Thinking about math is one of my favorite things to do, and today I got to chat with Ann Elise Record about thinking about math. We covered everything from Building Thinking Classrooms, fluency, learning progressions… and ALL the things!! 

In this episode we will chat about: 

• Building Thinking Classrooms with HIGH expectations for all students 
• Permission to teach a different way! 
• Learning Progressions in math & how to support students thinking about math
• Subtraction strategies with real math examples

You’ll hear Ann Elise & I thinking about math and wondering about how we can get EVERY child & teacher thinking about math. 

Connect with Ann Elise Record: 

• https://www.anneliserecord.com/ 
• Instagram: @ann.e.record
• Padlets mentioned can be found here

Bring engaging conversations about math to your classroom! 

Check out the guide to engaging math discussions below

The post 59: Thinking About Math with Ann Elise Record appeared first on Mona Math.

Equity in the classroom is on all of our radar these days, or should be. In today’s episode we’re chatting about math equity in the classroom. We’ll break down how we used to do things and how we can do better. Using books, quotes, and research to ground our work of knowing better and doing better in equity in the classroom. 

Today we’ll chat about: 

• 3 things we used to do, and how we can do better
• ways to engage every student & hold high expectations 
• book recommendations to continue the work 

Links & Books Mentioned in the Episode: 

Choosing to See, Pamela Seda

 Taking Action Grades K-5 NCTM Book

 Taking Action Grades 6-8 NCTM Book 

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. 

Want to read more about equity in math?

The power a teacher holds to help their students develop a positive math identity is huge. As the instructional leader in your classroom the way you present mathematics, grant access to mathematical situations, and position math challenges can impact your students’ math identity.

Equity is a word we’ve heard a lot in the past few years… and I’m not tired of it… because we’re just getting started. 

For way too long our classrooms, especially our math classrooms, have been places that reserved the challenge and complex thinking for the few that excelled at math. 

For too long our math classrooms have been about getting through the activities in the lessons and completing the problems instead of about understanding our students’ thinking and capitalizing on their strengths. 

For too long our math classrooms have supported the status quo… not making waves in what society has always told us, math has one answer and certain genders and races are just better at it. We’ve accepted that stereotype as our truth, our destiny. 

For too long we’ve looked at our students’ parents and forgiven them for not knowing how to help their student or the new math, without a second look at the valuable math experiences they hold. 

Holy shit teacher friends it’s TIME for more equity talk. We are just getting started. So, although you may be tired of hearing, I hope you’ll stick with me on this podcast and listen because I think you know, as much as I do, how important this work is.

Driscoll and his colleagues in 2016 wrote about equity in math saying… equity is giving access “to each learner with alternative ways to achieve, no matter the obstacles they face” and believing in each learner’s potential “to do challenging math reasoning and problem solving” 

So, what does that mean for us at this moment on this podcast? I think today’s conversation needs to break down what we’ve been doing, why we can’t do things that way anymore and what we can do instead.

Let’s pause to say equity work is often hard. Emotions come up. Be mindful of them and don’t avoid them. As Elana Aguilar (author of Coaching for Equity) says about when emotions come up in equity work, “I greet them. I’m getting curious & finding out that emotions are not that scary and that I can access them in a way that gives me strength, courage, and power.  There’s enough space in my mind, heart, and life for feelings, and there’s no way to avoid them if I want to build equitable schools.”

So let’s start identifying some of the things we’ve done and how we can do better…. 

• Reserving the challenge & the complex thinking. Sometimes we reserve it for the early finishers or the “high group”. Sometimes we say our remedial group just isn’t ready for that work or we give them a different (easier) version of the work.
  • Why is this a problem? Because all children have the right to participate in all the parts of our math lesson… including being challenged and supported. I believe teachers are doing this because they truly care about helping our students be successful… but what happens when we don’t allow our students to be challenged or think in complex ways because we’re not sure they’re ready and we’re afraid they’ll fail or struggle too much… What happens is they miss that opportunity. Their work gets simplified and time and time again they miss those opportunities to do complex thinking. And then, over time we realize our students aren’t achieving because they aren’t being taught the material that can help them achieve. 
  • We have to stop coming to our math learners with a deficit mindset. We have to see each child as having the potential to do the challenging, complex work of mathematics. We have to create learning spaces and instructional opportunities for every single child to participate in problem solving and developing math reasoning.
    • The best way I know how? Problem solving every day in Word Problem Workshop. One worthy, complex math task– time to launch & understand the problem, time to grapple with it independently, time to discuss it collaboratively. 
• Our instructional strategies are set up in centers or lessons with a focus on completing the problems, and filling the holes… we miss the opportunity to see our students’ thinking and see what they DO know.
  • Why is this a problem? When we maintain a traditional sense of success in the math classroom we are missing out on the important shift that has taken place in math research and instruction over the last 25 years. Effective math teaching calls for us to implement tasks that promote reasoning and problem solving, to facilitate meaningful mathematical discourse, to use and connect mathematical presentations, and support productive struggle of mathematics.
    Instead, when our class focuses on correct, fast, sit and fill in, do as I say we miss the opportunity to leverage our students’ mathematical strengths as a place to start our conversation. 
  • We have to see our students as mathematicians. Promoting participation and engagement in lessons in all sorts of ways. We have to show our students we believe they have good ideas and their ideas have a place in our math classroom… even if those ideas are different. We have to start looking for our students’ strengths and using them in our lessons as a starting place for new learning.
    • The best way I know how? Get to know your students’ thinking through truly listening. See their brilliance as it is, listen to their voice, look at their work, watch them work. 

• Why are we talking about equity so much in schools? Because for too long we’ve just accepted the stereotypes as fact. Math isn’t for everyone. Boys are better at math and science. Oh of course the asian kids are in the advanced class. These types of comments and beliefs have to end and it’s our job to disrupt them. We must disrupt the stereotypes of math, culture, family, gender that are present in our schools.
  • Why is this a problem? I think it’s obvious, but in case it’s not. Math intuition and math ability is not connected to genes, ancestry, race or ethnicity, or gender. Everyone is able to do math. And as professionals we have to not only believe that about our students, but also about ourselves, our colleagues and our students’ families. 
  • Our students’ families and our students’ background and experiences are valuable assets in the math classroom. We have to use these experiences to help our students see that math plays a big role in their lives, now and in the future. Our elementary students come to school full of life experiences– splitting sandwiches with their siblings fairly, counting, stacking, noticing, wondering, classifying… all before they step foot into our school.
  • As teachers we can either harness that wonder and excitement for math or we can spoil it. When fear and anxiety of getting the answers right or solving it the right way take over that confidence is gone. Through ambitious and effective math teaching practices we can help our students develop and continue to build positive math identity. 
  • The best way I know how to do this? Actively build a positive math culture in your school. Talk to your students about their math identity. Stay vigilant on how students talk about themselves as a mathematician. Find every little moment to work in a comment to promote their positive math identity. 

This is a topic I’m so passionate about because I’ve seen the power it has over students. From the 3rd grader I had who was years behind at the beginning of the year, but an expert arguer. Through our daily math discussions that often turned to arguments he blossomed in math. He looked forward to it, trying out new strategies only to come to the carpet to explain how he solved it. He used to cry when redirected, pouting and yelling…. To let me question him during grapple time… pushing and pushing him to clarify his argument and think deeper about math. He grew as a person, a math person. At the end of the year he exceeded his growth goal on the NWEA Map test and reached attainment for 3rd grade. What that taught him, and I was that effective teaching practices work, but most importantly we’re all math people and we all have something valuable to give. 

If you want more information on equity in math I suggest you check out Pamela Seda’s book Choosing to See: Af framework for equity in the math classroom. It is phenomenal  https://amzn.to/3MpjLjz 

 Also, in the book from NCTM called “Taking Action: Implementing Effective Math Teaching Practices” the authors offer 5 equity based practices to support math learning. https://amzn.to/3ZG7mul 

They are: 

1. Go deep with mathematics 
2. Leverage multiple mathematical competencies 
3. Affirm mathematics learning identities 
4. Challenge spaces of marginality 
5. Draw on multiple resources of knowledge 

As always, my DMs are open on Instagram. I love connecting with you each week about the podcast. Please hop over to instagram as you finish and tell me what’s resonating with you. What question are you left with or where are you hoping for more clarity. I’d love to chat.

Your Guide to Student Centered Math

The post 58: Math Equity in the Classroom appeared first on Mona Math.

Social Emotional Learning in Math is important all year long. In this interview with Caitie we’re chatting about how to incorporate SEL in mathematics. Caitie shares ideas and strategies for incorporating social emotional learning in math class without extra effort or planning. 

In this episode we’re chatting about: 

• Math Status – Smarter Together 
• What you can do to help students take risks & participate fully in math class
• CASEL competencies and how they relate to SEL in Mathematics 

Caitie is now supporting teacher business owners with strategy, systems & online marketing! Be sure to check out what she has to offer on IG @Caitiecupplescreative

Links Mentioned in the Episode: 

CASEL & Standards for Mathematical Practice Article 

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 

Bring Student Centered Math to your Classroom!

Check out the guide to student centered math classrooms below

The post 57: SEL in Mathematics an Interview with Caitie Cupples appeared first on Mona Math.

Are you looking for activities for fact fluency assessment & learning? This is the episode for you. We’ll chat about how activities for fluency can improve students flexibility and accuracy with math facts. 

In this episode we’ll chat about: 

• a clear definition of what fluency is in the classroom 
• how to build fact fluency without tests & worksheets
• activities for fluency that actually work 

Check out episode 39 Math Talks https://monamath.com/podcast/39/ 

Math Fluency Materials on TPT 

Visit my Instagram @HelloMonaMath for pictures & in real life examples of fluency in action 

Want to read more about Fact Fluency?

Do you know all your facts?
No seriously, if I started saying facts do you know them all? You probably do because you’re a great math teacher… me on the other hand. The answer is kinda. I have strategies that I could figure them out, but I never really moved on from the counting strategy for many of my multiplication and division facts. Yikes!

At some point we want our students to commit their facts to memory. After repeated practice with models and strategies to help them understand and see, we want our students to just know that 4×5 is 20 or harder that 6×8 (this is one I don’t automatically know, embarrassing… but this is why it’s SO important) its 48. 6×8 is 48 

However, we don’t want rote memorization for the sake of memorization. This is not an episode accuracy and speed. I don’t suggest those as the main focus of your students fluency. Instead. Let’s define fluency… 

Based on the work of MANY smart people… we know that fluency is flexible, efficient, and accurate. Much more than get the answer fast. So, how can we help our students develop flexibility in their fact knowledge, while also being efficient and accurate.

The thing is, we can’t just make this happen for students. It develops over time just like learning to read and write. Our students will learn a bit each day or week. They will understand the associative property and learn a whole set of facts! But that might not happen until they’ve had lots and lots of exposure to models and math discussions of those models. Then, one day they will start to use it in their own solving and see it works efficiently and is accurate… and then they will add it to their tool belt for the future.

I don’t want you to think that just because students practice flash cards over and over again that’s enough. It’s not. Students have to work out the strategies to understand how the numbers go together or are broken apart to understand the fact before they can commit it to memory or get the answer efficiently. 

NCTM Principles and Standards for School Mathematics states, “Computational fluency refers to having efficient and accurate methods for computing. Students exhibit computational fluency when they demonstrate flexibility in the computational methods they choose, understand and can explain these methods, and produce accurate answers efficiently.

That means students need to have methods to compute… they don’t have to have their facts memorized. We want them to be flexible in choosing a method that will get them the answer more efficiently. Most importantly, we want students to be able to explain their method. When you can describe something then you actually know it. If you’re just doing it because you memorized it or following steps you were told to do, then you don’t know it… you know the steps.

Here’s an example: Inside of my curriculum workbook were a few review addition and subtraction facts at the start of the unit. I asked students to do them and watched as they solved. One 3rd grader starting using her fingers to solve 8+9. I asked, “What do you know that could help you?” She looked up at me and said… “Oh! I gotta make a ten” It’s 17. I took one from the 8 and made a ten. That was way easier. This example shows exactly what we want our students to do– solve efficiently, flexibly use strategies to get accurate answers. However, she needed a prompt and nudge. She doesn’t need a sheet of practice problems on the +9 facts. Instead, she needs more opportunities to explain her thinking, apply it and describe HOW her strategy is efficient. Maybe even critique the reasoning of her peers. 

But how do you do this in the classroom? 

• Use number talks (episode from Jan 30th, I’ll link it below) https://podcasts.apple.com/us/podcast/39-lets-talk-math-talks/id1594635190?i=1000597253445 
• Give students time to discuss their strategy, consider other strategies and critique ther reasoning of others. Keep the conversation focused on strategies and efficiency. 
• Use models and manipulatives to help students “see the facts”. In order for students to move to symbolic representations they must have experience manipulating and drawing. Make time for this. 
• Avoid pages of fact practice… it creates anxiety and pressure around learning facts and puts the emphasis on accuracy and loses the flexibility and efficiency piece 

In my classroom… 

I help students own their math learning of facts and fluency. We have individual practice time each day where students use a computer program like math fact lab or reflex math. We also have several different ways to practice facts (worksheets, brochures, games).
Students “opt in” to a test when they are ready. So, students will say I know all my 6 facts for multiplication. I’m ready for a test. The test I give them has 10 or less questions. A few with a model that they write a number sentence to match. 6 to 8 multiplication facts to answer. Multiples to record. Word problems to write a number sentence to match. A number sentence that they write a word problem to match.

Is this testing a bit more than their fluency, yes. However, this gives me a more holistic view of what they know and can do in terms of flexibility, efficiency and accuracy. 

Once they take it I return it to them with feedback– mostly just a quick conference ont their strengths and what they need to work on. If they pass they get a “medal” that has the fact family on it… the “6s’ ‘ medal. They absolutely love this little recognition and can collect all their medals until they finish all the facts and get an actual metal metal!

If you want to check out what these assessments look like check out my instagram stories where I’ll be posting an image of them. I’ll also put a link to the multiplication & division tests, well system in the show notes in case you’re looking for an assessment system for your students. https://www.teacherspayteachers.com/Product/Fluent-in-Math-Multiplication-Division-8055560 

Wrapping up this chat today, let’s remember that fluency means flexibility, accuracy and efficiency. Students won’t achieve that by memorizing answers or steps. Give your students a variety of experiences in math to practice their strategy flexibility. Ensure they use manipulatives or drawings to build their conceptual understanding before they memorize or solidify a fact. Consider creating or using a system where students take the lead on their learning through goal setting, practice, and assessment. 

Your Guide to Engaging Math Discussions

The post 56: Activities for Fluency and More! appeared first on Mona Math.

Did you get into teaching thinking you’d never have a job as a math teacher? That’s the case with many elementary teachers. Job Math Teacher isn’t always on the top of our list.

In this interview we talk with @MsMazuredu about her experience as a math teacher in the intervention setting.

In this episode you will chat about: 

• how Tori came into her position & her math mindset
• what she does to prepare to teach math lessons 
• how being in your space of learning can be an asset when teaching 

Find Tori on Instagram at @MsMazuredu

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.

Bring engaging conversations about math to your classroom! 

Check out the guide to engaging math discussions below

The post 55: Real Teacher Job Math Teacher & Interventionist appeared first on Mona Math.

Planning math lessons doesn’t have to be frustrating or time consuming… AND planning math lessons with your math curriculum no matter the curriculum you use! You’ll want to tune into this episode to find out about how I’m planning math lessons with MY curriculum. Summer PD on this topic, for FREE monamath.com/summerpd

In this episode we’ll chat about: 

• planning math lessons using math curriculum
• how to supplement math curriculum when planning math lessons
• 5 ways to use math curriculum for planning math lessons 

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. 

Want to read more about planning math lessons using your curriculum?

Everyone has a curriculum or some resource provided by the school or district… and everyone has an opinion about it. 

Whether you like all, some, or none of your curriculum doesn’t really have that much effect on your teaching.
Hear me out.

Most curriculums are similar in most ways. 

• The lessons are aligned to standards 
• They cover the same topics at the grade levels 
• Elements are similar– activities, practice problems, homework, online practice

However, your teaching has to do with YOUR choices. YOUR instructional methods.

Your curriculum is what you can use to guide that, but I believe that you can do good teaching with any curriculum you have or don’t have. 

So, I am currently the 3rd grade teacher in a Chicago neighborhood school that uses GoMath. I pretty much like none of this curriculum. I fall into the “likes none” of this curriculum. 

I find it is very heavy handed in helping and guiding students. 

There is little room for flexibility or exploration. 

It leans heavily into teaching strategies step by step and having students practice. 

Also, the layout of the workbook leaves NO room for showing work or writing out their thinking… which leads to an emphasis on the right answer on the line. 

However, I still have a buzzing with excitement, a rigorous and joyous classroom of mathematicians… and I use GoMath.

I use GoMath as my pacing guide, I use the assessments (with some modifications to increase the rigor), and I use the workbooks for practice.

I also supplement with a few things.

-Number sense routines to build flexibility and ultimately fluency 

-Word problem workshop where students problem solve… everyday 

-independent and self paced fact practice 

-strategic re-teaching small groups 

Let’s dive into each of those elements briefly 

1. Number sense routines to build flexibility– I like to use a few things to “warm up” our brains. I use the routines from the book by Jessica Shumway “Number Sense Routines”. https://amzn.to/3ZDqSru 

A few inside that book that are my favorite are counting around the circle and what I call (she calls it something else) Today’s number. 

1. Counting around the circle is a great way to engage every child. You sit in a circle and each child says a number, counting up by a certain interval. So maybe count up by 5 tenths starting at 2. Then, count up by ½ starting at 2. While they count you record the numbers each child says. Then, students notice & wonder looking for patterns. 
2. Today’s number is great for flexibility in making representations of numbers in multiple ways. You give students a number and ask them to make it in as many ways as they can. This is SUCH an easy, no prep warm up. Once they have a few minutes you can do a quick share out in partners or groups and then debrief as a whole class. 

So the way I plan these warm ups is in conjunction with my curriculum. I look at the standards and lessons in the unit and decide what parts of math knowledge or the standards aren’t fully covered or what misconceptions or lacking skills will students have? Then, I choose the numbers and activities to build those skills.

2. Word Problem Workshop– I typically use problems or problem types that align with the curriculum. Sometimes I even pull a really good problem right from the lesson. However, I strategically choose a problem that will achieve the lesson goal. So, when I’m teaching fractions on a number line and equivalent fractions on that number line… I choose a problem that leads students to using number lines and then having a discussion about equivalence. WHen I first started I used the problems right from the curriculum or at the guidance of my math coach. This is where I Had to do the most growing in my own math knowledge. I didn’t want to just keep teaching my students the steps to carry out these different strategies and have them copy what I did. I wanted them to discover it and have the experience of manipulating it… creating their own meaning. We know from research that when students develop their understanding from their own experience it’s more meaningful and lasts. So, I spent a lot of time learning the content through anticipation. Really thinking about all the ways my students might solve and considering the misconceptions or roadblocks they might run into.
   
   Once we have a word problem workshop, most students have experienced the goal of the curriculum’s lesson… then I have them go back and do 3 or 4 problems from the workbook to apply their knowledge.
   
   
3. Independent fact practice. Fact knowledge is essential to upper grade math. Our students need to produce their facts and have efficient strategies. I like to use MathFactLab or Reflex math for students to get a few minutes of ongoing practice throughout the year.
   
4. Re-teaching strategically. I use exit tickets with my students everyday to assess the goal of the lesson/word problem workshop. Depending on how students do over time on these I use that data to pull small groups for a quick re-teaching. I use the book https://amzn.to/40AgWQN Making Sense of Mathematics for Teaching the Small Group by Dixion to structure those groups. 

Your curriculum doesn’t have to be the worst part of your math block. 

You can use your instructional knowledge and skills to bring it to life in both your facilitation and planning 

1. Plan using the curriculum as a guide 
2. Use instructional strategies like math discussions, word problem workshop, exit tickets, strategic grouping, warm ups to help you bring the content to life. Don’t forget to look in your curriculum’s lessons for ideas too. Sometimes on the sidebar of the teacher guide there are some good tips for warm ups or routines 
3. Work on your own math knowledge so that you understand the full trajectory of how students might show up to this particular lesson. Remember, just because we teach it doesn’t mean our students know it. Students are on a learning journey… they might not be ready for this lesson yet, but stay the course and keep giving them opportunities to explore and make meaning, and discuss their reasoning with others. Each day we all get a little bit better. 
4. Seek out support. You’re learning and getting better too! Work with your grade level team to plan for math. Everything’s better together… so talk with your colleagues, ask for your building instructional guide to support your planning. Send me a message! And if you’re in the Chicago area or Midwest let’s talk about having me come to your school to support your work! 
5. Flex on your facilitation. The questions you ask, the way you approach students can make ALL the difference. You get to decide the norms in your math classroom– focus on the process and the thinking. Start now with students you interact with in math today.. by just asking them, “why”. 

Let’s wrap this chat with this final thought. Your curriculum is just ONE part of your math tool box. You have so much to offer your little mathematicians. Don’t get bogged down in having to cover it all or focusing on what lesson and what unit. Focus on what matters most, students being active learners constructing their knowledge through exploration, discussion, and reflection.

Your Guide to Student Centered Math

The post 54: Planning Math Lessons with Math Curriculum appeared first on Mona Math.

What is Standards for Mathematical Practice (SMP) #8 Repeated Math Reasoning 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 #8 Express Repeated Math Reasoning 
• Questions to ask your students to promote SMP #8(You’ll wanna write these down!) 
• Ways to integrate SMP #8 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 #8 Math Reasoning appeared first on Mona Math.

Standard algorithm in math is common. Students are taught this algorithm standard by their parents as a way to help students. However, it often leads to confusion and prevents students from learning! 
Find out more inside this episode all about using an algorithm standard ways aren’t best. 

In this episode we’re chatting about the standard algorithm and what to do instead during elementary years

In this episode you will chat about: 

• why the algorithm standard is not the best way to teach students math 
• what you should be doing instead of the standard algorithm in elementary school
• ways to incorporate other methods 

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. 

Want to read more on the Standard Algorithm?

What’s wrong with the Standard Algorithm? 

Ahh… the hot topic- the standard algorithm. Ha! But you might actually be thinking, what? Why is this a hot topic mona?

I realize that it is a hot topic for me because I have some STRONG feelings about the standard algorithm so I thought I’d share them with you here today. 

First, let’s talk about what I mean when I say the standard algorithm. The standard algorithm is the “way we learned” or the traditional method for solving… for addition and subtraction it means stacking the numbers on top of one another and adding or subtracting vertically, borrowing… you know. 

For multiplication the numbers are also stacked and then remember how you multiply vertically and then diagonally, don’t forget the zero place holder?
Long division is the standard algorithm for division. 

As I described those algorithms, how were you feeling? Do those bring up any memories for you from your childhood math classes? Any struggle or memories of practice problems? 

That’s what it is for me… I still remember the multi digit multiplication practice problems and NEVER remembering how many zeros to put. Then when we added in decimals… I was so confused. However, I remember in 6th grade my teacher would let us sit in the hallway or group our desks together with friends and my friends taught me the steps (better than I learned in class) and once I learned the steps I just FLEW through the homework. I realized early in middle school that these algorithms meant I just had to follow the steps and then it was done. Zero understanding, but that didn’t matter to me. I got it done and got an A 

So, I actually don’t think the standard algorithm is all negative. I think the Standard algorithm has a place in math and sometimes is the most efficient and effective strategy. However, there is a time and a place for the Standard Algorithm and that is where my issue with it comes in. 

TOO often I see parents teaching this algorithm to their students way too early. And I get it. Parents are coming from a good place, they want their child to succeed and they want to help them. I truly believe all parents are doing their best and I know that’s why they show their students the standard algorithm in 1st grade. 

I’ve also seen many teachers do this as well. Teaching the standard algorithm because that’s what they know well and feel confident teaching. Teaching other ways feels like “new math” or just doesn’t make sense. I’ve heard teachers say there are all these strategies and I’ll teach those ways,  but really the best way is the standard algorithm. 

The Standard Algorithm in First or Second Grade

Let’s talk about what happens when a first or second grader learns the standard algorithm. I’m really going to try not to overstate this… 

They completely lose the opportunity to develop number sense and conceptual understanding of base ten.

The goal in first and second grade is to develop an understanding of quantity and how those quantities go together when adding. We want students to develop flexibility in their ability to manipulate numbers. What I mean is we want our students to look at 12+ 9 and see that they could easily make a ten by moving one from the 12 to the 9 to make a 10, then 10 + 11 is 21. OR they could take 8 from the 9 and make 20 with 12 + 8. Then, add the extra left over from the 9 for 21 

We lose this opportunity when we teach students to stack the numbers and add. In the standard algorithm students would write 12 and 9 underneath it. Often, making the mistake on where or what place value they put the 9 in. Then, they would make 11 and have to “carry” the ten over to the tens place. Students often call this a 1, but it’s a ten.

Teachers & parents end up spending  a lot of time teaching the steps of this. Showing students how to line up the numbers in the right place value. Assuming they are teaching them place value because they are showing them on to line up the numbers by their places… justified to the right.

We spend a lot of time talking about bundling the ten and ones into a ten and carrying it over, but students often call it a one. 

What happens? Students end up just learning the steps and mimicking the teacher without real thought being put into what they are doing.
What else happens? Students get STUCK in this strategy. They stop being flexible and start solving every single problem like this.

What if… we opened up our problem solving time and let our young students explore blocks.
What if we gave them a challenge to find 10s in the 12 + 9=
What if instead of teaching the standard algorithm we used strategies and routines that helped our students build this same understanding, but without the steps and the processes. 

Let’s talk about WHEN the standard algorithm makes sense.

I like to think of the SA as another tool in the tool belt of strategies. Sometimes in older graders it’s just not possible to do the math in our heads by flexibly manipulating the numbers. Sometimes it makes sense to write it down. And, for some 3rd graders instead of stacking the numbers to subtract the place values they break it up into expanded form… 

349 – 198= 

300- 100 = 200 

40 – 90 = -50 

140 – 90= 50

9- 8 = 1 

151

However, as students start to understand this place value expanded form strategy better they start to find more efficient and effective ways to record their thinking. That’s when they standard algorithm makes a whole lot of sense 

349

198

____

151

The goals is: 

• Students can flexibly solve problems. Just think about it like this… my mom (shout out if you’re listening mom) can stand in a store and calculate the % off in her head in seconds. She can give you a “that will be about ____” right down to the cent in seriously just a few seconds. That’s the goal. We want our students to be able to use strategies flexibly so they can solve REAL LIFE PROBLEMS without getting out their calculator or a pen/paper to solve. How does that happen? Practice at being flexible. Many strategies. Confidence in knowing what the numbers mean and an understanding of what you’re trying to find. 
• Goal is not to keep the SA from students, but to support students in developing their conceptual understanding.
  

So, as we are thinking about the standard algorithm I want you to ask yourself these questions: 

• Do my students know the steps or know the math 
• Did my students come to this strategy organically because of their own understanding 
• Are there other strategies my students could learn to help them be more flexible 
• Could I give students a bit of time to explore this before I show them a way. 
• What does the student already know about this? Could we start from there? 

In closing… I don’t think there is anything wrong with the standard algorithm. However, I do think it is used too soon and too often with students because of our own insecurity with math. 
As we are planning our math lessons, spend time anticipating all the ways students might solve. This can help you as the teacher feel more confident in letting your students be flexible and explore different strategies, because you’ve already thought of them. Write those strategies down so you can refer to them as you see what your students are doing. 

Resist the urge to teach your students the standard algorithm.
The standard algorithm MIGHT show up in your curriculum. That doesn’t mean you have to teach it.
In the CCSS add/sub, multiplication & division SA doesn’t show up in the standards until 4th grade. Even then, it’s just ONE strategy to solve.
And one final thing… Just because you teach your students the SA and they are able to carry out the steps doesn’t mean they have any more knowledge of math. If they are just following the steps of the algorithm and getting the answers then we’ve shown them what we value is answers, not thinking.

Gosh… I could go on about this FOREVER! I’m going to stop there for today and say.

I know this might push against some of your values and beliefs and be in direct conflict with them… and that’s okay. Change is change. If you’re ready let’s chat about HOW to move away from the SA and into a more flexible place. If you’re not ready or you disagree… that’s okay too!

My DMs are ALWAYS open on IG at HelloMonaMath. Let’s chat about the standard algorithm. Ask me your questions, challenge me, I’m here!

Your Guide to Engaging Math Discussions

The post 53: Standard Algorithm or Inventive, which is best? appeared first on Mona Math.