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 

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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