Sunday, April 29, 2018

Multiple Opportunities to Practice Independently

It's important that students have multiple opportunities to practice independently, whether you're in a traditional or standards based classroom. The nice thing about a standards based class is the opportunity to tag independent practice with the standards so that they are organized and easily accessible.

I put some nails in my wall (oops!) to create a "Practice Wall" of worksheets. When students need extra practice, they just pull out one of these. They mostly consist of practice I've already assigned for homework, but there is often a little bit extra. I post answer keys online and use the Homework Sandwich method from Bruce Jackson. While I do give feedback to students one-on-one, this lets them practice and get their own feedback whenever they're ready.

All the videos, formative assessments, and online answer keys all tagged with the same standard too. This makes it easier to go between them - the same number indicates the same standard. I also open up all of my online quizzes for unlimited re-trys (after I see the data from the first try in class) so that students can continue to practice and improve. Again, they're getting their own feedback.

But all of these opportunities have been about content. About once a week, we have can activity where students get feedback on practice standards. They are typically in the style of a five practice routines, and feedback could be verbal or written (using a practice standard rubric). Again, it's all about empowering the student to practice and giving formative feedback when they do.

Friday, April 27, 2018

Scholarship Standards

Many teachers who use standards based grading only count content (and maybe math practices) into the final grade. I think it’s important to think about effort and behavior, but in a way that makes sense with standards-based grading. I also wanted to personalize it to meet my student’s needs. I created a rubric that has 10 goals. Each quarter, students choose three goals, and reflect on each of their goals every class in a google form. At the end of each quarter, we meet and they can change their goals.

This gets translated into their scholarship grade. So, students are essentially grading themselves. There are students who need to be reminded they were late to class, or disorganized, but if you're paying attention, most students are honest.

Below is the worksheet that I give students. Here is an electronic version you could print. We typically start there, and then move to a google form once students are comfortable. You can actually have google send these reflections home to parents. Check out Marissa Walczak's post about it here.

The best way to improve in any field is to reflect in order to analyze your practice, find room for growth, and determine the most efficient way to improve. Math class is no different! Please read the goals below and identify three that you think that will help you grow the most. If you feel there are more than three you want to focus on, choose goals closer to the top of the list.

Each class, you will reflect on your three goals with a google form. You will be asked to rate yourself using the language found in the rubric below. At the end of the reflection, you will think about what you can do to improve on your goals. These reflections will be used as part of your scholarship grade, and I will conference with you periodically about your reflection and growth. If you feel that you are having difficulty with your goals, or believe you have mastered one or more of your goals, please meet with me to discuss changing your goals before the next unit.

Not There… Yet!
(0 points)
Getting There
(½ point)
Met Goal
(1 point)
I was more than a minute late to class, including getting my materials
I was less than a minute late to class, including getting my materials
I was on time to class and started the warm up immediately.
The teacher needed to remind me to go get my materials
I asked the teacher to get my materials or provide extra materials
I had all of my materials at the start of class, including video notes and homework
I was not focused, even after redirection from the teacher
I needed some redirection from the teacher
I was focused without redirection from the teacher
I needed to be reminded how to transition from one activity to the next
I transitioned from one activity to the next with some talking or distraction
I transitioned from one activity to the next without any talking or distraction
I was unable to find all of my materials
It took me a few seconds to find some of my materials, and I needed to be reminded to use them
I was able to find all my materials easily and use my tools (notes, calculator, whiteboard) strategically
I needed to be reminded to start a problem
I started a problem, but needed reminding when it became too difficult
I started problems quickly and persevered through difficult problems
I did not participate in class
I participated in class by talking to the teacher directly
I participated in class by responding to my classmates using talk moves
I did not use precise language today
I attempted to use precise mathematical language, but was sometimes inaccurate
I explained my ideas using precise mathematical language, both when writing and when speaking
Peer Tutor
I did not help others today
I helped others by reminding them of the steps needed to solve a problem
I helped others by explaining an idea conceptually and letting them solve the problem
Role Model
I was not a role model today
I served as a role model by demonstrating BARK
I served as a role model by encouraging others to act with belief, awareness, respect, and kindness

Norming our Personal Philosophies of Grading

Standards based grading is all about assessing what we value. Whether you are doing this by yourself or with a team of teachers, it's important to have a personal philosophy of grading. Since every classroom is different, you'll need to adapt your standards based method to meet the needs of your students. A philosophy can help you do that. A philosophy can also give you something to fall back on when you're challenged by a student or parent.

So, here are three activities that tend to help:

1. What does it mean for a student to pass your class?

In some places, passing is a 60. In others, it’s a 70. Think about what it means for a student to barely pass your class for the year. Then, think about what it should mean for your student to pass for the year.

2. What is the purpose of a final grade in your class? A card sort.

Below are a list of purposes a final grade might have. Number the following purposes from most important to least important. Alternatively, you might just circle the top three purposes. Note that this activity is best done as a card-sort with slips of paper.
  • Feedback About Achievement for the Student
  • Feedback About Achievement for the Parent
  • Feedback About Effort & Behavior for the Student
  • Feedback About Effort & Behavior for the Parent
  • Informing Daily Instructional Planning
  • Informing Long-Term Unit Planning
  • Informing Intervention or Support Teachers
  • A Motivation Tool for Students
  • A Prerequisite to Pass to the Next Level Class
  • A Factor in Entrance into College
  • To contribute to their GPA and Class Ranking
  • Once you are finished, turn and talk to your partner about the following questions:
  • What were your top three purposes? Why?
  • What were your bottom three purposes? Why?
Once you rank, think about the following questions:

  1. What were your top three purposes? Why?
  2. What were your bottom three purposes? Why?
  3. How could we change the way we assess to target the most important purposes?
  4. Are there any purposes that might be inappropriate to include in a final grade, but that are still important? How can we incorporate those into our classroom practice?

3. What’s in a grade? Assessing what we value with colored manipulatives.

Since standards based grading is all about assessing what we value, let’s norm our grading system. I have created four large categories that most graded assignments in our class can fit into with descriptions below. In a true standards based system, we standards would be reported separately. Unfortunately, many schools still use a traditional model that requires us to give each student one final grade at the end of each marking period.  

Typically, this activity would be completed with a pile of red, blue, green, and yellow chips that correspond to the categories. Each of chip represents 10% of your ideal total grade makeup for your class. Your job is to take 10 chips that best represent how you would create your final grade. If you're on paper, just shade in 10 squares.

Content Grades: Blue Chips

This grade represents a student’s progress towards mastery of content standards. This could also be called the “traditional” math grade. Typically, these skills are not very transferable. 

☐   ☐   ☐   ☐   ☐   ☐   ☐   ☐   ☐   ☐

Practice Grades: Red Chips

This grade represents a student's progress towards the math practice standards. These could be seen as an “application” grade. Typically, these skills are transferable to other fields.

☐   ☐   ☐   ☐   ☐   ☐   ☐   ☐   ☐   ☐

Scholarship Grades: Green Chips

This grade represents a student’s progress towards the transferable qualities of being a “productive student”. Typically, these skills are transferable to all other academic settings.

☐   ☐   ☐   ☐   ☐   ☐   ☐   ☐   ☐   ☐

Completion Grades: Yellow Chips

This grade represents the completion of a specific task. Often an “all or nothing” grade to elicit a behavior.

☐   ☐   ☐   ☐   ☐   ☐   ☐   ☐   ☐   ☐

Once you are finished, turn and talk to your partner about the following questions:
  1. What categories have the most or least number of chips? Why?
  2. Does our ideal system match our current system? What would we need to change?
  3. Does your grading system reflect your classroom practice? In other words, if you allocated 50% of your grade to practice standards, does 50% of your classroom practice include the mathematical practices?
  4. Are there any aspects that would be inappropriate to grade, but that are still important? How can we incorporate those into our classroom practice?

Building a Flexible Standards-Based Classroom within a Traditional School Setting

Hi, I’m Bob. I’ve been using standards-based grading (SBG) within a traditional grading setting for five years. I’ve done it at two schools, in two different environments. I’ve also worked with a grade-level team to make the transition. However, in every environment I've been in, I'm either the only or one of the only teachers to use SBG. As a result, I've had to bend some of the "rules" of SBG. I like this quote from Frank Noschese:

A traditional system done in the spirit of SBG is much, much better than an SBG system done poorly.

There are some great resources for making a whole school shift to standards based, but this is not one of them. These resources are aimed at teachers who want the benefits of standards based grading, but who work within a traditional grading system.

What do I mean by a traditional school? I mean a school where...

...grading software allows for points, or maybe category weights. No standards.
...assessments are named in general topics like “Quadratics”, points are assigned to each question, and the student gets one score on the top
...most assignments are viewed out of 100% (students will rush to a calculator to find out that 5/7 =  is)
...the end of the year grade is either out of 100, or A/B/C/D/F, and a GPA is used
...classes are tracked, and perhaps GPA is based on those tracks (honors student can get a higher GPA) is encouraged that certain behaviors (homework completion, participation) are scored by completion
...there is no scholarship or participation grade separate from the letter grade
...most stakeholders want to see lots of grades in the grade book and don’t want you waiting for a summative to put in a grade
...textbooks and worksheets are used often

So, how do I work around these constraints? Click below to find out!

Norm your personal philosophy of grading

Focus on assessing concepts with content standards (coming soon)

Push students to work like mathematicians with practice standards (coming soon)

Encourage good habits through reflection and scholarship standards

Give students multiple opportunities to practice

Encourage and facilitate growth (coming soon)

I begged, borrowed, and stole from a number of great people. Click below to read blog posts and articles from a number of talented and thoughtful people!

Frank Noschese
Matt Townsley
Dane Ehlert
Dan Meyer
John Stevens
Sam Shah
Matt Vaudrey
Dylan Kayne
Daniel Schneider
Bruce Jackson
Anna Blinstein
Marissa Walczak

Saturday, November 25, 2017

An Autopsy of a Sophomore Statistics Unit

This year, we flipped our sophomore geometry class around. Typically, we end the year with a statistics and probability unit, but this year we started with it. In fact, we extended the units from the end of August all the way until Thanksgiving break. Our beefed up units included:
  • Creating data displays
  • Probability using Venn Diagrams and two way tables to find unions, intersections, and conditionals
  • One variable measures of center, spread, and shape
  • Measures of location (z-scores and percentiles)
  • Experimental design and survey methods

There were many reasons we made the change, but here are a few:

  • Connecticut is using the SAT as its high school accountability test, and it has a fair amount of statistics on it (and very little geometry)
  • Statistics has been the last unit in our districts 6-8 curriculum, and we all know what happens to units at the end of the year...
  • We used to have 1-var stats and linear regression in algebra I, probability in geometry, and polynomial regression in algebra II, but teaching everything separately felt very disjointed.
  • Our department generally agreed with Arthur Benjamin's ideas about teaching statistics.

Now for the autopsy (complete with emojis)...

😒 It was a struggle for our geometry teachers to change gears at the start of the year. We found that many of the routines that work in geometry don't work as well with statistics. I have typically used a Which One Doesn't Belong to start every geometry class, but I found it very difficult to find or make ones that worked in statistics. Over time, I found that other routines such as Would you RatherClothesline Math, and some 3-act tasks were better suited to starting a lesson.

😩 The shift in content was also tough for teachers. At our school, statistics is typically offered as a senior year course, and our 9th and 10th grade teachers hadn't seen some of the content in years. Remembering how to calculate z-score took a minute; remembering how to teach the meaning behind it took longer. Shout out to the teachers who provided resources that made it so much easier:

😁 On the other hand, students felt much more at ease as compared to previous years. We have previously started the year with coordinate geometry, which relies heavily on skills from algebra I.  I've started the year with Jo Boaler's Week of Inspirational Math for the past three years, but students that didn't fare well last year see the writing on the wall and begin to withdraw early. Starting with statistics circumvented that issue and promoted more of a growth mindset.

😃 Starting with statistics also felt natural, because at the start of the school year you're trying to learn more about your students. Those student surveys and "getting to know you" activities suddenly had more of a purpose. It felt natural to ask students what town they lived in (we're a magnet), then ask how long they rode the bus to get to school, then make a histogram of those times, and finally look at the center and spread of the data.

😏 Staying with statistics for an extended period of time let us talk about social justice issues. For example, after looking at the bus ride data we were able to have an informed discussion about the impact of magnet school busing on our students. Unfortunately, these conversations tended to be limited to one lesson. I would love to have students explore social justice issues further, but I'm not quite sure how I would go about it, if my sophomores are ready for that, or if there is enough time.

😓 Speaking of not enough time, we're now in a situation where our normal geometry curriculum is compressed by six weeks. Since the SATs don't focus on geometry, most higher-ups doesn't see an issue. However, I know that our team of geometry teachers will need to start picking and choosing what topics in geometry we can spend less time on. Wish me luck!

The conclusion: the stats unit will live to see another year!

Saturday, October 14, 2017

Human Box Plots

Class walks in.

"Hey everyone. I put some marks on the floor. Try to stand in the right spot according to your height."

"Oh yeah, I made these too. Figure out who should hold these. I'll just wait over here."

"Can we make it look a little more 'box-plotty'? Yeah, like that. Smile!"

Someone moved just before the picture. 
Can you find the error?

Besides this being a goofy team building activity, it provided a good reference point for students to understand how boxplots work: There should be (roughly) the same number of people in each quartile. Small quartiles don't mean there are less people with that height; it means that the same number of people are crammed into a smaller range. You can see the girls peeking through in the middle. Big quartiles don't mean there are more people with that height; it means that there are the same number of people spread out in a bigger range. Just look how much space the girl in red off to the right has! Every time a student had a misconception about box plots, I reminded them of this activity.

Saturday, September 30, 2017

Standard Deviation Boccie

I wanted to create some sort of mildly competitive a game that would convey the idea that standard deviation (or any measure of spread) does not depend on how high or low the average of a data set is, but on how much all of the data points vary from that average. Unfortunately, the objective of most games is to either get a high score (e.g. cup stacking challenge), or meet some other specific criteria (e.g. landing on red in roulette).

It turns out that boccie is one of the few games where the winner is not the person that throws toss their ball the farthest, but the person that can toss their ball closest to a designated ball, regardless of how close or far away it is. The real rules can be found here, but we needed to make a few modifications to make it work for us. There was no pallino, and the score wasn't calculated by counting how many balls were closest to the pallino. Here are some instructions:

(1) Put some sort of lines on the floor so students will be able to tell how far they've tossed the balls from where they are standing. I used chart paper, but you could easily just lay a measuring tape on the floor, or count floor tiles.

(2) Place the class into pairs - these pairs will be competing against each other. Each pair should take turns rolling 5 crumpled balls of paper onto the floor (we used ping pong balls originally, but they rolled too much). It helps if the two partners have two different colored balls.

(3) The objective is to get your balls as close as possible to each other, while making your opponent's balls more spread out. You are allowed to knock your opponent's balls away from the group as you toss.

(4) Once all 10 balls have been tossed, ask students to record the distance of their five balls from where they stood. If there is time, groups can play a second or third game.

(5) Once everyone in the class had played at least one game, ask students to find the standard deviation, range, and IQR of their 5 balls from one of their games. 

I asked students to determine which partner won, and why. This led to a really great discussion of how we calculate all three measures of spread, what the advantages and disadvantages of each measure is, and which measure was appropriate for this game. We didn't have enough time to delve too far into a discussion, but I could see this turning into a 5-practice routine where groups need to defend which measure of spread would be best for this game. I also think this is a great way to visually see the differences between standard deviation, range, and IQR for students that have trouble calculating each.

Who wins this game?