##
* *Reflection: Student Communication
Patterns, Progress Reports, and Practice - Section 2: Progress Reports and Project Return

I have found it exhilarating to watch and to participate as "Growth Mindset" has become a widely lauded and accepted part of the educational lexicon. It feels to me like all educators buy the idea that we want students to understand that they can get better at learning, and we're all working hard to find ways to help students buy into that idea.

Generating strong student buy-in is our current challenge, and the key idea for me to recognize now is that it doesn't happen all at once. Today, when I distribute these mastery-based progress reports for the first time, there is plenty of pushback from students. Invariably, some students ask, "Why don't you just grade like other teachers?" It's so important for me to patiently provide students space to ask that question. At this time, we as teachers have had months or years to process the idea of growth mindset and what it means for our classroom practice, but we're still teaching students who have, for the most part, been raised in the old culture of passing tests, earning grades, and moving on from there. We're still teaching kids who believe that some people are good at math, and others are not. A shift in mindset does not happen immediately.

So when kids push back, I say, "I'm going to show how to use this progress report to learn as much as you can this year. That's what you're here for: not to show me what you're already good at, but to show me that you can learn something new, and at the end of the year, your grade will reflect how much you've learned."

If you as a teacher are experimenting with standards-based grading or grade reporting, or ways to build a culture of growth mindset in your classroom, please do not be discouraged when all the changes you've dreamed of seeing don't take root right away. Kids have to grow into growth mindset and all that accompanies it. And in my experience, they always do. I provide students with a progress report like this one at five-week intervals throughout the year. Every five weeks, buy in grows, until in the Spring the question changes from "Why don't you grade like other teachers?" to "Why don't all teachers grade like this?"

*Growing Toward Growth Mindset*

*Student Communication: Growing Toward Growth Mindset*

# Patterns, Progress Reports, and Practice

Lesson 2 of 12

## Objective: SWBAT consider where they've been so far and where they're going this year.

*43 minutes*

As will be the case every day this week, today's opener consists of a series of patterns problems. Just like yesterday, today's problems review what we've done so far while adding a few new tidbits of mathematical knowledge. That newness begins with the framing of the problems:

**The rule for a pattern is t(n) = 3n - 22.**

That's how I quietly introduce function notation. I go about my business, circulating throughout the room and getting everyone started on the day's work until the first student asks, "What's t(n)?"

I respond, "Thanks for asking about that - now I know you're paying attention!" I ask how many people have seen this notation before, and it's brand new to virtually everyone. I say that this is called "function notation," that it's a very powerful tool, that you'll see it a lot in your continuing study of mathematics, and that "I feel excited and honored that I get to be the guy who gets to show you this for the first time."

The first question is about the first five terms in the sequence. Up to now, our "rules" have just consisted of the right-hand expression side of things, and students have grown comfortable using these. It doesn't take too long for students to tell me that the first few terms are -19, -16, -13, etc. I simply build on this knowledge by writing these values on the board using the new notation. "The first term is -19," I say, writing:

**t(1) = 3(1) - 22 = -19**

I ask the class: "Can you see how I indicated that I'm talking about the first term?" I want kids to see function notation as a **tool (MP5)** that arises naturally from a need for efficiency in mathematics. When they see it this way for the first time, especially after having looked at pattern rules for weeks now, this feels sensible to most students. "So how would I talk about the second term?" I ask. We continue, and I line up the first five terms. It really clicks for a lot kids when, beneath these initial five terms, I add the 200th term.

This gentle introduction really seems to work for a lot of kids. I still have to be careful to help the students who read "t(n)" as "t times n", but even there, I tell them that I'm glad their paying attention (and we talk about homonyms, homophones, and homographs). When we read the notation aloud then, it really does feel reasonable and natural to say, "Term 1 is, Term 2 is, Term 200 is..." I save the words "t of n" for another day, again in an effort to make this make sense.

The third opening problem was new yesterday: given the value of a number in the pattern, can you figure out what term it is? Kids are still making sense of this, but now I can write

**t(n) = 281**

before asking what **n **will have to be and writing the equation that we'll solve.

The fourth problem introduces yet another new idea - inequalities - and with some classes I won't get to this today. But I allow students to grapple with it, and if there's time, we'll run through the example. Here's your hint, however:

**t(n) >= 0**

*expand content*

**Distribute Mastery-Based Progress Reports**

Today is the first time that students are seeing their mastery-based progress reports for this class. I distribute reports to each student, and help them understand what they're looking at. There are three levels of organization here. First, learning targets are split into Mathematical Practices and Content categories. In each category, the learning targets are written in order, then beneath each learning target at the assessments and grades for each.

I share this example with students: Example Progress Report 1, and I show them the levels of organization. I remind them that Mathematical Practices are graded as an average of all scores, while the content targets are graded by Maximum Value.

We also note that everyone has a "U" on SLT 1.1, which is our focus this week, and that the three quizzes listed for this SLT haven't happened yet - they're dated for the next three days, and the "M" grades for each are placeholders.

**Return Number Line Projects**

In order to help students even better understand my implementation of mastery-based grading, I ask them how many grades they can find for the Number Line Project. There are four: beneath MP1, MP7, SLT 1.02 and SLT 1.03. For the majority of students, the grades are different between the learning targets. Once we've noted this, I return graded projects to everyone. I tell students to look at their project rubrics for how they've been graded, and then to find the corresponding grades on their progress reports.

"What you should see here is that I don't just give you one big grade for the whole project," I explain. "You receive high mastery scores for what you've done well, and you get low grades for what's incomplete or not quite right. This means that you can give yourself a pat on the back for your good work, and you can make a plan for how you're going to improve wherever improvement is needed."

**Get Organized!**

I explain that all the parts of the Number Line Project are great tools, and that students will want them for reference as the year moves on. I give students a few minutes to make sure that their binders are organized and they've filed their projects.

**Looking Ahead**

I show students the frequency distribution of score ranges in their class. Plenty of students are below that 1.6 threshold right now, and few are above 3.0. It's important for them to see this, and for us to think about how we're going to improve upon that. Again, we're building a growth mindset here. "What matters is what you've learned by the end of this class," I say. "Your grade right here is not a final grade - that will come at the end each marking period and at the end of the year. Let's continue to work hard, learn as much as you can, and that's how you'll be successful in this class."

*expand content*

Every day this week, students will spend time solving linear equations. One important element of this work is that I've defined eight levels of equation solving for students, and it's up to students to try to progress through these levels. Today, I provide another Kuta Software worksheet that has four equations at each level from 1 to 6. There are only 10-15 minutes left in class by the time we get to this, but that's enough for many students to race through the first few levels. Tomorrow, students will have the chance to choose the level of the quiz they'd like to try.

My two most important talking points with kids are as follows:

- Showing some work is a way of
**demonstrating perseverance**. On simple problems it shows how you've**made sense**of this kind of problem. On the more difficult problems it shows that you didn't quit when things got hard. Along these lines, tomorrow's quiz will also be graded on**Mathematical Practice #1**. - As we move on, you must get used to showing these steps. A lot of people may be able to solve a one-step equation in your head, and some of you have proven that you can solve two-step equations without showing any work. What happens when the problems get more complicated, however? You're going to have to be able to go step by step.

As indicated on the weekly homework sheet that I distributed yesterday, tonight's homework is a set of one-step equations in the textbook.

*expand content*

Hi James! I absolutely *love *your projects, ideas, and thought-provoking questions (for me and the students), and because of your openness and resources, I'm really looking forward to teaching Algebra 1 for the first time! I have so many thoughts and questions I need to process after reflecting on this last year of teaching, but one thing I know I need to improve on is student data tracking. Students were usually very surprised/confused by their tests and end-of-semester grades, which is not empowering for them and puts the focus more on grades and not on growth. How did you create your progress report? How helpful has it been for students? I love the public tracking you do on the different levels of equations, which I'll definitely be incorporating. Do you do anything else to keep students understanding and aware of their progress towards mastery? I also want to try standards-based grading this year! Thank you! ~Catherine

Hi James! What do you consider levels 4-6 for building equation solving skills?

| 2 years ago | Reply

Hi Nancy,

Each student has a copy of McDougal Littell Algebra 1 (2007 edition).

James

| 2 years ago | Reply*expand comments*

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- UNIT 1: Number Tricks, Patterns, and Abstractions
- UNIT 2: The Number Line Project
- UNIT 3: Solving Linear Equations
- UNIT 4: Creating Linear Equations
- UNIT 5: Statistics
- UNIT 6: Mini Unit: Patterns, Programs, and Math Without Words
- UNIT 7: Lines
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- UNIT 9: Systems of Equations
- UNIT 10: Quadratic Functions
- UNIT 11: Functions and Modeling

- LESSON 1: Solving Linear Equations: Assessing What You Know So Far
- LESSON 2: Patterns, Progress Reports, and Practice
- LESSON 3: Linear Equations: A Subtle Note, and Choosing Your Own Adventure
- LESSON 4: Building on Our Knowledge: Intro to Inequalities
- LESSON 5: Solving Equations by Constructing Arguments (Day 1 of 2)
- LESSON 6: Solving Equations by Constructing Arguments (Day 2 of 2)
- LESSON 7: Collaborating to Level Up
- LESSON 8: Justifying the Solutions to Linear Equations
- LESSON 9: Developing Arguments and More Properties
- LESSON 10: Review: What Can You Do So Far?
- LESSON 11: Critiquing and Revising Arguments (Day 1 of 2)
- LESSON 12: Critiquing and Revising Arguments (Day 2 of 2)