What is Standards for Mathematical Practice (SMP) #6 Math Precision as it relates to math proficiency? On this mini math chat we will break it all down!

We are chatting (quickly) about: 

• What is SMP #6 Math Precision
• Questions to ask your students to promote SMP #6(You’ll wanna write these down!) 
• Ways to integrate SMP #6 into Word Problem Workshop!

Need a refresher on What are the standards for mathematical practice common core?

  Go listen to episode #47 now! 

For the next several weeks we will be doing a mini series (every Wednesday) on one of the Standards for Mathematical Practice. Be sure to come back each Wednesday! 

In these Mini Math Chats you can expect quick & actionable episodes full of ideas to implement in your classroom today. 

Want to know more about how to help your students achieve Math Proficiency everyday in math class? Grab my guide to engaging math discussions here MonaMath.com/discussions

Leave a review! 

Do you enjoy Honest Math Chat? I’d LOVE your feedback! Leave a quick review!

Bring Student Centered Math to your Classroom!

Check out the Student Centered Math Classroom Guide below

The post Mini Math Chat: SMP #6 Math Precision appeared first on Mona Math.

Concrete models in math can help your students develop a deep understanding of math for years to come. Don’t underestimate the power of concrete models in math. 

In this episode we’re chatting about how concrete models in math can help build your students’ math intuition.

In this episode you will chat about: 

• the meaning of math intuition 
• how manipulatives can encourage math intuition 
• 4 ways to support students with using concrete models in math

Links Mentioned in the Episode:  

Guide to Engaging Math Discussions

Books I love & mentioned often: 

Adding it Up https://amzn.to/3FzM4as 

Children’s Mathematics Cognitively Guided Instruction  https://amzn.to/3FzLMQU 

Principles to Action: Ensuring Mathematical Success for All https://amzn.to/42o816h 

5 Practices for Orchestrating Math Discussions https://amzn.to/3zagEEl 

Leave a Review!

If you love listening to Honest Math Chat, please take a few seconds to leave a review so other teachers know this is a valuable place to spend a few minutes each week. 

Want to Read More About Concrete Models in Math?

What role do manipulatives play in your students’ math experience?

I know that many of our curriculums come with a set of manipulatives. Then, if you’re anything like me, we put them into our favorite colorful bins and add a cute label. Display them on a bookshelf and it looks inviting. However, most of the time I didn’t disturb them. If the lesson asked for rulers or the use of pattern blocks I just kinda skipped over that part… thinking about how it would be a management nightmare. And really, how much are they really going to even help my students? 

Somewhere in the back of our minds… we know that’s not accurate and it probably is worth the time, but we just have so many things to cover before the end of the year and we know that manipulatives are going to slow us down. 

What are concrete manipulatives? 

They are math “tools” that help students solve by representing their thinking or manipulating the math. 

Quote: “Intuitive experiences must be acquired by the student through his/her own activities- they cannot be learned through verbal instruction” -Erich Wittman “The Complementary Roles of Intuitive and Reflective Thinking Mathematics Teaching” 

So what this quote is saying is to build intuition with mathematics a student must do the thinking, reasoning, and experiencing themselves. That we can’t just tell them- i do (you watch) we do it (together walking through the steps) now you try it doesn’t work. We can’t take the opportunity away from our students to actually gain intuition.

Does that make you feel uncomfortable? For me it does because that means the entire (and I mean every single math class I took) was teaching me wrong. But it makes sense, because I really started to learn math… intuitively when I started to play around with it IN FRONT OF MY STUDENTS. 

So what is math intuition anyways? It definitely isn’t a gene or a way you were born. Math is not innate or natural to some more than others. But it is “that having a feel for math” that comes from experience and practice.

“Burton 1999 says, ” My intuitions are based on my knowledge and my experiences. The more I have, the more robust my intuitions are likely to be.” 

That means as teachers we can help our students DEVELOP math intuition. 

So how do manipulatives come into play with math intuition? 

Mathematician Reuben Hersh argued that manipulating objects, symbols, and representation and mental images is HOW we develop math intuition. He said, “intuition is the effect in the mind of manipulating concrete objections- at a later stage, of making marks on paper, and still later, manipulative mental images. This experience leaves a trace, an effect, in the mind. That trace of manipulative experience is your representation of the natural numbers. We have intuition because we have mental representations of mathematical objects. We acquire those representations, not mainly by memorizing formulas, but by repeated experiences. (Hersh 1997) 

This experience leaves a trace in the mind. WOW! So that means we have to be thoughtful about the experiences we give our students with manipulatives in order to help them build math intuition. 

How can you support students with concrete models? 

So how can you support your students with concrete models while also not going crazy with managing their behavior and it taking WAY too much time. Let’s talk about 4 key things to do with manipulatives to make them meaningful. 

1. Build a culture of mathematics. One where students feel safe to take risks, make mistakes, and tinker with math. But how does this relate to manipulatives? I believe it is the basis for everything. Our classroom culture is our foundation. So therefore we have to start there. Ensuring every single student FEELS like a mathematician. 
2. Expectations are high. I mean this for all parts of math. Meaning you expect students to use the manipulatives as a TOOL not toy. Meaning tey will use those math tools to solve problems, represent their thinking and explain and justify that thinking to their peers. THe expectations are that we all do math here because we are all mathematicians. And that extends to the manipulatives. 
3. Make it normal to use manipulatives. When I taught 6th grade and we were learning about angles and finding the area of triangles, a manipulative we used often was tracing paper. Now, if I kept the tracing paper on the shelf in the corner of the room… NO ONE would get up to get the tracing paper they needed to solve the problems. A few might ask me to get it for them. You know… fear of embarrassment of walking across the room to get something that might be perceived as whatever it was perceived as… you know 6th graders– draw NO attention to myself kinda vibe?
   When I kept the tracing paper cut into smaller rectangles in small bins on their tables every single day… students used it, helped each other and it became a tool we referred to consistently in our discussions.
   And not to mention it really helped students understand the formula for finding the area of a triangle. 

So create the classroom where every single day there is a choice of manipulatives. Think about creating bins of manipulatives to live right on students’ tables. They can go get them at math time and are welcome to use them at any time during math. When it is every once in a while we use manipulatives that feel different, when it’s normal, routine… students are more likely to incorporate that into the way they “do math” 

4. Highlight the use of manipulatives. Watch and listen to your students as their model their thinking with manipulatives. You’ll see that students OFTEN use manipulatives in ways you weren’t expecting. This is important to note. You should also ask students to describe their thinking to their peers. Giving students ample time for focused, academically productive discussions helps move their math understanding. Remember our initial quote from Erich Wittman…  “Intuitive experiences must be acquired by the student through his/her own activities- they cannot be learned through verbal instruction” You can tell them all you want on HOW to use the manipulative to help them understand… but until they do it, watch the person sitting next to them do it or even see it demonstrated by their crush under the elmo (haha sorry still in middle school teacher life) they won’t get it. Give your students opportunities to experience and share those experiences, then respond to those experiences of others in the math discussion. 

So let’s review… 

Manipulatives are the way we can support our students in building their math intuition through experiences. Manipulating those concrete objects helps students later make connections to visual and symbolic representations. 
First build a strong culture of mathematics in your classroom where students are comfortable taking risks and explaining their mistakes. Then, set high expectations– for problem solving & the use of manipulatives. Also, You’ll want to make this a normal situation in your class– one that uses manipulatives everyday to build that math intuition. Finally, SHOW students how you see manipulatives being used around the classroom. Better yet amplify th invoices of your students by having THEM share how they are using the manipulatives. 

Your Guide to Engaging Math Discussions

The post 51: Concrete Models in Math & How they Build Math Intuition appeared first on Mona Math.

What is Standards for Mathematics Practice (SMP) #5 as it relates to math proficiency? On this mini math chat we will break it all down!

We are chatting (quickly) about:

• What is SMP #5 Math Tools 
• Questions to ask your students to promote SMP #5(You’ll wanna write these down!) 
• Ways to integrate Math Tools, SMP #5 into Word Problem Workshop!

Need a refresher on What are the standards for mathematics practice common core?

Go listen to episode #47 now! 

For the next several weeks we will be doing a mini series (every Wednesdsay) on one of the Standards for Mathematical Practice. Be sure to come back each Wednesday! 

In these Mini Math Chats you can expect quick & actionable episodes full of ideas to implement in your classroom today. 

Want to know more about how to help your students achieve Math Proficiency everyday in math class? Grab my guide to engaging math discussions here MonaMath.com/discussions

Leave a review! Do you enjoy Honest Math Chat? I’d LOVE your feedback! Leave a quick review!

Bring engaging conversations about math to your classroom! 

Check out the guide to engaging math discussions below

The post Mini: SMP #5 Math Tools appeared first on Mona Math.

What is a base 10? Have you ever really sat down and thought about what is a base 10? We’re breaking it down and chatting about how we can use base 10 with our students! 

In this episode we’re chatting about what is a base 10 & the implications for our own instruction:

In this episode you will chat about: 

• the meaning of base 10 
• why it matters 
• how you can support students in their base 10 development 

Links Mentioned in the Episode: 

Guide to Engaging Math Discussions

Books I love & mentioned often: 

Adding it Up https://amzn.to/3FzM4as 

Children’s Mathematics Cognitively Guided Instruction  https://amzn.to/3FzLMQU 

Principles to Action: Ensuring Mathematical Success for All https://amzn.to/42o816h 

5 Practices for Orchestarting Math Discusions https://amzn.to/3zagEEl 

Leave a review!! 

If you love listening to Honest Math Chat, please take a few seconds to leave a review so other teachers know this is a valuable place to spend a few minutes each week. 

Interested in Reading More? Read on about Base 10!

The first time I heard about “base 10” was in college. I had a great math methods teacher that made us grapple and discuss and push ourselves… Unfortunately the methods didn’t really stick with me as I went into the classroom. I actually probably needed WAY more time.

I was recently talking to a literacy coach and she shared with me some research about teacher professional development. Which in turn, sent me down a rabbit hole of research.

 I found a review of 1,300 studies done on professional developments’ effect on student achievement. What it found was… , “Studies that had more than 14 hours of professional development showed a positive and significant effect on student achievement from professional development. The three studies that involved the least amount of professional development (5–14 hours total) showed no statistically significant effects on student achievement.” 

7 Collectively, the studies that Yoon et al. (2007) reviewed suggested that the duration or “dosage” of PD may be related to impact. The average number of contact hours was about 48 hours across the nine studies, The six studies provided more intensive PD, with contact hours ranging from 30 to more than 100. With the exception of one study with 83 contact hours, all the studies with 30 or more hours of PD resulted in significant effects on student achievement

So, maybe if I had more professional development in my early years of teaching on math instruction or more than a 3 credit hour class on the topic I would have started my career teaching gin a different way 

What is base 10? 

A place value system– assigns a value to each place in a number. 

Guide to Student Centered Math

What is Standards for Mathematical Practice (SMP) #4 as it relates to math proficiency? On this mini math chat we will break it all down!

We are chatting (quickly) about: 

• What is SMP #4 Model with math 
• Questions to ask your students to promote SMP #4 (You’ll wanna write these down!) 
• Ways to integrate SMP #4 into Word Problem Workshop!

Need a refresher on what are the standards for mathematical practice common core? 

Go listen to episode #47 now! 

Looking for more?

For the next several weeks we will be doing a mini series (every Wednesday) on one of the Standards for Mathematical Practice. Be sure to come back each Wednesday! 

In these Mini Math Chats you can expect quick & actionable episodes full of ideas to implement in your classroom today. 

Want to know more about how to help your students achieve Math Proficiency everyday in math class?

Grab my guide to engaging math discussions here MonaMath.com/discussions

Leave a review!

Do you enjoy Honest Math Chat? I’d LOVE your feedback! Leave a quick review!

Bring Student Centered Math to your Classroom!

Check out the Student Centered Math Classroom Guide below.

The post Mini Math Chat: SMP #4 Model with Math appeared first on Mona Math.

What is Standards for Mathematical Practice (SMP) #3 as it relates to math proficiency? On this mini math chat we are breaking down how to construct viable arguments!

We are chatting (quickly) about:

• What is SMP #3
• Questions to ask your students to promote SMP #3 (You’ll wanna write these down!) 
• Ways to integrate SMP #3: Construct Viable Arguments into Word Problem Workshop!

Need a refresher on What are the standards for mathematical practice common core?

 Go listen to episode #47 now! 

For the next several weeks we will be doing a mini series (every Wednesday) on one of the Standards for Mathematical Practice. Be sure to come back each Wednesday! 

In these Mini Math Chats you can expect quick & actionable episodes full of ideas to implement in your classroom today. 

Looking to improve your student’s math proficiency?

Want to know more about how to help your students achieve Math Proficiency everyday in math class? Grab my guide to engaging math discussions here MonaMath.com/discussions

Leave a review! 

Do you enjoy Honest Math Chat? I’d LOVE your feedback! Leave a quick review!

Bring Student Centered Math to your Classroom!

Check out the Student Centered Math Classroom Guide here!

The post Mini: SMP #3 Construct Viable Arguments appeared first on Mona Math.

Kym is a Math Intervention teacher and this conversation is AMAZING! We are covering all the things… math mindset, building math classroom community, engagement strategies, & quality professional development. We’re covering it all with Kym and it’s such a real and relatable conversation. 

Come listen in & chat with us on Instagram! 
Find Kym on Instagram at @yaymath_pcs 

Links Mentioned in the episode: 

• Making Sense of Math Grades 3-5 
• Making Sense of Math for Teaching Grades K-2
• Making Sense of Math for Teaching 6-8

Loved chatting about math intervention and math mindset?

Leave a Review!! I’d be honored if you shared what you love in review form so other educators know this is a worthwhile place to hang out each week.

Ready to build YOUR math community?

Get my 8 best tips to building your math classroom community at monamath.com/community 

Bring engaging conversations about math to your classroom! 

Loved what you heard on this episode about math intervention and math mindset? Level up your math class with engaging math discussion. Check out the guide to engaging math discussions below.

The post Math Intervention and Math Mindset: A teacher interview with Kym appeared first on Mona Math.