Unit zero is how I introduce the class to students. It consists of several lessons that walk students through the syllabus, how and why the class is structured the way it is, daily classroom routines, and other "housekeeping" items that we all have.

The head fake (ala The Last Lecture) is that the content is delivered exactly how the mathematical content will be delivered all year. Unit 0 is made of a series of lessons, each designed around a learning outcome, that students work through at their own pace. Students move from one lesson to the next after demonstrating they are proficient at that learning outcome via a mastery check. At the conclusion of all the lessons, there is a "unit test" where students can demonstrate and showcase their learning.]]>

Below is a short list of what I've learned this week. And a list of what I still need to figure out.

- I am loving Canvas right now. I'm so happy that I embraced our LMS this year. (This is the first year our school is using Canvas). It's been easy to create a communication strategy with my students.
- Create a simple communication strategy. Remember you are one of maybe 6 teachers sending information to your students. If everyone sends 2-3 emails per day with links, attachments, etc. they will be overwhelmed. My strategy has been to send all communication to them via Canvas Announcements. I post an announcement every morning. Yes, every time I send one they get an email, but it's usually the only one from me. The announcement includes all the information they need for the day, including links, attachments, etc. The biggest advantage I see is that there is a record of every Announcement and I can refer students back to each one.
- I'm utilizing
__Remind__for quick one-on-one communication. It's a great service that allows us to text back and forth easily and quickly. __Edpuzzle__has also been a fun tool to integrate. It's keeping students accountable as they watch short video explanations. I've integrated notes to students as well as short answer and multiple choice questions.- Let's not forget
__Google Meet__for synchonous meet ups. I'm able to give just one link for all my students in all my classes to join our sessions.

One of the most important things not just for competency-based learning models but for all schools, is to norm for subjectivity and variance among teachers. Teachers should go through a process where they individually rate a student’s performance based on the rubric, then debate within small groups to come to a shared understanding of the standards, which helps to shrink any variance in teacher judgments.

Here is one idea to use as a norming exercise in your next PLC...

Source: https://www.gettingsmart.com/2019/11/shining-a-light-on-the-future-of-learning-at-aurora-institute/

It's important for your department to have a clear understanding of what it means to meet a learning outcome. In our case, the rubrics we use look like this...

So the exercise we use starts with a teacher bringing an assignment and student artifact to our PLC. It's important that this assignment has learning outcomes attached but that the student artifact doesn't have any teacher comments or assessment notes. Then we follow these steps.

]]>- The teacher explains the assignment and the resulting learning artifact. (3 min.)
- Collectively, teachers discuss how the learning outcomes apply to the assignment and criteria for meeting. (5-7 min.)
- Individually, teachers assess the learning artifact.
- Collectively, teachers discuss how their assessment and why or why it does not demonstrate proficiency of the learning outcome.

A carefully selected subset of the total list of the grade‐specific and course‐specific outcomes within each content area that students must know and be able to do in order to be prepared to enter the next grade level, course, or the next level of learning.(Ainsworth, Rigorous Curriculum Design, 2010)

A majority of time will be spent on foundational learning outcomes as well as time and support for students who haven't mastered them and provide extensions for those who have. Use data from these outcomes to help guide instruction.

Here is a process to help you determine which learning outcomes are foundational.

Here is a process to help you determine which learning outcomes are foundational.

Make no mistake, foundational outcomes are not the only learning outcomes students will learn in class. They are simply the minimum they will need to demonstrate proficiency in to progress to the next level.

Now that your PLC has unpacked the learning outcomes (see previous post), it's time to identify those that are foundational.

To help in this process it is useful to think of outcomes in the following three ways:

**Endurance: **Knowledge and skills of value that will be revisited several times throughout unit, semester, year, etc.

**Leverage: ** Knowledge and skills that are valued in multiple disciplines.

**Readiness for Next Level Learning:** Knowledge and skills that are necessary for success in the next grade level or in the next level of instruction.

Foundational outcomes should score high in all three of these areas.

To identify foundational learning outcomes,

Now that your PLC has unpacked the learning outcomes (see previous post), it's time to identify those that are foundational.

To help in this process it is useful to think of outcomes in the following three ways:

Foundational outcomes should score high in all three of these areas.

To identify foundational learning outcomes,

- Individually, you decide. On your own, read each ouctome and mark those you believe best meet one of the criteria: endurance, leverage, or readiness.
- Discuss the choices within your PLC, looking for commonality and agreement first. Then discuss the outcomes not in common.
- Perform an analysis that shows the number of foundational outcomes associated with each competency.

Pro Tip: When considering whether to select one similar outcome over another, determine which one is the more comprehensive or rigorous one, not the one that is more foundational. ]]>

Many learning outcomes address proficiency in specific skills in order to demonstrate proficiency at the outcome and eventually competency level, but these skills are not explicitly stated in the learning outcome statement.

Consider the following problem,

Describe the solutions to cx^2+Ax+B=0

, When I asked this problem in class, the learning outcome I associated with it is

The other issue to address is from the student point of view. Students need to know what learning outcomes they are working on and what skills they need to be proficient for that outcome.

In my mind, the two learning outcomes I've listed above are confusing to students. It's not clear what skills they need to master to show proficiency in these learning outcomes.

The solution is to unpack learning outcomes. Unpacking is the process of deconstructing learning outcomes into component parts to identify key learning skills and the types of learning experiences, activities, tasks, and asessments that align with those outcomes.

An activity for your next Professional Learning Community (PLC) meeting is to do this work. One way to start would be to bring in a recent assignment and ask your colleagues to assign learning outcomes to it. Then use the following framework (adapted from http://sacsteacher.weebly.com/unpacking-the-standards.html) to promote discussion.

]]>*I can solve equations and inequalities in one variable.*

*I can create equations that describe numbers or relationships.*

The other issue to address is from the student point of view. Students need to know what learning outcomes they are working on and what skills they need to be proficient for that outcome.

In my mind, the two learning outcomes I've listed above are confusing to students. It's not clear what skills they need to master to show proficiency in these learning outcomes.

The solution is to unpack learning outcomes. Unpacking is the process of deconstructing learning outcomes into component parts to identify key learning skills and the types of learning experiences, activities, tasks, and asessments that align with those outcomes.

An activity for your next Professional Learning Community (PLC) meeting is to do this work. One way to start would be to bring in a recent assignment and ask your colleagues to assign learning outcomes to it. Then use the following framework (adapted from http://sacsteacher.weebly.com/unpacking-the-standards.html) to promote discussion.

- Identify the learning outcome
- Why did you choose this outcome? What does it mean to you?
- Determine other content and skills this learning outcome should align with.
- Create learning targets, which are student friendly statements, that specify each of the component skills associated with this learning outcome.

I try to present math topics four ways: verbally, algebraically, graphically, and numerically. There is more than one way to think about a problem and there is often more than one solution. By teaching this way I'm frequently surprised and delighted about how my students solve problems.

The picture above is an example of this. This is a question on a recent test. We've been studying properties of integrals and this is a straight forward question.

I expected the solution outlined below and the solution in the picture above was presented to me. This makes me smile!

]]>I expected the solution outlined below and the solution in the picture above was presented to me. This makes me smile!

I started my career grading homework. I don't remember how often or on what criteria I used, but I know I experimented with both. I tried collecting every set, randomly choosing days to collect homework, collecting sets every Friday, randomly choosing a few students to collect their homework, etc. I also experimented with a number of grading criteria. I've graded on completeness, accuracy, ungraded with comments, etc. Setting up a grade book in this phase also ranged from using a weighted average, adjusting points for homework to signify importance, all or nothing, etc.

I never felt satisfied that any of my attempts were actually helping my students learn and understand. This practice also didn't seem to inspire learning. It seemed so industrial and repetitive. If you look back at my assignment sheets you'll see "do 1-50 odd on page 123-124".

I flipped my class. Homework now consisted of asking students to watch 5-20 minutes of video clips with someone explaining a concept and working example problems. The next day, in class, students would work through different types of problems in class, usually in small groups. Two problems quickly surfaced.

First, the problems we did in class couldn't come solely from the textbook because students just wanted to get them done and sometimes not making the connection to what they watched the night before. My attempts to change the atmosphere involved hand picking fewer and more thought provoking problems, mixing up small groups, guided discovery problems, etc. I was still not totally satisfied.

Second, I realized students were passively watching the videos. My homework was no different than asking them to sit on the couch and watch a sitcom. To address this I'd ask students to take notes and bring them to class the next day, write a summary of the ideas in their journal, etc. Whatever I tried, it seemed they were still simply going through a process but not actively engaged in the learning process.

I want to inspire learning, not force it.

Not fully satisfied that the time and effort I was putting into homework was translating to improved student outcomes, I decided to simply not grade homework. Feedback on how students were learning was going to be given by more frequent quizzes and tests. Two shifts quickly emerged.

First, student stress seemed lower. The pressure of doing homework for a grade was a constant low frequency vibration in their lives which eventually manifested into a significant amount of stress for some students. Basically, not grading homework gave students more control over how they spent their time and identified their priorities. I didn't mind that occasionally some students came to class without their homework done and I certainly didn't call them out on it. I felt comfortable knowing that I don't know everything about the challenges our students are facing; social, academic, or family pressures. If coming to class unprepared became a pattern with a student, it provided me an opportunity to engage with this student in a positive way as a conversation versus a punitive approach with a lower homework grade. My relationship with student started changing for the better. We were becoming allies in the learning process.

Second, more frequent quizzes and tests reduced the stakes of each. I experimented with frequency and settled on a quiz every 3-4 classes and a test after 6-8 classes. Quizzes usually took less than half the period while test a full period. This routine gave students opportunity for more specific and individual feedback on their strengths and weakness as well as insight into what I wanted them to learn. Based on the assessments, they were able to get the sense of the level, rigor, and types of thinking expected.

I finally felt that our class transforming away from feeling industrial and towards students being a more active and engaging in their learning, but a couple of issues surfaced. With more frequent assessments came the added responsibility of me having them ready on schedule. I write my own tests and quizzes. The other issue was student absences. The number of students and different classes I was teaching had me devising an elaborate make up system. Student absences could also delay when I handed the quizzes and tests back.

Ultimately for me, the purpose of homework is to give students the opportunity to think, reason, organize, and analyze. The primary purpose of homework is not to practice. It's also not always about getting the problems correct. Home work is part of the learning journey but not the end goal to master.

My classroom is now more inquiry and discussion based. The types of questions I ask are more open ended and request students to make conjectures, look for patterns, compare and contrast, explain, justify, discover patterns, etc. The heart of the class is the problem sets that I write. Each day students are given 5-10 questions. The questions usually have students discover, practice and apply topics and skills.

We start class by have students choose a problem to write on the board and show their progress. Then, one by one, they present their work and explain their thought process and solution or what caused them to get stuck. Then the class adds to the discussion by verifying, offering alternative process, or working together to brainstorm ways that progress towards a solution.

We usually have more students than problems which gives me the opportunity to personally check in with students who are not presenting. During student presentations my primary purpose is to be an advocate of their ideas and encourage the class working towards a solution.

When the class is at in impasse or needs to make progress, you'll hear me say, "Is there an idea from a previous problem that might help us here?" or "That's an interesting idea, can someone expand on that it?"

Considering all the phases of homework that I've tried, students get more frequent and meaning feedback during their presentations. It might be a stretch, but not a big one, for me to say that in this phase every student gets feedback on every problem every day. When they see other solutions on the board students can identify the mistakes they made, alternate approaches, and the ability to compare what they did to what others did.

I still give a full period test every 6-8 classes but quizzes are rare.

Other advantages to this phase are that it incorporates differentiation, a high degree of student engagement, connections, more ownership responsibility of their learning.

So this is where I am today. I'm still dialing in the details, but I'm happy with he big picture. I'm still learning, growing, evolving, even as I approach 30 years in the classroom.

You: The Problem Sets…Doing the problem sets initiates the process. Students work on six to eight problems each night – sometimes recognizing the need for an elegant tool developed in a previous problem, sometimes plugging away with a brute-force solution, and sometimes having little idea where to begin beyond sketching a diagram. Students must attempt problems for which there are no worked example solutions they can mimic. Instead, the problems require them to consider a question, and search, create, and organize their own “toolboxes” for possible resources and strategies.

We: In Class…The classroom is where the real power of teaching and learning together happens. Students bring their work to class, and immediately go to the boards lining the walls to “put up a problem.” With class sizes of about 12, sometimes all the problems are taken, but they might join up with another student and compare approaches. After about 10 minutes, students gather back at the table to discuss each homework problem. The author of each solution presents her thinking, and the class responds. In a class where students have become comfortable with each other, with making mistakes and exposing misconceptions, what usually results is a lively conversation in which the teacher is on the periphery. The students are generating the work, the questions, and the answers for their classmates. The teacher is not superfluous. It is not an easy task to foster an atmosphere that results in this kind of sharing of ideas and a sense of responsibility from the students for the collective work of the class. At the same time, the teacher needs to develop the sense of when to hold back and let the group wrestle with elusive concepts, and when to step in to help guide them forward.

I: Synthesis…This is a time for the teacher to help connect the dots and organize the material in a cohesive manner. Sometimes this is a 5 minute talk after all the solutions of a single problem set have been discussed to highlight a theme or strand. More often, it’s a guided discussion after all the solutions of several problem sets have been presented that weaves together the topics, themes, and previously learned material into a cohesive structure where students can see, in one place, how it all fits together.

Assessments

Formative: When students are going to the board and “putting up a problem” it’s hard to hide your preparation or not engage in this process. Organization and curation of their “toolboxes” is also vital and include completed problem sets with annotations, review notes, and tests.

Summative: Every 2-3 weeks there are in classes written tests. There are also 3-4 extended projects, one per quarter.

]]>We: In Class…The classroom is where the real power of teaching and learning together happens. Students bring their work to class, and immediately go to the boards lining the walls to “put up a problem.” With class sizes of about 12, sometimes all the problems are taken, but they might join up with another student and compare approaches. After about 10 minutes, students gather back at the table to discuss each homework problem. The author of each solution presents her thinking, and the class responds. In a class where students have become comfortable with each other, with making mistakes and exposing misconceptions, what usually results is a lively conversation in which the teacher is on the periphery. The students are generating the work, the questions, and the answers for their classmates. The teacher is not superfluous. It is not an easy task to foster an atmosphere that results in this kind of sharing of ideas and a sense of responsibility from the students for the collective work of the class. At the same time, the teacher needs to develop the sense of when to hold back and let the group wrestle with elusive concepts, and when to step in to help guide them forward.

I: Synthesis…This is a time for the teacher to help connect the dots and organize the material in a cohesive manner. Sometimes this is a 5 minute talk after all the solutions of a single problem set have been discussed to highlight a theme or strand. More often, it’s a guided discussion after all the solutions of several problem sets have been presented that weaves together the topics, themes, and previously learned material into a cohesive structure where students can see, in one place, how it all fits together.

Assessments

Formative: When students are going to the board and “putting up a problem” it’s hard to hide your preparation or not engage in this process. Organization and curation of their “toolboxes” is also vital and include completed problem sets with annotations, review notes, and tests.

Summative: Every 2-3 weeks there are in classes written tests. There are also 3-4 extended projects, one per quarter.

After showing the above clip to the class, we had a conversation about what they noticed and wondered. There are comments generally fell into two categories:__modify each of the given steps__ to apply more to our discussion based learning environment.

**1. Preview:** This step is taken care of with our problem sets. The psets are are designed topic centric and use previously learned material to introduce new material. I need to remind students that they are not expected to come to class the next day with all the answers. Instead, they are expected to put in a focused effort to get through all the questions and develop questions that they need to get answers in class the next day. I also tell them that if they shouldn't spend more than an hour on a pset. I tell students that this is the reading and the prompts that your English teacher assigns before class. It's not a very productive English class when no-one has read the book.

**2. Class:** Students need to be active and engaged in class. After students put their efforts on the board, we discuss each. During this discussion the details come out and we write them on the board in a different color. This becomes their notes and annotations and I try to connect these to their learning outcomes.

**3. Review:** At the beginning of class I always ask what they thought is the theme of the problem set. I ask them to write this on the back of the pset. The theme becomes the title to their review. Before they start the next problem set, they should take 10 minutes to look over their notes and annotations of the preview set and summarize the main ideas on the back of the pset. This process should take no more than 10 minutes and feeds back into the preview step because a lot of times the problem sets build off each other.

**4. Study:** Steps 1-3 are what students are doing a majority of the time. Once or twice a week they should engage in the study step. This is a 60-90 minute session focused goal driven session. Ideas for what to do during this time come from the book, __Powerful Teaching__.**5. Assess:** This step is something I ask them to do all the time. Students should continually ask themselves, "Am I learning the material or just memorizing it?" and "Is this the most effective way for me to learn the material?" Also, every few weeks I ask them to tell me 1) what is working for you? 2) what challenges are you facing? and 3) what can I do to support you?

**Bonus:** I ask students if they every have 5-10 minutes a day when they are flipping through Instagram, SnapChat or on a bus to game. This is a great time to view some of the videos I make available to them. Sprinkling them into your week is a game changer.

**Summary:**

Most of the time students spend between 45-60 min a day where the first 10 minutes is spent reviewing that days pset and notes from class. The remaining time is spent doing the next pset. Once or twice a week they should plan on a goal oriented focused period of time to synthesize the material.

]]>- I don't have time to do all that.
- This doesn't apply to our class because it's not a lecture and we don't have a book.

- Brain Dump: Write down everything you can remember about the last few problem sets, then edit it after looking through all the summaries of each pset.
- Quiz yourself: Re-work the problems without looking at the solutions.
- Teach it to yourself in the mirror or a person or a stuffed animal or a pet.

Most of the time students spend between 45-60 min a day where the first 10 minutes is spent reviewing that days pset and notes from class. The remaining time is spent doing the next pset. Once or twice a week they should plan on a goal oriented focused period of time to synthesize the material.

1. Talent is not born, it is grown.

- Be deliberate...slow down your practice. Show your work. Get it out of your head and onto paper. You need to see what you are doing.
- Being deliberate actually rewires your brain. How

- Neuropathways are road in your brain to habits, thoughts, skills, etc.
- The more we travel these pathways, the stronger they become. Traveling these pathways is called practice.
- How can you strengthen, change, or alter these pathways, deliberate practice.

- Myelin is insulation around axions that stops energy leaks and strengthens connections.
- How do you grow more myelin?
- Limit distractions - Stop the chatter.
- Start slowly and deliberately.
- Spaced practice.
- Visualize success.