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### Emphasize the process over the product

For as long as I can remember, math was about finding the right answer. Some people even say that they like math because there is a right answer and a wrong answer. That is changing. With standards that emphasize understanding over rote memorization of procedures and increasing calls for balancing content with process, math instruction is beginning to look different. Students need opportunities to see that while, yes, there might be only one right answer, there are many approaches to solving the problem. Even if the problem is as simple as finding the sum of 6 + 7.

*I know that 6 + 6 equals 12, so 6 + 7 is just one more, or 13.**I decomposed the 6 into 3 and 3. I used one of the 3s with the 7 to make 10, and then added the other 3 for 13.**Seven and seven is 14 and one less is 13.**I put 7 in my head and counted on 6 more using my fingers.*

I recently taught a lesson in a 1st grade classroom, and I knew some kiddos would know the solution as soon as we finished reading the problem. So before I began I made them promise to keep their solutions in their heads because the really “fun” part of the lesson was discussing all the different ways we could solve the problem and how we could communicate our mathematical thinking. Just look at all the wonderful thinking we captured from our discussions!

### Give students think time

Face it, we don’t all process at the same speed. It’s time to think about the routines in our classrooms and reflect on what we are rewarding, speed or depth. Often, we ask students questions, hands fly up, and we call on the same five hands every time. Build think time into your routines. I’m a big fan of Sherry’s Parrish’s number talks. When I began using them in my classroom, I adopted the thumb-to-chest signal from the videos in the book for children to indicate they were ready with their answer. No hands shooting up in the air and waving around, because how distracting is *that* if you’re trying to think? I soon realized that I liked the signal so much that I began using it all the time in place of raised hands. It is a subtle shift that makes a big difference to students who need a little more time. It is also an expectation that I’m going to wait until I see “thumbs” from most all students before I call on anyone, and that I’m more interested in how you got your answer than the actual answer itself.

### Quit timing students

There is just so much research to indicate that timed tests are the beginning of math anxiety for large numbers of students and that the effects are long-term. This is a harmful practice that needs to be stopped. We would never put a reading passage in front of students, time them for a minute, and put big red x’s on any words they didn’t have time to read, so why in the world do we still do it in math? Do we want students to have automaticity with their basic facts? Of course we do! The difference is how we achieve automaticity, and it’s not from rote memorization and timed tests. Students learn their facts through reasoning strategies and they develop automaticity through practice with games. Be mindful of games like Around the World that not only emphasize speed, but do it in a very public way. Be sure to check out the links in this post, because several of them contain freebies that you can download and use in your classroom. But here’s one more little idea that requires nothing more than a deck of playing cards. Remove the Jacks, Queens, and Kings and use the Aces as 1s. Students turn over two cards, add the numbers, tell the sum, and explain their solutions. The player with the greater sum takes the cards. If both sums are the same, the cards remain on the table and are taken by the winner of the next hand. This game works for multiplication as well, of course.

I really enjoyed reading through this. I have a child who is quick to answer and one who takes a bit longer but they both come up with the same answer… I’m wondering if there are some simple exercises that I can do with my first grader to increase his confidence in his ability to solve problems? I’m a working mom so would need to work with him in the evenings… just looking for a starting point… we’re trying the game where Uncle X trades with Aunty Y to conceptualize adding and subtracting. I’m just not sure what level he is supposed to be operating at so I am not really sure how to help him. ANY advice would be really helpful

Have you talked to his teacher? It might be best to support what he’s already doing in the classroom.

Great website. I was never a strong math student in school. I see now that there are gaps in my understanding and reasoning! Example: I was never able to master memorization of basic addition and subtraction facts (but didn’t struggle with multiplication facts).

When I taught first grade, i taught my students strategies for the addition and subtraction facts and it finally clicked for me too—I learned the strategies along with my students. This motivates me to teach math well to my own students.

I will teach 3-5 grade enrichment next school year and am eager to read through your blog for more great information.

Thank you!

Everything you said was exactly my experience! My facts were memorized, but had absolutely no fluency with addition and subtraction. Now I’ve become so obsessed with mathematics and want to show my students the same!

I think this was the case for many of us! I’m so glad the tide is turning. 🙂

I particularly liked the section on “Give Students Think Time.” Many times I find myself calling on the same few students when asking for an answer to a math problem. I look around the room and see some students very hesitant in raising their hands. The hand will slowly go half way up then is brought down. I agree that the hand waving and students making grunting noises is very distracting, not only to me, but to those students needing a little more “think time.” I plan to incorporate the “thumb to chest” signal in my classroom.

Please help clarify if the standard is “fluency within 20”, what would “fluency” look like if not quick recall?

I ask because I was told that fluency is the ability to recall fact within 3-5 seconds.

I need to be able to explain.

Fluency does imply quick recall. What’s different is the way we go about developing automaticity, or fluency, by using a strategy-based approach that stresses the relationships between numbers vs. rote memorization. If you have to put a time range on it, 3-5 seconds seems reasonable. So, thinking of the progression, students in 1st grade are learning their basic addition and subtraction facts. By the end of 2nd grade, through practice, they should have fluency with the facts.

Fluency is actually defined as a persons ability to solve problems with appropriate strategy selection, flexibility, accuracy, and efficiency. FOUR aspects. Efficiency is not just speed, it is also about making a good strategy choice. Counting on is not a good option for 7 + 5, even if it’s done quickly. What you are referring to with getting an answer within a few seconds is automaticity. Also called mastery. That’s the end goal. But the way to get there and have students that don’t forget their facts and actually know useful strategies is to slow down and have time to learn and think through strategies!

Thank you for that clarification! I think the confusion arises because different standards have their own meanings of “fluency,” and it is often quick recall. It would be nice if we were all working from the same playbook.

Agree! And this definition of fluency came out of the National Research Coyncilbin 2001 and was quoted in the CCSS. But still the word is mis-used all over the place.

Great article. I am a strong proponent of non-timed math. It is not a race against the clock. as most of the education system is still like this such as timed essay writing for an English class. When it comes to math, the process and understanding the steps of the concept should come first, no matter what. It is on its way out, however, I tutor students who are anxious when it comes to math tests because they feel rushed for time, only adding to their anxiety levels, which ultimately factors in to their lower performance on tests. When I work on-on-one with students and administer practice quizzes that are non-timed, they feel relaxed and score better than on their school based timed tests. It is discouraging to know that they are capable of performing well, but the pressure of time causes them to be categorized as a lower achieving student within a grade-book.

As a pre-service teacher, I really appreciate this article. Our new curriculum, designed around core competencies, focuses on the process rather than the result. It is far from the rote memorization of math that I experienced as a student. I am so looking forward to using your ideas. Thank you.

Love this article – I am trying so hard to get my math teachers to understand this. Time doesn’t show understanding. It only shows memorization which cannot be used in other settings. I was always good at math, but now I know I was good at memorizing processes and had no clue why I ever did anything except that’s what the teacher told me to do.

Ive always used the Jokers as zero telling the kids that zero is a jokester- trying to throw you off! Any number × 0 is 0!

That is a great one!

I like that!

Leave the face cards in and use them as zeros… students need more regulator practice making numbers with aero and understanding how that impacts a number value. Or place holder..

Yes, I have heard using the Queens for zeros!

60years ago, my math needed help, i figured out those tricks for adding. Thankyou for reminding me. I now tutor children. Will use.

Great ideas for younger students, do you publish ideas, resources or games for middle school, ELL, or SPED students specifically?

No, I’m strictly elementary. 🙂

A really excellent article.