thought about the response as having a CER structure.  My ideal response: 

Claim: the claim should state their interpretation of the result: "this equation has no/infinite/one solution(s)"

Evidence: the evidence should reference the mathematical work. Something like "because when I solved, the variable disappeared and I was left with 5 = 5, which is true."

Reasoning: The reasoning should synthesize the claim and the evidence. "Therefore, I can substitute any value for x and my equation will balance."

After I showed exemplar student work, I let students go back and revise their original writing--in another color. 

I didn't explicitly teach this lesson using CER because I didn't want to get cookie-cutter responses. However, I explained that their writing should follow a rough CER structure. I don't know how I feel about that. Like I said, all of this is a work in progress for me. 

Sadly, I didn't save any student work from this lesson. 

Lesson 3 (week 6, Day 1) 

Lesson Goal: Students will review for the test. Students will explain their math thinking. 40 minutes. 

This was the Middle Bits activity (thanks Shira Helft for sharing this great idea!).  The concept of MIddle Bits is that the student is given a question AND the answer and they need to fill in the middle part (the middle bits--haha). 

How I run Middle Bits:

1. I intro the rubric. I let students know that the expectation is they work together (each partner using a different color pen) and they support each other. I made very clear that since I am not able to see or hear all the great conversations they are having, I want them to put a star on the paper at any point where they stop to discuss a point of confusion or mistake. After they get started, I usually circulate to look for students that are putting stars and show that work on the doc cam so they see how important that is to me...it is also on the rubric. Each partner only gets one paper.

2. I hand out a rubric to partners. We also go over it as a class.

3. Partners need to switch off the work. So if I do the "math" for one problem, you do the writing. Then, we switch for the next problem and you do the math and I do the writing. 

4. I usually stop the class 3 or 4 minutes in to do a shout out to partners that have exemplar body language. They are leaned over the paper together, writing at the same time, no one has arms crossed or is daydreaming while the other works. I have all freshman, so I need to make very clear what I expect!

Lesson 4 (week 6, Day 2) (this is a repeat of Lesson 2 from above)

Lesson Goal: Students will write mathematical reasoning to interpret the result of math work. 15 minutes this time since it was a repeat. 

This lesson went well the first time and it was a good chance to do a quick writing activity in class again that had space for revisions--so why not do it again!

Unit Test Work

This was the summative assessment for the Solving Unit. Granted, writing mathematical reasoning wasn't the primary objective in this unit, but we did spend a lot of class time on writing lessons and practice. Overall, I was very happy as I graded the unit tests! Even students that had the wrong mathematical solutions had solid writing. I was especially happy to see the consistent use of transition words...something I hadn't seen in my algebra 1 students' work before. So I felt like this was evidence of my growth as a teacher.

I think this work also highlights the point that writing mathematical reasoning is difficult for students because there are multiple academic demands happening simultaneously: students have to know how to do the math, as well as how to clearly expresses their thinking using academic language.

This also raises the question, if the math is wrong, but the writing is solid, how do I grade that? Or, if the math is great, but the writing is lacking, how do I grade that? What am I assessing here? And how do I grade that?

More questions than answers so far, but I'm happy with the progress I've made. I'll keep you updated as I continue to work on how to teach students to write mathematical reasoning.

My Dilemma in Grading Student PBL Work

There was this fear I had about PBL. I was afraid that the learning was not authentic because of the multiple opportunities students have to...