Blog Post #4: Replacing the Textbook Lesson

In this fourth and final blog post, I'd like to wrap up how starting your school year by establishing rapport with students through ideas that promote positive classroom culture, extending a Desmos lesson and/or providing chances for structured peer feedback, getting kids talking about math through study team strategies, and finally in this post making the decision to replace a textbook lesson with resources available and making it relevant and successful for my students.

If you haven't figured out from my previous blog posts, I am a big fan of College Preparatory Math, or CPM. It has some really great lessons and has cooperative teamwork opportunities built in to many of the lessons. My colleague, friend, and mentor Carrie Wong has continued to remind me though that I'm not teaching a curriculum, I'm teaching the Common Core standards. As I've taught more and more lessons, I've found ones that I've liked and didn't like. One I didn't like was a lesson on relative frequency tables that dealt with whether corn grew better in sandy soil or clay soil. Myself and my students couldn't get into it or relate to it.

In Graham Fletcher's NCTM Shadowcon talk one of his calls to action was to pick a standard you teach, and learn more about it. The standard chose was CCSS.MATH.CONTENT.8.SP.A.4
Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. I also consulted the Progressions documents where I was reminded that MAD or Mean Absolute Deviation is a 6th grade standard that I doubt any of my students are familiar with. I possibly missed an opportunity to teach this when representing class averages of paper airplane throws.

I searched on Illustrative Mathematics for a task and found a suitable one. My hook for the lesson was my hypothesis: I grandly pronounced that "if you play a musical instrument, I believe you are more likely to also play a sport." I asked students how we could answer this question. They replied that we should survey every student. So, I had students answer the questions in a certain order and check off yes or no for each question on a class roster on a spread sheet (example and more details).

I asked students if we could see if my hypothesis was correct. They thought it was hard to tell, and I agreed. This created a need for an organized way to analyze the data. That's where the frequency table serves its purpose. I created a Google drawing template that you could use with your class, that has some of the academic vocabulary also. To extend this lesson, it's possible make the connection between this display and a Venn diagram display.

After analyzing the class data, have students come up with their own hypothesis that could be answered by asking two questions with yes or no answers. I believe this raises the Depth of Knowledge (DOK) level of the task by having students create their own as well as motivation because they have the freedom to create their own survey. After the teacher approves it, give the students time to survey each other.

Students came up with the following hypotheses:

• if you play video games will most likely wear eyeglasses
• if you hate math probably hate school (eek!)
• if you have an iPhone also probably have Snapchat
• if you play video games you probably go to sleep after midnight
• if you don't have a pet you want a pet

I believe this lesson could still be improved with a rubric outlining how the final poster would be scored, which would help students fulfill the requirements.

In conclusion, students are motivated when a math concept can be tied to their personal interests. This is also evident in my first blog where students love hearing about their commonalities and differences with the mystery student activity, in my second blog when students are given the chance to analyze each others work giving peer feedback, and in my third blog guiding students to work cooperatively with each other with creative study team strategies.

If you have suggestions on how to improve this particular lesson, or have a lesson you have created or tweaked to motivate your students please share it.

Blog Post #3: Cooperative Learning Strategies

Cooperative learning is a learning and teaching style that contrasts greatly with the traditional direct instruction model. In direct instruction, the teacher generally does an example for the class, then with the class, and finally the students try it on their own (I do, we do, you do). In cooperative learning it's generally the students starting the problem, working it out together, with the teacher providing closure where students present ideas as well as allow opportunities to connect the ideas and add in academic vocabulary. According to my review of the research, fewer students can access the content using direct instruction and usually forget it quickly. Cooperative learning allows for opportunities for productive struggle where students feel safe to make mistakes in a safe environment, and learn from those mistakes with explanations from their peers and teacher.

Group work takes commitment. For many teachers and myself, it is difficult at the beginning. You want to fight the urge of giving up control. This is precisely though how the students have time to try out ideas, listen to each other, and gain confidence amongst their peers and the whole class. It can and will be frustrating at times. Remember: we aren't all naturally great at group work. I had to teach my accelerated class the word "tact" after dropping my jaw at what they were saying to each other and/or how they were saying it. Students knew I was serious about talking to each other "tactfully," which is explaining or disagreeing with someone without hurting their feelings or making them feel dumb. It takes practice, and with the following suggestions of establishing study team norms and using study team support strategies, your students will improve and you will see positive results.

Each year I introduce the study team norms and reinforce them with participation quizzes (I'll expand on those later). I basically use no talking outside your team, keep the conversations on math (realistically 90% of time), asking questions not giving answers, the team is not done until everyone's done, don't work ahead, keeping desk clear of clutter, justifying your answer, asking your team before the teacher, and more. A colleague of mine, Aristotle Ou, developed the study team norms with each class. This idea was suggested to him by the Week of Inspirational Math on youcubed.org by having students finish two statements: "When working in groups I like when... and I don't like when..." The list is phenomenal with gems like "I don't like when people are off topic, give up, say the answer before you tried it, etc."

One of the most important and effective study team strategies suggested by CPM (College Preparatory Math) is the participation quiz. Basically, you put a grid on the board and/or your clipboard of the group seating arrangements. Before they start the lesson, you could highlight one of the study team norms you will be looking out for especially. Then you update the board as the lesson progresses with positive and negative quotes that are evidence of sharing ideas, critiquing ideas, and checking if teammates understand it. They love getting the instant feedback, and are not distracted by it. Sometimes they even read off the study team role cards I have at their desk a suggested question, which I am OK with.

Another strategy I've used is called red light green light. In the example linked, students worked on three situations where they had to analyze if they were proportional or not and justify with a table, a graph, and an explanation. Then a representative from their group goes up to the board, checks the answer. If they are wrong, that's a red light to stop, and discuss the mistake with their group and fix it. Then they have the green light. If they got it right the first time, green light. This sounds like a simple strategy, but students are motivated when they don't need the teacher to confirm whether they are right or not and empower students to be responsible for their own learning.

A partner and group strategy that I also like is called Rally Coach or Pairs Check. Students work on a problem in a pair. The catch is, one person is talking and explaining the problem while the other is writing and saying nothing. Then they switch roles if the writer disagrees. Then the pairs check with the pair across the table from them to see if they got the same answer. This strategy increases accountability for students that hide in a group of 4.

The final strategy I'd like to share is called Hot Potato. A group of 4 has 1 piece of paper, and each student has a different colored pencil. They then do one step of a problem, then pass the paper on to the next person, who completes a step, and so on. This strategy is effective because students actually lean in and watch what a person contributes to a step. I also can look at a paper and instantly see if everyone is contributing.

How have you gotten students to work efficiently in groups?

Blog Post #2: Extending a Desmos Lesson to a Second Day & Productive Peer Feedback

In this second blog post I would like to outline how I extended a Desmos lesson to the next day and how I taught my students to give productive feedback on each other's group posters.

First of all, if you have never tried the activity Desmos: Marbleslides Parabolas, stop what you're doing right now and try it. I used it last year with my accelerated 8th grade math class. To give you some context, we use a model suggested by where in 6th grade students take a prealgebra readiness test (called MDTP out of UC Berkeley) and a MAC test which is 5 MARS tasks covering each of the major Common Core strands. So, it checks where they are at procedurally, as well as where they are at conceptually with their ability to explain their ideas. Then I taught them for 7th and 8th grade, but taught 3 years of math in 2 years (CC 7, CC 8, and CC Algebra). When topics overlapped we used the 8th grade lessons.

Students completed this in partnerships and for those that finished they made a screencast of successfully completing a challenge. Some great examples can be found here and here with a full blog post of instructions.

After seeing their responses to the prompts, I took a screen shot of the question as well as their responses and put them on Google slides. Then I was able to print them so they were 4 slides per page and 4 slides on the back, that folded into a pamphlet (PDF available).




Desmos allows you to make the names anonymous so no one was humiliated by their responses. Some were proud of their lack of precision and claimed which answers were there. I instructed students to first read the question prompt. Then they looked at each responses and rated them with a check if they totally agreed, a carrot (^) if it was right but incomplete, and an X if part of their statement was incorrect and you disagreed. We did this for each response, starting and stopping the class and allowing students to share their critiques of their peers responses. This provided a great opportunity for classroom discourse as well as attending to precision of academic language.

A second activity that I use is gallery walk post it note feedback. This is not a new strategy, but I was constantly frustrated with the unhelpful feedback I was seeing students give, and their peers were disappointed as well. For example, I don't want feedback to be about how colorful it is, how pretty the title is, what they didn't get to finishing, etc. So, I decided to do something about it, and take time to teach them what productive and unproductive feedback looks like. I was inspired by a tweet by Norma Gordon that included this image.

I incorporated it into a Google Slides presentation after Common Core 8th grade students had completed their posters on the Formative Assessment lesson "Solving Linear Equations in One Variable." Basically students categorized equations as being always, sometimes, or never true and making the connection to infinite, one, and no solution, respectively.


After this, students were given a post it note and given two directives: write down an aspect of the group's poster that you agree with and why. Also, write down an aspect of their poster that you disagree with and give them a suggestion that will move them to revise their work (an example from the slides is: Have you tried see if zero is a solution to the equation?)

These big ideas came from reading Dylan Wiliam's Embedded Formative Assessment book and taking an online course called Formative Assessment insights. The research says that students are more invested in their work when they are given feedback by their peers. The goal, is students realize their mistakes and fix them.

 By reviewing the above slides with them, students came up with disagreeing tactfully about 2-x=x-2 being always true and they showed how substituting x=1 did not make it true.

How have you extended a Desmos lesson to the next day without computers productively? Also, please share how you have succeeded in getting students to give productive feedback to their peers.

NCTM Blog Post #1

In my four part blog series, I want to share how I have implemented ideas from others to create a positive classroom culture where students are seen as responsible for their learning. In this first post, I'd like to propose a few ideas to create routines in class that promote personal relationships: a tip on doing attendance the first day of school, name tent feedback, daily high fives / fist bumps, and weekly activity called "Mystery Student."

In the second post I want to outline how I extended a Desmos lesson with students analyzing each other's responses to items from the previous day. I will also talk about how I helped students improve their skills at giving productive feedback to their peers.

In the third post I outline a study team strategy that motivates students to check their own answers and revise their thinking while working on cooperative problem-based lessons. I want to know other strategies that teachers have been successful with.

In the fourth and final post, I detail how I replaced a textbook lesson with a task from Illustrative Mathematics and extended it to a higher DOK level by having students create their own two questions to investigate and create a two way frequency table.

The first day of school is a big deal for students and teachers. First impressions are important and it's a fresh start for everyone. I tell my students at the beginning of the year that I will not judge them by what they did with another teacher in a previous year. Our relationship is based on what happens between us. A lot of students are relieved when they hear this and appreciate the fresh start especially if they're not a fan of group work or math in general.

I take attendance with the roster at my door on the first day of school because many students have English names that are not on the roster, or go by a nickname. I also like to avoid butchering the pronunciation of a student's name. Then students sit wherever they want before an activity that has them match their card or graph to three other students in the class. It also provides me information about who knows each other.

After saying their name, I offer a high five or fist bump. This tradition continues daily at my door as students enter my room. It's a great way to practice their name from day one on as you greet them and it also provides a positive start to each class period and day. This has in the past made me aware of how a student was feeling about me that I needed to have a conference with to figure out why they weren't feeling comfortable with the high five. This great idea was provided by Glenn Waddell with a video link on his post.

On the first day I borrowed an idea from Sara Vanderwerf and her name tents. It provides a great opportunity for students to ask me questions and for them to review what they learned about that day. It's a big commitment the first 5 days to collect them daily and pass them back, but well worth it. A bonus perk to this is that when you pass the name tents out during the warmup, you are literally taking attendance and streamlining your first 5 days of school (the attendance secretary will be happy they won't have to nag you!). After calculating percent errors using Estimation 180 as the warmup the first ten days a student reflected on the notation of the single quotation mark (apostrophe) and double quotation mark when dealing with Mr. Stadel's height of 6'4". It's a talking point later on in the year during a MARS task where some students interpret 1 foot 6 inches as 1.6 feet (link includes PDF file to 8th grade task via insidemathematics.org).

The last idea is one borrowed from Mark Cote, one of the leaders at College Preparatory Math's Academy of Best Practices professional development, and who used it an activity there. Each of the 32 teachers filled out a slip of paper with their hometown, grades they taught, and something that no one knows about (could even have been a two truths and a lie scenario). Then as a brain break during the sessions everyone would stand up and Mark would say, "Stay standing if you teach middle school. Stay standing if you teach on the west coast." The object is to narrow it down from general qualities to more specific and unique qualities. Last year and this year I have used the Mathography assignment from CPM's Core Connections Course 3 (link).

• I then use these Mathographies weekly, usually on Fridays, as a "Mystery Student" activity. I ask all students to stand up and I say, "Stay standing if you like working in teams, if you see yourself as a leader, if you have at least one sibling, if you play more than one instrument, etc." A funny anecdote was for one student I said, "Standing if you like EDM music?" A student said, "Huh? What's that?" I replied, "If you don't know, than that means you aren't a fan so you should sit down." This activity provides a brain break as well as a chance for students to learn about their similarities and differences. Also, for students that really don't like math and/or school, they will ask, "Can we please do mystery student?"

I have students type or handwrite their short autobiography letter, and I take notes at the bottom after reading it. The example below shows that this student had logged over 1,000 hours on one video game!

You also find out about some real issues such as living with a grandparent, parents being divorced, relative being sick, and some that haven't heard of Jo Boaler's research on not telling your child that you were bad at math (rather than lying and say you liked it):

What activities do you incorporate in your classroom to learn about your students and for them to learn about each other? How do you work on improving the culture of your math class? In the next blog post, I will show how I extended a Desmos lesson to the next day without the technology and giving productive feedback to their peers.

Martin Joyce is a middle school math teacher who blogs at http://joyceh1.blogspot.com and tweets from @martinsean. He has taught every level of middle school from 6th grade math support to 8th grade accelerated Algebra 1. His passion is developing student's math identity with cooperative learning, Desmos lessons, peer feedback, and is constantly reading books and blogs to refine his craft.

Appetizer Recipes

OK, so I'm tired of going to different web sites to look up different recipes. I'm going to keep them here and by me putting them here I'm clearly endorsing them having made them.

Appetizers:

Guacamole recipe:
Ingredients
3 Haas avocados, halved, seeded and peeled
1 lime, juiced
1/2 teaspoon kosher salt
1/2 teaspoon ground cumin
1/2 teaspoon cayenne
1/2 medium onion, diced
1/2 jalapeno pepper, seeded and minced
2 Roma tomatoes, seeded and diced
1 tablespoon chopped cilantro
1 clove garlic, minced


Directions
In a large bowl place the scooped avocado pulp and lime juice, toss to coat. Drain, and reserve the lime juice, after all of the avocados have been coated. Using a potato masher add the salt, cumin, and cayenne and mash. Then, fold in the onions, jalapeno, tomatoes, cilantro, and garlic. Add 1 tablespoon of the reserved lime juice. Let sit at room temperature for 1 hour and then serve.


Read more at: http://www.foodnetwork.com/recipes/alton-brown/guacamole-recipe.html?oc=linkback

Cajun meatballs recipe:

• 1 pound lean ground beef
• 1 1/2 teaspoons hot pepper sauce
• 2 tablespoons Cajun seasoning
• 1 tablespoon Worcestershire sauce
• 1 tablespoon dried parsley
• 1/4 cup finely chopped onion
• 
  1/4 cup fresh bread crumbs
• 1/4 cup milk
• 1 egg
• 1/2 cup barbeque sauce
• 1/2 cup peach preserves
• I didn't do it with the peach preserves but I bet it would be better with it.

Directions

1. Preheat oven to 350 degrees F (175 degrees C). Lightly grease a medium baking sheet.
2. In a large bowl, mix thoroughly the ground beef, hot pepper sauce, Cajun seasoning, Worcestershire sauce, parsley, onion, bread crumbs, milk, and egg.
3. Form the mixture into golf ball sized meatballs and place on the prepared baking sheet. Bake in preheated oven for 30 to 40 minutes, or until there is no pink left in the middle.
4. In a small bowl, combine the barbeque sauce and peach preserves.
5. When meatballs are done, place in a serving dish and cover with the barbeque sauce mixture. Toss to coat.

Salad Dressing recipes

Caesar

Picasso Art Lesson

This goes back to my student teaching days with Mr. Glenn Berry of Nesbit Elementary in Belmont... great lesson about opposite colors.

My sketch. Split face down middle. Cubism is seeing 2 different perspectives at once. So the face on the left is a side profile view and the face on the right is facing straight ahead.

Look at a color wheel. Opposite colors are vertical to each other (ex: purple and yellow, orange and green, etc.)

Student sample work from 6th grade art explorative

Preview or followup name activity. Draw horizontal line. Draw 2 diagonal lines that are somewhat vertical and steep. Mark out your opposite colors and write block letters over horizontal line. Continue contrasting opposite colors.