In my 3rd year of teaching, I taught first and second grade. There were so many behavior problems such as kids rolling on the carpet, having fits, peeing their pants, asking to get water or go to the bathroom just to get out of the classroom, yelling out, refusing to do their work…. NO ONE was having fun, myself included, and they were barely learning.

What I know now… I’d do almost everything differently so I could love teaching math.

Join me for 6 ways to love teaching math– even if you’ve NEVER liked math in your entire life (because that was me)!

On This Episode about Ways to Love Teaching Math:

• the freedom to get creative
• providing the time for students to explore
• real world experiences in math
• how you can begin to love teaching math

Let Me Tell You a Story…

In my 3 year of teaching I taught 1st 2nd grade multiage. We integrated everything, utilized small groups and zoned in on grouping kids to meet their needs– we differentiated a lot…except for math. For math we switched rooms, my second graders walked down the hall and the first graders came to my classroom. I had no idea what I was doing and was just trying to get them to count the things and fill out workbook pages… it was terrible.

I hated teaching math.

There were so many behavior problems- kids rolling on the carpet, having fits, peeing their pants, asking to get water or go to the bathroom just to get out of the classroom, yelling out, refusing to do their work…. No one was having fun, myself included, and they were barely learning.

What I know now… I’d do almost everything differently

Which spurred an idea for this episode. If I could talk to my 24 year old self and give her some advice… this is what it would be.

6 ways to love teaching math– even if you’ve NEVER liked math in your entire life (because that was me) 

**Which has me thinking– if you have people in your school that are like me, share this episode with them. Say something like, “Hey I know math isn’t your thing like it is mine, but my favorite podcaster, Mona just did an episode all about how she hated teaching math and gives 6 ideas to make it more fun for the teacher (and the kids). I’ll text you the link you should listen to it.” 

That would mean the world to me… to reach some teachers like me, to help them feel productive and joyful during that time instead of just trying to get through it as quickly as possible… dang that’s so relatable to me and I’m passionate about helping those teachers!

#1 Linking Your Passion to Math

As elementary teachers we can’t be passionate about everything. If we give EVERYTHING to EVERY subject we burn out, quickly. So, that’s not what this episode is about. Instead, it is about taking what you already do and are successful with and apply it to math. 

So, what do you love about teaching?

What parts of your day are your favorite with your students?

What was my passion?

Getting to know my students. I lived for that first circle up in the morning. In fact, I just LOVE to circle up, get eyes on everyone and chat. Morning meeting was my favorite time of day. We do a check in- share how we’re doing, say good morning and be greeted by the class. Then, we’d have time to share to get to know each other better. And then play a game– usually that was tied to our character goal for the week. If we were working on the value of new friendships we’d do a game that helped us mingle. Maybe, if we were working on integrity we’d do a game that required you to be honest. I think my favorite part of the morning meeting is the end- the debrief. We’d talk about why all of this mattered. How it related to what was currently going on in our class, our school, our world. We’d give context to our games and greetings and talk about how these skills could make a difference in our world.

So that feeling is what brought me joy…

so I started to take it with me to every subject, even math. How could I start getting my students to FEEL like they knew each other and could sit down together and chat, and talk about big problems in the world and how the little steps we were taking could tackle those big things?

Maybe yours is read alouds,  or group work- watching students light up about a story and make connections, or seeing how they navigate working together and getting fresh ideas from others. Maybe you love to incorporate service learning or writing projects that you can share outside of the classroom?

Take a second to think about what you do best in the classroom… What makes an impression on your students, what do they remember you for?

Then, let’s do more of that in math!

#2 Freedom to Get Creative

You have a curriculum and resources that was written for kids all over the country/world. It wasn’t written for your students– that’s where you come in. YOU know your students. You understand their strengths, interests, areas of need for more support,  you know when they  need a challenge or a scaffold. 

This is your permission slip to be creative.

You’re creative in every other part of your day, you CAN BE CREATIVE IN MATH!  

You are the expert in the room. SO, integrate problems into your science unit, bring a read aloud into math and then solve related problems, use music, try those engagement techniques you use to get students excited during writing…try them in math!

#3 Routines Really Make a Difference

Having a routine for math will simplify your life and allow you to focus on what matters. Many times our curriculum changes the routine each day. I say, instead of everyday doing something different… set a routine and stick to it. Routines create predictable, safe environments and that is a place where learning can happen best. 

So, reduce the stress of figuring out what we’re doing today in math and just stick to a routine. You can insert the parts of your curriculum lesson into the routine. Here’s an example of a routine you might use: for a 50 minute math block (hopefully you have longer)
-warm up 5 to 10 minutes
-launch the tasks (5 mins)
-Exploration time (10 mins)
-Discuss & Share (20 mins)
-Reflect & Apply (10)

#4 Providing Time for Exploration

Teaching isn’t telling. Teaching is about designing experiences for students where they can learn a concept in a way that connects to what they already know and take it to the next level.

Math is a lot like science, STEM, right? We embrace inquiry in science class, but often in math we do the opposite… We just tell kids what they should know (telling isn’t teaching) and then expect them to be able to do it right then. And even though that’s the way we’ve been teaching math & been taught math for decades, that’s not the best way. I know! It’s annoying to think that you were taught and then taught to teach in a way that’s not the best way… stick with me here.

Teaching students math is best done through a more inquiry based approach. Allowing students to explore the problem first, and using what they know to solve or even attempt to solve. Then, providing the support and explanations to help them solidify their understanding.

Let Me Give You An Example

If you teach 2nd grade and the students have a problem like, “There are 14 beads on the table. Ms. Swift brings 98 more beads to the table to make bracelets. Now, how many beads are on the table?” This is a simple join problem– we start with some, more are added, how many do we have now?

So, students should be able to understand that context after you launch it with them– then we let them explore. Because they have strategies– from kindergarten & 1st, from their home life, from being a human for 7 years… so we put out the manipulatives, pencils, and paper and we see what they will do. Some will start drawing by 1s- draw 14, draw 98. Others will group them into tens and ones, 1 ten, 4 ones, 9 tens, 8 ones. While some will start at 98 on their hundreds chart and count up by 1s 14. Others might know that you can add the tens and add the ones.

THEN, after students have had time to look and think and solve… then we bring them all together to share their ideas and share how they solved. This gives us something to talk about in the discussion or debrief. 

This flips what you do on its head a bit right? Instead of showing them what to do first I want you to let them explore first and then formalize that exploration after with an explanation.

#5 Get Students Talking

In order to do that you’ll need to have students that will talk in math class. Students will need to know how to explain their thinking. You’ll need to start talking in math. I don’t know about you but I love talking…so this one was hard for me at first because I love to do the talking… haha 

But seriously, one of my favorite things to do is to facilitate a discussion. To listen closely to students to see what THEY think and ask questions to get them to explain their thinking. Asking the right question that really gets kids excited is my teacher fuel (other than coffee). It fills me up to see kids getting excited to share because I’m not talking, but instead turning the floor over to them.

#6 Real World Experiences in Math

Now, in order to really love math… lets take math out of math… lets look OUTWARD. We make art about the books we read to inspire others to read, we create posters in science to help solve an environmental problem by inspiring others to change their habits, we write to solve problems & get others to listen, we do work in school to help our students develop the skills they’ll need to change the world, right?

Yes I want my students to be able to do well on the standardized math test, and know the standards. But I also want my students to go into the world with the skills to think creatively, problem solve, have agency and passion to make a difference and shape the world into what they want. 
So let’s do more than make the problems include our students names, our school mascot, or the students’ interests. Let’s relate it to what they are reading about in ELA or the opinion writing they are doing. Maybe there’s a local or school issue your students have been talking about (maybe it came up during morning meeting)… while your students are learning to add, subtract, multiply and divide they are also learning to problem solve…and problem solving skills are applicable outside of math.

That being said, don’t overlook the “real world” problems that face kids… like birthday party planning, budgeting their holiday lists, or helping their grandma at the grocery store. The more you know your students and their lives, passions, questions, and curiosities, the better you will be able to sprinkle real world scenarios into math problems.

Let me know what you are going to start today to start to love teaching math! DM’s are always open @hellomonamath

Links Mentioned in this Episode on how to Love Teaching Math:

 6 Ways to Teach Math Like You Love It!

Go to my instagram @hellomonamath & share with me how you’re listening!

MY TEACHER HOT TAKE

• Teacher PD should match the TEACHER’S goals, not the schools goals.
• PD should be provided by teachers, that understand what it’s like to teach in this post-covid world.

Other ideas for increasing your leadership:
Unlock Your Leadership Potential: 10 Energizing Tips for Educators

The post 97: 6 Ways to Love Teaching Math appeared first on Mona Math.

Jump in to Part 2 of my chat with Peter Liljedahl!  In this episode Peter and I dug into the concepts that will likely come up in your consolidating.

Did you miss Part 1? Listen in here where Peter Liljedahl and I chat about consolidation in a Thinking Classroom.

On This Episode with Peter Liljedahl

• How students represent their thinking 

• How representations can move students from simple understanding to more sophisticated understanding 

• How having multiple ways to represent and understand a math concept is what peter calls a Thick Understanding 

• How you Build a Thinking Classroom when you have a pacing guide and standards you must teach 

• Productive struggle 

When I say that this episode is JAM packed with goodness… I mean it.

About Peter Liljedahl

Peter’s website: https://www.peterliljedahl.com/
Facebook Group – Building Thinking Classrooms
 Building a Thinking Classroom in Math (Article on Edutopia by Peter)

5 Representations of Thinking

*From NCTM, Principles to Actions: Ensuring Mathematical Success for All  

• Talking it (verbal) 
• Symbolically representing (Numbers) 
• Drawings of tools (Physical or Visual)

2 Schools of Thoughts About Representations

1. Multiple representations thickens their understanding
2. Multiple representations mediate from A to B

Multiple Representations Thicken Understanding

When we can think about different representations of square numbers it creates a thick understanding, so in the future when I see a square number I have multiple representations to tap into. SO I have multiple ways of thinking about a task. It gives me more receptors when a task is posed. I have more representations that I can access to understand a task.

Tax Collector

A popular task from Building Thinking Classrooms – find it in Chapter 6

Thin Understanding → Describes students that are adding from left to right and ignoring place value. They have a thin understanding of addition 

Multiple Representations Move Us from A to B

Physical Manipulatives → Drawing → Symbolic → Abstract Understanding

Using representations can be mediators 

Example: Using a ruler (number line) to subtract in younger years, but in 9th grade we want students to have an abstract/symbolic understanding of subtraction 

Best way to ensure students have a Thick Understanding & are moving from Physical to Virtual to Abstract is to always require them to have at least 2 representations in their work. 

• talking & writing 

• tools & talking 

• drawing & talking 

So… be sure your students are:
Describing the model they drew.

Talking about the context and writing a number sentence to match. 

Using manipulatives and discussing how they relate to the context

“Thick Understanding allows you to be more flexible and more strategic in being more effective or efficient in their problem solving.” -Mona

You can’t actually force people to learn things in your timeframe

Somedays the discussion things just kinda fizzle out and you don’t get to that nice clear learning target but we will try again tomorrow. This is a HUGE mindset shift. 

We can… 

• bring the student to the water, but we can’t make them drink

All we can do is till the soil and hope that something grows. 

So… we have to be nimble. 

If they aren’t making the connections then we can ask ourselves “What can I do?”

• I can give them a hint. 

• Show a representations 

• Send them to observe another group

• Be patient 

• Give what I can 

• Evaluate ask, “where are we today?” 

Consolidation in Any Form

“Move from Bottom Up” 

Start with something everyone can do and understand. Common, easiest, concrete way of thinking about this task and then move up. That way we are moving through every child’s zone of proximal development & were able to lift everyone a little bit.

At the end of a consolidation everyone should be a little further along than they were at the beginning. But they shouldn’t ALL be up at the ceiling– that’s too big of a lift. We have to be responsive to what we have in the room that day. You may have had the best laid plans (Your threshold), but we have to be willing to raise or lower the threshold based on what your students are doing and understanding.

This is harder to do than you think.

Peter Liljedahl’s Take on Pacing Guides & Learning Goals

{John SanGiovanni and I dug into this topic on our interview– Listen here}

Peter Liljedahl acknowledges the reality of pacing guides and standards, but urges teachers to Ask yourself, “Achieve some learning or achieve no learning” 

In pursuit of the intended learning goal, sometimes only just a few kids will learn and others will learn nothing.Alternatively, we could have had all kids move a little closer toward the goal, and maybe not all achieve the goal… but everyone could learn a bit instead of only a couple kids mastering the learning target. 

Nudge students along in their learning journey.

It doesn’t mean that every child is going to master every standard on that day. 

The better you know your standards or content and understand it more and do this more you can better help them along on their journey. 

Peter Liljedahl discussed how a teacher asked him during a lesson observation, “What are you paying attention to?” 

He reflects on this by saying: “We have been trained to pay attention to the errors and the math because we’re pursuing the right answer. Instead, we have to focus on the learner, body language. 

Attend to Students’ Body Language

Body language can tell the teacher everything they need to know.

As you’re monitoring solving… Read the room’s body language.

Body language can tell you where students are in their learning. Their emotions are telling me about their progress. 

However, Peter Liljedahl acknowledges how difficult this can be by saying…

“When we teach math the students get in the way.”
“When we teach students the math get in the way.” 

We have to be aware of the balance between teaching the student & math

Productive Struggle

Check out this episode all about productive struggle & the research that supports it!

Reflecting on what you’re paying attention to when there’s productive struggle. 

Teachers Ask:
“What do you do when they’re getting it all wrong during productive struggle?”
– Pay attention to the student & if they’re showing you with their body language that they’re still productive let them keep going 

Productive Struggle in a Thinking Classroom: 

• Challenge doesn’t equal productive struggle 
• Meet challenge on the heels of success they are more willing to productively struggle 
• Quick wins = success and then they are willing to be challenged 

Confidence & self efficacy is build through those quick wins and allow students to struggle

What Do We Do Tomorrow?

1. Do self reflection. Where are you right now? You might not be ready for consolidation. Establish routines for yourself & your students first. 
2. Do I have a convergent or divergent task?
   1. Divergent- capture different ways of thinking for a gallery walk. In 5 minutes, look at three boards. Keep it simple! 
   2. Convergent- have a sequence of tasks that get harder. Floor- middle- ceiling & ask students to put the tasks in order. Let them stand & you scribe. 

**don’t over think it 

Lightbulb moments happen during consolidation. “Never Skip the Debrief”… but realize you won’t always hit a home run! 

Be sure to stop along YOUR journey to reflect and acknowledge the successes you are experience in your classroom and celebrate that! Reflect on the opportunities you’re giving your students to think in math is such a gift.

Other Related Episodes:

Interview with Peg Smith, Author of 5 Practices Listen Here

3 Common Mistakes when Trying Something New in Math Class Listen Here

Mentioned in this Episode

 Building Thinking Classrooms
 Modify your Building Thinking Classroom

Have Questions? My DMs on IG are always open@hellomonamath

The post 96: Peter Liljedahl – Building Thick Understanding in Consolidation appeared first on Mona Math.

We work tirelessly to ensure our students feel safe to take risks in our math classroom communities.

But to achieve that safety, our students need to be fully seen for who they truly are. By using the words of Black Mathematicians and other diverse math leaders we can empower and inspire our students to feel like they belong in our math classrooms.

In This Episode About Black History Leaders We’ll Chat About:

• who we are teaching
• listening to student conversations
• doing the “get to know you” community building once a year

Month’s to be Aware of: 

Black History Month- February
Asian Pacific American Month- May
Hispanic Heritage Month- Sept 15-Oct 15
Indigenous People’s Month- November
PRIDE- June

Want to Read More on Black History Leaders?

It’s that time again… where we start to honor those underserved populations in certain months. Coming up, Black History Month.

Although, I firmly believe that these months are important in bringing awareness and honor to those people that have been historically under represented and under served in our society… it is my mission that those underserved people are represented fully in our classrooms daily.

The thing is… 

We all have children that come from diverse backgrounds. Representation matters. 

Some of our students don’t interact with people that are different than them regularly, representation matters. 

Why?

Our students need to SEE themselves in our classroom. 

When student see others that look like them, think like them, have a similar living situation they see themselves.

But Why Does That Matter?

Our students need to feel a sense of belonging before they can analyze or synthesize. Higher order thinking skills can’t come until basic needs are met. A basic need of humans is to feel like they belong, like they are safe. 

WE can (and should) create a sense of safety and belonging in many ways. Things like… 

-using math norms 

-developing a growth mindset 

-using reflections 

-forging strong relationships with an among your students 

-teaching students how to collaborate 

Those are all ways we develop a classroom where students feel comfortable. A place where they feel like they can speak and will be listened to. Where they can relax because they know they won’t be judged or made fun of if they make a mistake or share something personal.

Let’s Connect All of This to Math

Often we think this type of thing matters more in subjects like writing or reading when students will be sharing connections to the text or sharing a personal narrative they wrote about an important time in their life. 

However, that’s just not true. We are ALL teachers of children, not curriculum or standards. 

Our society needs people who are emotionally intelligent, confident, and relatable. That happens through teaching the whole child…. Seeing them for who they are and honoring them for their uniqueness. 

That Brings Me To Another Point…

This is not about showing students who we want them to be, but instead SEEING them for who they are. The unique elements (good, bad, and quirky) of their identity. Yes, of course we have role models and people we want our students to aspire to be like… but this post is not about that. This post is about creating a space/classroom where students are honored for who they are.

How Can We Do That?

Sharing inspiring words and work of those that have come before us. I do this every day in my middle school classroom. We always start with a quote. It is such a quick and easy do-now that takes 5 minutes and really pays off in setting the tone for our work that day. 

I really love using mathematicians!
WHY? Because mathematicians don’t get talked about enough. In fact, I bet your students couldn’t even name a mathematician if you asked them to. So, I say… let’s change that! 

I like using quotes to start our math class from mathematicians that may or may not look like my students. People of various backgrounds, ages, and walks of life– as a way to show my students the possibilities for their own future. A way to show them the obstacles these people faced, the strategies they used to overcome them and what they accomplished. 

3 Reasons Not to Save Talking About Black History Leaders for February

1. The time is NOW to create a sense of belonging and safety
2. Representation matters
3. The possibilities are endless

Related Blog Posts:

Black History Figures Inspire Math Classes (on MiddleWeb.com

Black History Leaders that Empower Students (BLOG POST)

Black History Month People (BLOG POST) 

3 Ways to Use Black History Quotes in Your Class

Related Resources:

Math Affirmations 

Math Classroom Norms 

Classroom Community Resource Bundle 

Math Stories Autobiography Writing Project

Mentioned in the Episode on Black History Leaders: 

 Guide to Engaging Math Discussions

 Mathematician Posters 

Fun fact!! I live in Chicago, right next to the train. You’ll hear it a few times in the recording

Have Questions? My DMs on IG are always open @hellomonamath

The post 95: How Black History Leaders Can Help Our Students Feel Seen appeared first on Mona Math.

Are you ready to start 2024 as the year to bring THINKING and sense making to your math classroom? Building a community is essential for building thinking classrooms. Let’s discuss the 3 mistakes I want you to avoid in 2024 as you build your math community.

In This Episode about Building Your Math Community:

• who we are teaching
• listening to student conversations
• doing the “get to know you” community building once a year

Why You Should Focus on Building Your Math Community:

Building a community is essential for building thinking classrooms. Last week we heard from Peter Lijedhal about consolidating, however that is a very advanced strategy. Peter himself said he thinks it is the hardest practice in the book. So, you might not be there yet… that’s okay because you can always go back to episode 93!

I think the first thing, and constant things we should do in our classroom is build community. A math community is special, it’s different than other parts of our classroom community. As elementary teachers that teach all subjects we have to build a community of readers, and community of writers, but also foster inquiry in our scientists and mathematicians and social scientists… it’s a lot to think about how each part of our day requires a bit of a different set of norms. However, considering what makes a mathematician and getting to know your mathematicians is at the heart of building a community.

3 Mistakes to Avoid in 2024:

1. Don’t Forget You Are Teaching Humans

Humans, our little human students, have SO many experiences that have shaped them into the little souls sitting in front of you each day. What I mean by that is… they know WAY more than you’ve ever taught them. In most cases, they already know what you’re teaching them. We often forget that our students are noticing groupings and skip counting at early ages, that they deeply understand fairness and equal sharing, and they’ve watched and helped their families solve complex problems. The list go on and on of the experiences our students have had as whole humans outside of our classrooms and textbooks. So, in 2024 let’s not forget about those experiences, but let’s USE those experiences and empower our students to bring those experiences to their work in our classroom. 

Your curriculum does a good job of incorporating culturally diverse names and situations, which is great. But what’s better is talking with your students about their experiences and letting them bring their expertise to the problem solving table. You can do that by opening up your math tasks– stop requiring students to solve in certain ways dictated by your curriculum and ask them to solve in their ways. 

2. Don’t Miss Out On Listening In To Student Conversations

One of the BEST things we ask our students to do in math class is to describe their thinking. The curriculums I coach teachers around have it embedded– turn and talks, share with your partner, YAY! However, a mistake I often see made is using this time to look ahead in the lesson plan or advance the slides or write the problem on the board that will be discussed next. I urge you not to do that and instead lean in. Student conversations with peers are PURE GOLD.

As you heard me say in last weeks’ episode with Peter and I say almost daily in my classroom is… “I’m mining your brain.” I find out what students truly understand by listening to them… not just when they are talking to me or the class and answer a question. I listen to every conversation. I want to hear how they talk to their peers when they describe their math thinking.

Have you witnessed this…

You ask students to share their thinking with the class in the math discussion and the student gives you what feels like “the right explanation” even though you KNOW they didn’t do it that way or you’re not convinced they actually believe it… their response feels like teacher pleasing. That’s because it probably is. The best way we can prove to our students that we want their messy, in-progress thinking to be shared is to normalize it, celebrate it, and pull it out of them. I LOVE getting my students to explain their thinking when they are confused… It’s when I see the most “I agree” signals from others and the conversation takes off because students all of a sudden realize they too aren’t alone in being unclear. It breaks down the walls and lets the group truly work through their reasoning.

So, how do we get students to be vulnerable and share their true reasoning, even if it’s messy, and stop the teacher pleasing with their responses? Here’s the tip…. Listen to their conversations. Try not to talk, just listen. If you do talk, say something like, “Ooo! Share that. Just like how you said it during the discussion. Keep going.” then walk away.

3. Doing the “Get To Know You” Community Building Once a Year

Don’t make this mistake, friend. I know we’ve all heard it and this has to happen throughout the year… However, making time for it is difficult, I know. I’m not advocating for you to do the same activities you did in August now, in January. Instead, I think our activities should mature and evolve just as the year does. You can do things with your class now you could NEVER have done in August. So, now is the time to push them with a harder group initiative or a juicer question to share about. You’ve built trust with them and among them, so now is the time to use that trust to push and dig a little deeper in those relationships. 

I’m a huge fan of giving the math survey or this math trauma survey multiple times a year to track progress and see how students’ mindsets are shifting about math.

This will give you some really interesting data to discuss with students, your colleagues, math coach, or leadership.

Calling All Math Coaches

If you’re a math coach I want to tell you that starting today registration is open for the Math Coach Huddle– a unique group of math coaches coming together virtually each month to collaborate and learn with each other & myself.

We will have a training, feedback protocols and time for collaboration around specific topics all tailored for math coaches. I

know how alone it can feel sitting in your office planning for another observation, grade level meeting or PD without a thought partner. That’s why I created this group– the group I wish I had at the start of my math coach journey.

You can check out all the details here.

I hope to see you inside the Huddle and work closely with you in 2024. 

Teacher Friends, I’m Not Forgetting About You!

Don’t worry if you’re feeling a bit of FOMO, tons of great stuff coming your way in 2024! In the meantime, if you haven’t checked out my BEST strategy for getting every learner engaging with word problems (even if they’re below or can’t read) then you MUST go check it out now…. you can do that here.

It’s 2 quick video trainings for $27 and I promise you’ll see a boost in students’ engagement in problem solving and feeling more empowered. 

Mentioned in this episode on Building Your Math Community:

Ep 93: Building Thinking Classrooms Professional Development with Peter Liljedahl

  Math Survey

 Math Coach Huddle

Training: Every Student Access to Word Problems

Go to my instagram @hellomonamath & share with me how you’re listening!

Have Questions?

My DMs on IG are always open @hellomonamath

The post 94: 3 Mistakes to Avoid in 2024 in Building Your Math Community appeared first on Mona Math.

On Today’s Episode about Strategies for Consolidation:

• Consolidation
• Being a curator
• Learning with your students

Meet Peter Lilijedahl, Author of Building Thinking Classrooms

Peter Liljedahl is an educator and researcher known for his significant contributions to the field of mathematics education, particularly in the development of “Building Thinking Classrooms.” With a passion for fostering deep mathematical thinking and problem-solving skills, Peter Liljedahl has dedicated his career to reshaping classroom environments. His work emphasizes collaborative learning, problem-solving, and student engagement, leading to more effective and meaningful mathematics education experiences. Through his innovative teaching methods and research, Peter Liljedahl continues to inspire educators worldwide to create dynamic and thought-provoking learning spaces.

What is Consolidation?

• Depends on the task 
• Rich task→ exploring and inquiry based thing…vs. Thin slicing sequence → looking for patterns 
• Rich tasks→ divergent tasks
  • Many different ways to solve 
  • Gallery Walk→ Select things students have done at the board, sequence the ideas (easy to hard, common to uncommon, concrete to abstract)
    • Teacher creates a narrative

Why is Consolidation Important?

• They are in thinking creation space 
• Informal ideas 
• These ideas will float away if they are not formalized 
• Why Consolidation: “Our effort to help students turn chaos into order, organize, structure, formalize their thoughts.” 
• Pull on their sense making – tentative knowledge.
  • We’re not lecturing and giving them OUR understanding and ideas. 
  • We’re helping them finish the sense making process

2 Rules:

1. We don’t do all of the steps for 1,2,3. We go with the first step. They are seeing how the steps are the same for all
2. Never finish any of the tasks. It leaves their brains a bit itchy- they want to solve it. Focus on the process but we always get to the answer.

Today’s Key Take Aways

• Use the students work to tell the story – you are the tour guide
• Don’t have students from the group present their own work – have someone from outside of the group explain what they did
• Use students’ conjectures to build the story
• Sheep dogging→ pressuring students into doing it the way the teacher understands
• When students diverge→ become a learner from the students
• We’re all in this thinking thing together. 
• Mine your brain.
• Knowing the math gives you the confidence to improvise as needed. Use the skills to interpret what the students are doing.
• We don’t always have the knowledge necessary
• Students bring things into the classroom from their multi-cultural world that we’ve not encountered
• Routine→ This allows students to practice this everyday. Students who aren’t ready, can observe today and can then jump in the next day.

Links Mentioned in this Episode:

Peter’s website: https://www.peterliljedahl.com/
Facebook Group – Building Thinking Classrooms
 Building a Thinking Classroom in Math (Article on Edutopia by Peter)

 Building Thinking Classrooms
 Modify your Building Thinking Classroom

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The post 93: Peter Liljedahl: Two Strategies for Consolidation appeared first on Mona Math.