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How to Learn Math is a free class for learners of all levels of mathematics. There are 6 sessions, the first three are approximately 10 minutes long and the last three approximately 20 mins long. It combines really important information on the brain and learning with new evidence on the best ways to approach and learn math effectively. Many people have had negative experiences with math, and end up disliking math or failing. This class will give learners of math the information they need to become powerful math learners, it will correct any misconceptions they have about what math is, and it will teach them about their own potential to succeed and the strategies needed to approach math effectively. If you have had past negative experiences with math this will help change your relationship to one that is positive and powerful.

The course will feature Professor Jo Boaler as well as videos of math in action - in dance, juggling, snowflakes, soccer and many other applications. It is designed with a pedagogy of active engagement.
Main concepts to learn in this course:

Knocking Down the Myths About Math

Math and Mindset

Mistakes and Speed

Number Flexibility, Mathematical Reasoning, and Connections

Number Patterns and Representations

Math in Life, Nature and Work

There are no prerequisites for this course.

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How to Learn Math is a free class for learners of all levels of mathematics. There are 6 sessions, the first three are approximately 10 minutes long and the last three approximately 20 mins long. It combines really important information on the brain and learning with new evidence on the best ways to approach and learn math effectively.

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The Mathematics Assessment Project is part of the Math Design Collaborative initiated by the Bill & Melinda Gates Foundation. The project set out to design and develop well-engineered tools for formative and summative assessment that expose students' mathematical knowledge and reasoning, helping teachers guide them towards improvement and monitor progress. The tools are relevant to any curriculum that seeks to deepen students' understanding of mathematical concepts and develop their ability to apply that knowledge to non-routine problems.

More about the Math Assessment Project

100 lessons for formative assessment, some focused on developing math concepts, others on solving non-routine problems. A Brief Guide for teachers and administrators (PDF) is recommended reading before using these lessons for the first time.

A set of 94 exemplar summative assessment tasks to illustrate the range of performance goals required by CCSSM. The tasks come with scoring rubrics and examples of scored student work.

Complete summative test forms and rubrics designed to help teachers and students monitor their progress using a range of task types similar to the 'Tasks' section.

5 Prototype modules that encourage groups of teachers to explore the practical and pedagogical concepts behind the materials, such as formative assessment, collaborative learning and the use of unstructured problems.

The Teaching for Robust Understanding of Mathematics (TRU Math) suite is a set of tools with applications in Professional Development and research based around a framework for characterizing powerful learning environments.

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The Mathematics Assessment Project is part of the Math Design Collaborative initiated by the Bill & Melinda Gates Foundation. The project set out to design and develop well-engineered tools for formative and summative assessment that expose students' mathematical knowledge and reasoning, helping teachers guide them towards improvement and monitor progress.

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Peter Liljedahl's research, discussed by Laura Wheeler

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Icebreakers that Rock | Cult of Pedagogy

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Too many classroom icebreakers require students to take big social risks with people they barely know. Or they don’t really help students get to know each other. Or they are just plain cheesy.

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Teach the Math Practices to all students, students with learning disabilities and English language learners. Instructional Routines are the key to mathematical reasoning for all students.

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Even better than a pair-share

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I recently did a 1 hour Global Math Department Presentation on 'Stand & Talks'. UPDATE 11.15.18: You can view a recording of that presentation HERE. In the presentation I share a link to a google folder of additional resources I've developed since writing this blog post.

This post is my #1 tip for math teachers in 2017-18. It has been the secret to increasing the number of students who talk out loud about math each day in class to nearly 100% - everyday. The best news is anyone can do this. It's easy. Once you start doing this and seeing results you will also be excited to change tasks to increase discourse. This post is LONG, but stay with me. This tip has really been amazing in my own practice. I do it everyday in my classes now and it has radically changed the amount of discourse in my classroom.

Recently I was sitting at a coffee shop blogging and at the table next to me was a recent education grad doing a practice interview with someone. He was asked to prepare a 4th grade math lesson he needed to teach to those interviewing him. I could not help but listen in to his answers. He was eager, serious and obviously had little experience like all newbies. His answers were full of the things that they teach you in your college ed programs saying words like 'do now', formative assessment, exit tickets and think/pair/share. He said the right things, but his answers were hollow, missing the practicalities of how these things played out in a real class. When he said 'think/pair/share' I inwardly cringed, because I know better now. I use to say I used 'think/pair/share' and/or 'turn & talk' all the time - now I know better and I do better.

I thought I would share with you something that has transformed my classroom culture. It is a small tweak anyone can do A.N.Y.O.N.E. It does not matter how you define yourself as a teacher - traditional, radical, groups, rows.....This tweak is the one thing observers in my room always comment on (in a positive way). " Sara, how do you get every student to talk?" " Sara, I've never seen _______ speak in class ever." This tweak has made me look good. Seriously, you need to do what I am going to write about every day in your class. Every day. If you work with adults, you need to do this with adults. I started doing this regularly 4 years ago and seriously for the last 2 years and my classroom discourse has changed. I don't recommend this because it will make you look good to observers, I recommend this because it is best for students and without much effort on your part will change your classroom culture related to student discourse.

Let's be honest, this doesn't work as well as leaders claim.

Think/pair/share (or turn & talks) as an instructional tool has been around for years. You will hear the phrase in most teacher interviews and at teacher conferences. Mentors recommend this move in post-observation meetings. There are things that are amazing about this move. The silent think time removes the stigma that being good at math is being fast at math. It invites so many learners into believing they are mathematicians. Here is where it falls about. We then say as teachers, "Turn to your shoulder partner" and discuss what you were thinking about.

This is what it is suppose to look like. Every student is talking to their partner or group. They all have eye contact with one another. None of them have phones out in their lap texting. Everyone is 100% engaged. i don't know about you, but in my classroom, the only group that looks like this is the one I was standing next to looking at. I always have a few groups that take 2-4 minutes for even one word to come out of their mouths. 2-4 minutes to get started is often way longer than I want to give before we have a class discussion. When I do have a class discussion, I still hear from the same 2-5 students I always hear from.

Note: I do think there are teachers who can pull 'think-pair-share' off successfully all the time. It is way better than doing nothing. It is great for EL students as well as many others. One of my favorite bloggers, Jennifer Gonzalez has a podcast titled "In praise of 'think, pair share'". Check it out HERE. That said, I still think this one tweak would enhance the best practices she shared.

THE INSTRUCTIONAL MOVE

I lovingly call this move ' stand & talk'. If you've been doing think/pair/shares with students already, then this tweak will be easy for you. Basically you give students some private think time (30-120 seconds), have them stand-up and walk across the room to find a partner and share their thinking. It is a smidgen more complicated than this though - because you need to give them something to talk about, something to notice and describe. The success of stand & talks is dependent on the work of the teacher prior. I will tell you that in my own experience, other than maybe the first one or two

Stand & Talks I've done, it takes the same or less amount of time to do a S&T versus a turn and talk and the results are better.

I love doing stand & talks because it fits two of the goals I have for my classroom - that students will move at least every 20 minutes everyday and that students will will say (notice and describe) mathematical concepts before I say it for them. I also know talking out-loud engages students brains differently than just sitting and getting information.

side note: someday soon I am doing a blog post on ideas for incorporating movement in the secondary math classroom. A small way to give students a ' brain-break' is to have them stand up and walk across the room. An easy best practice (movement) that is rarely seen daily in secondary math classrooms.

To help you understand 'stand & talks' in my classroom I will share with you a script of sorts for doing one, tons of examples of what I ask students to stand and talk about and some tips for implementing them in your classroom. Here we go.....

A STAND & TALK IN ACTION (a script)

When I train teachers on doing stand & talks I start by doing one with them & following up with the question, ' What teacher moves did you see me doing during the last 5-10 minutes " Since this is a blog, I will do my best to replicate this. Here we go...

Note: Depending on what I am using with students, I may or may not give time prior for individual think time - I often do, but not always, it depends on the task.

(nothing on my screen) "Learners, I'd like everyone to stand up. Do not have anything in your hands. No calculators. No notebooks. No phones or pencils. Nothing. (I wait until everyone stands before I give my next directions). In a moment I am going to give you something that I want you to look at with a partner. I want you and your partner to notice at least 10 things on the sheet. I want to hear you asking each other things you wonder about. Look closely at all the details. You will be working with this partner for just a few minutes. You can work with anyone except for the people at your table. Please go now and find your partner, no groups of 3 & I will bring you a 1/2 sheet to look at."

Notes:

I give directions after everyone is standing because if I do it when they are sitting they are much slower to get up and find a partner. Later in the year, my beginning directions are much shorter than this, because students know what to do when working with a partner.

As students find partners I am handing out a 1/2 sheet for them to look at. I like to hand things out myself, because this gets me moving around the room with my students. It also allows me to link up students who do not have a partner - usually I have just a couple of students who don't have a partner right away and usually only because they can't see who is still looking.

Once I've passed out the 1/2 sheets - this takes me 30 seconds or less, I turn on the same thing they are looking at on my screen. Here is the one I do with teachers (and my students) when I model the procedure for them.

As partners are working I continue to move around the room, listening in. Often students don't even notice me. I give students usually 60-180 seconds to talk. I rarely comment as they talk to one another. I only intervene if partners are not talking to one another, and this is rare.

You will hear me announce to the class during this time - if there is a lull things like....

Me: "I should see you pointing at your card"

Me: "I want you to notice at least 10 things" (hint, use a big # like 10, 15, 20...)

Me: "What do you wonder?"

Me: "Everything on the card is there for a reason, what else do you notice?"

I then ask students to take their seats. (note: about 40% of the time I have the next conversation while they are still standing). Students generally do this really quickly.

Me: "What did you notice? Shout out your noticing and wonderings"

In the case of this task Here are typical things my students say.

I noticed....there are different colors.

I noticed....triangles

I noticed....lines

I noticed....some lines are dotted and some are solid.

I noticed....points

I noticed....some points are open and some are filled

I noticed....a test point

I noticed....a horizontal line at -4

I noticed the test point is at the origin

I noticed....3 equations

I noticed....the equations have less than and greater than symbols

I wonder....why some sections are darker.

I wonder.... why there is a point inside of the triangle

I wonder....why some lines are dotted

and so on and so on.....

Note: I use this task at the start of our systems of inequalities unit. My goal if for my students to see the details of the structure before I tell them things like "When you graph a line with this symbol < you use a dotted like". My students rarely say the things math teachers say when I use this with them, they go right for 'correct mathematics' and say things like "I notice a graph of the solutions to a system of inequalities". Even when I ask teachers to notice and wonder things their student would notice and wonder, they struggle to see the details students notice first. I don't care that students in their partners use the word 'inequality' with this - it always comes out in our class discussion.

During the class discussion, after I started using Stand & Talks, I noticed how many more students volunteered to speak - students I'd never heard from before.

The 2-4 minute S&T not only increases the quantity of students that contribute to the class discussion, but it also increases the quality of what they say. I rarely have a S&T where not every single student is talking out-loud to their partner.

Just in case you are curious, I use this image to further the conversation with the class round inequalities. By adding letters to each region, I find students are also more willing to contribute to the class discussion. (side-note: I often get asked how I made this graph - and of course the answer is Desmos - it is so easy there)

MY TIPS FOR SUCCESSFUL STAND & TALKS

The first few stand & talks you do will take just a bit more time so you set up the norms for future stand and talks . The most important thing you want to do is make sure everyone stands and moves across the room to work with someone not in their table group. (no leaning or sitting unless there is a health reason, but I even make people in casts stand - though they do not have to move across the room). It is important that you make this a no-opt out experience. I will go around the room using non-verbals and or saying something if necessary to assure everyone is standing and talking to only their partner (not from their table) and that the only thing in their hand is the 1/2 sheet I gave them to look at. Demanding 100% will assure the success of all future S&Ts . This takes very little managing after the firs couple of S&Ts .

When I first do these at the start of the year, I tell students why we are doing this. See this post for more on students understanding the definition of math and knowing what mathematicians do. S&T's allow my students to do what mathematicians do - notice and describe. I catch them and name when I see them being mathematicians

Work in partners always. There should be at most one group of 3 and I get to make it. As students make groups I am walking around the room handing out what I want them to work on. As I do this I help students find a partner if they don't have one. I just say "Ayan go over and work with Bo". I've not had a problem with students moving to work with someone. If I have other adults in my classroom, I put them students who don't have partners. My EL aide is great about seeking out a student to work with (and students love working with him and seek him out). Everyone talks.

I usually don't join in with a partner. The main reason for this is I am constantly circulating the room listening in on conversations. I rarely join in except for rare occasions to refocus the students. I do at times say to a partnership either "I am going to call on you to say that to the class" or "Make sure you say that out loud when we come back together as a class"

Make these experiences safe for students. I usually let students select their partner. I find my ELL student will seek out other ELL students and often speak in their first language. I almost always introduce a stand and talk by saying noting the time (1-4 min) they will be working with a a partner. Because I always keep these short, students seem to be OK working with anyone. Last year I never had anyone refuse to work with a single person in class. Students knew that working with this student was not a forever commitment.

I highly recommend if you want them to look at something up front you give it to them to held between them. One sheet per 2 people. I've been amazed how much students point at the paper, even without prompting from me. I don't always give them something to look at, but I'd say 75%+ of the time I do.

If possible, print out what they will look at on cardstock. Most of my stand & talks are 1/2 sheets on cardstock. Since I reuse these each class, I only have to print out 9 sheets of paper giving me 18 cards for 36 students.

If I want students to have a copy of what we are doing for themselves I still use the 1/2 sheet card-stock for partners and then say "whoever is holding the paper, come to my stool and trade it in for 2 copies for you and your partner." I do this as they are returning to their seats. I usually have my students then glue this (usually smaller) version of whatever we were looking at into their notebook. I usually have them get their own copy IF I want them to do something additional with it. (annotate it, solve something....)

I often use S&Ts when there is a lull in class and I need to infuse some energy. Most of my S&Ts are planned, but when we need a shot of energy I will say, "Please open your notebook (or white-board or...)up to what you were just working on. Please stand up, nothing in your hands, no phones, calculators or pencils. Walk across the room and find a partner you've not worked with in a while." Once students are with a partner I'll say, "Whomever is wearing the most black (or the tallest student, or the person standing closest to the door or...), bring your partner to your table and show them what you were working on in your notebook - stay standing" After 1-3 minutes I say, "Switch, go visit your partner's table and have them explain their work". It is amazing how 2-4 minutes of standing and talking re-engages students brains and energizes the room.

I think one reason S&Ts work so well, is it demphasizes me as the teacher and empowers the students. Since they are standing I am hidden. (even at my 5'11' height). S&Ts de-fronts the classroom.

TYPES OF STAND & TALKS

For my stand & talks to work, I've needed to give my students something to talk about. About 80% of the time I put one 1/2 sheet of card stock in the hands of each set of 2 students. Below I'll share with you examples I've used - many from my Advanced Algebra classroom with the hope to inspire you to create to fit your content.

Many of my stand & talks ask students to notice and wonder. I love, love, love having students notice and wonder. For example, before doing Fawn Nguyen's Noah's Ark Task I use this in a S&T .

I love doing stand & talks with new vocabulary. One of my favorite way for students to define new terms (or to review old terms) is with examples and non-examples. For example this is what I used when we defined polynomials....

This is one you can use for students to define polygons.

I teach a large number of ELL students and students in poverty. Anytime I am doing something where I the context may be a challenge, I often address this in a S&T . For example with playing cards. What do you notice?

Or this one to make sure that students did not confuse the non-math and math definitions for 'expressions'.

Or before doing a task about a walking race, I used this picture of a race-walker. You can read more about this task HERE.

If I am going to have my student read text, I often have them read it out-loud with a partner, taking turns to read sentence or paragraphs. I model how to point as you read and how to number paragraphs. Here is one text I had students read for a task at the start of my quadratics unit.

After reading this out-loud with a partner, I had them sit down and individually draw what they just read about. I found students own drawings were much better when they read this standing vs. them reading it alone or someone reading it to the class.

I have a daily goal for students to connect representations in mathematics. This may be at least 2 of the 5 forms of a function (context, graph, table, equation, words) or connecting a visual to a students calculation like this S&T to review multiplying integers before we multiplied polynomials.

I love the #connectingreps Connecting Representation instructional routine found in the New Visions Math Curriculum. Here are a few you can find HERE. They have a lot more.

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I use S&Ts all the time to review material that students should remember from prior courses. For example, at the start of my Advanced Algebra probability unit I used this visual with students and asked them to notice and wonder with a partner.

within 5 minutes our class had reviewed all the basics of probability - including giving a title to this visual. The students named these basics for themselves before I told them what to say. Here is what our work looked like 5 minutes later.

I highly recommend reviewing material this way with a S&T. Students know more than they think they know about prior material. Doing something like this is much faster than taking 3 days each unit to review material.

I like to use S&T's at the start of every unit by giving them something we will be studying in the unit to ponder. For example, here is a visual I use at the start of a unit on the Pythagorean theorem. What do you notice? What do you wonder?

At the start of units I also love to give students a sheet of pictures they will see in the unit and ask them to predict what we will be studying in the unit. Here is the one I use for unit 1 in Advanced Algebra. What do you think my students will learn in this unit?

are amazing with the 200+ visual patterns found HERE. Here are 2 that I used during my exponential equations unit.

Creating a scenario (also called numberless word problems & check out the graph in this post too) removes the numbers, labels, questions and more from a task. Here is one I use with positive and negative numbers.....

Instead of starting with the one that has the numbers already there.

It is amazing how much a student will notice and say if you remove the mathematical question from the task at the start. I encourage you to start with a 'scenario'. Here is a favorite one I used instead of starting with the classic 'painted cube problem. This one is from Nicole Paris. Love it.

I love this photo. Imagine the math questions you could ask about this. Before giving the questions for students start with a scenario.

I love, love this picture. This one is from my home state of Minnesota. What do you notice, what do you wonder? There are some great math questions in this pic.

This is a screen shot from the Wall Street's Journal 's time-lapse video

of an entire Pine City, Minnesota High School Boys Basketball game. The Pine City dragons take only 3-point and layup shots in their games. You can learn a lot more about why my hometown state team does this from a local news station.

Rather than say 'explain why' or 'prove', I often use the phrase "convince me which calculator is correct." Here is a S&T I did using this instructional move to talk about order of operations.

Convince me that these answers are correct.

Of course, 'which one doesn't belong?' tasks are great with Stand & Talks . I often do the class conversation on these as we all continue to stand with our partners.

I also recommend using with #smudgedmath or Open Middle Problems.

I also love using S&T's to introduce new mathematical notation to students. Do you know how much more quickly I could introduce summation notation using this than doing it any other way I've tried before? Seriously, so good. Students who had never seen sigma before were able to figure it out for themselves before I told them anything - in fact in this case I am not sure the class conversation after the S&T with a partner was even necessary.

Here is a S&T I did for students first introduction to augmented matrices. I've never had had so few errors with students setting up augmented matrices in my career with so little effort on my part.

I have lots and lots more examples of stand and talks I do with students because I do them all the time. If I showed them to you all, this post would be 10x longer. Perhaps I need to write a book of these. Ha.

ONE TEACHERS STORY

At the end of this school year I was sitting and talking to a teacher in my school I really

respect. I asked him how he was filling up the last few days. His eyes lit up. He was really excited about a task that he was going to use in his Pre-calculus classes. He had found this site where someone had stacked a bunch of baseballs. He was going to have his students notice and wonder first with this picture and then build a sum of a series.

Moved by his enthusiasm for the task, I said, "Can I offer you one tweak to what you are going to do?". He said ' yes.'. I told him that I thought he should do a Stand and Talk with the pictures during the notice/wonder time and described how to do it. I even made him a document ( Pile of Baseballs Stand & Talk) he could print out on cardstock (which I provided and printed this one time) so he could see that me doing this process took 5 minutes to set up. He agreed to give it a try.

The next afternoon he stopped by my classroom to let me know how it went. "Did all your students talk?", I asked. He smiled and said, "Yes, but I decided to test your theory and in my 2nd class I had them use the visual while sitting and there was far less discussion." I loved his test. It showed both of us that there is something magical about having students stand to talk to one another. I asked if standing took any more time and he shook his head no. This was all the evidence that I needed to keep going with Stand and Talks in my own classroom. I am hoping my coworker will use them much more when we return this fall.

In the past year I've become a huge fan of Peter Liledahl's work on Building Thinking Classrooms. In his work he has identified 9 strategies for engaging students in mathematics. 2 of his strategies have received lots of attention with the online mathematics community - Vertical Non-Permanent Surfaces #vnps and Visibly Random Grouping #vrg In his research on #vnps he measured 'time to task' as a reason for using this. Having students work vertically vs. at a desk changed the engagement in classrooms. If you follow the #vnps hashtag on twitter you will see enthusiastic teachers touting their success with this. When I read the research, it resonated with me because I had been having students get vertical (stand) for years and had seen huge increases in engagement. I think one stumbling block for some teachers using #vnps is not seeing how they can do this everyday. If you want to dip your toes into #vnps, then commit to doing this at least once every unit and use Stand & Talks every other day. For more information on Peter's work, I highly recommend his Global Math Department presentation which is FREE to view HERE.

A final note on #StandTalks

The secret is out. You must start doing Stand & Talks with your students. They are the best thing I started doing in the last 10 years of my classroom. I recommend doing them everyday, but just start with at least one.....but really.....If you think Stand & Talks are something you want to try, I recommend doing at least 5-8 of them over a two weak period. Do it several times before you give up on this instructional move in your classroom. Us math teachers need to get our students moving more, but ultimately my goal is to find ways to engage all students in discourse around mathematics and to empower them as learners. My wish is that you would see immediate results like I did.

Ultimately, I hope that in creating stand & talks for your classroom you adopt the lens that I bring to my classroom. How can I have students say things before I say things for them. What can I put in front of them so they notice the mathematics first? If I get this right, my students feel empowered as mathematicians and do not rely on me or others to make meaning of mathematics. This is my goal e.v.e.r.y - d.a.y!

As always, I love hearing from you when and if you use my ideas in your own classroom. Tweet me @saravdwerf or email me at [email protected] or comment below.

follow-up: David Wees tweeted me this resource ('Rumors' - a group learning routine) after reading this blog post. Thank you to everyone who connects me with more and more great stuff.

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STAND & TALKS. The best thing I ever did to get students talking to one another. - Sara VanDerWerf

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I recently did a 1 hour Global Math Department Presentation on 'Stand & Talks'. UPDATE 11.15.18: You can view a recording of that presentation HERE . In the presentation I share a link to a google folder of additional resources I've developed since writing this blog post.

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Lessons to establish culture and foster growth mindsets

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Choose your own maths adventure with our interactive tools that allow you to build a custom playlist of inspirational activities!

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Making the Most of GOHW_mtms2015-09-98a (1)

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Open Middle - Challenging math problems worth solving

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Open Middle offers interactive math problems designed to foster critical thinking. Explore unique challenges that boost problem-solving skills and creativity.