No requirement to assess fact fluency here. I don't know that I assess myself in the way you're describing because it's obvious if you just spend a few minutes with my students at the start of the year that they need more practice with math facts. I do spend a lot of time teaching and facilitating fact fluency practice in a yearlong progression with my students and do a lot of informal assessment to guide how we work through that progression - the goal is to do focused practice on all fact families, all four operations throughour the year.
Define timed practice? I do high-volume practice where I emphasize to students that the goal is to retrieve facts from memory. I don't explicitly time or track number of facts per minute, etc. The timing stuff takes a lot of time and I work through a progression so the timing/tracking feels like a lot of effort when we're going to move on to the next step in the progression soon.
I think this issue can be oversimplified. Yes, knowing math facts is crucial, but how kids get to memorization is important too. If kids are simply asked to know the answers quickly, we can miss gaps in foundational number sense. In the early grades, kids to need learn derived strategies for solving the ones they don’t know. For example, to solve 9+7, they can add 1 to 9 to make 10 and the add 6 more. This strategy comes after kids are fluent with combinations that make 10 and 10+ facts. Speed and accuracy are important, but so is flexibility. If a child forgets a fact, they need an efficient way to solve it. At first they can learn counting strategies, but then they should move on to derived strategies like the one mentioned above. I have observed students get stalled out on programs like Reflex because the program is simply assessing whether they get the right answer quickly. I watched one of my students get very fast at counting on his fingers, but the program did not teach him what to do next. Once I explicitly taught him derived strategies and had him practice, he mastered his facts in a couple months. He had been doing reflex for two years up until that point. It’s not as simple as going through flash cards. We do want memorization eventually, but we also want to build number sense. It’s like those babies that are taught to “read.” They really just memorized the whole word, but the aren’t actually reading. You can drill and drill math facts with young learners so they appear to have memorized them, but then they forget over time without foundational number sense. Math Fact Fluency by Jennifer Bay-Williams is a good resource for teachers.
Hi Abby, thanks for this comment. In your state or district, is there a requirement to assess fluency in any way? And then is anything done with that information?
I’m no longer in the classroom. I’m a private tutor of students in multiple districts. There are no district fluency assessment requirements that I’m aware of. My daughter’s school uses Reflex, but they don’t use a separate assessment.
We require fact fluency and assess it in 1st through 5th grade (district requirement). We send home information to parents about what their child still needs to learn and a set of 2 to 3 facts for a student to practice that week. The fluency goals are part of the teacher's and the building's yearly goals. We set aside at least 15 minutes each day for fluency practice. This is our first year with the requirement. We assess both untimed and timed, each assessment is used in a different way.
Parent here, commenting on an old issue about timed fluency tests. One of my kids has both dysgraphia and has now 99% recovered from a dysfluency of speech. His 3rd grade teacher did daily timed testing of math facts (starting with addition and subtraction in the fall, ending the year having added multiplication and division facts. All very good with me as a teaching method.
HOWEVER! History repeated itself. (My extreme nearsghtedness was discovered in 3rd grade because I was inaccurately copying math problems from the black board.)
The method that teacher used to test fluency was to write the problems on the board before school started and pull down the projection screen. At the bell, he would raise the screen and give students 3 minutes to write down and solve 10 problems at the beginning of most school days. In spite of his disabilities, my son was completely fluent with math facts. (Dice-centric tabletop role-playing games FTW!), but could not copy the problems from the board fast enough or accurately enough to do them all in the allowed 3 minutes because of his dysgraphia. When I drew this to the teacher's attention, the teacher tried doing oral math facts with the whole class instead. That became problematic because of my son's speech issues, and the speech & language therapist asked the teacher to stop.
My son was finally able to (and allowed to) demonstrate his fluency by using a computer learning program on the computer, so that he only had to type the answer. Using that process, he got over 200 math facts correct in 3 minutes, which convinced the teacher not to include any of the handwritten scores in his math grade. He did miss 1 problem in the first effort to do this, but it appeared to be a typo, (3 digit answer rather than 1) not that he typed a wrong answer.
I am 100% in favor of practicing and testing for fluency on math facts (and spelling, and science vocabulary, and ...) in the classroom. I have gifted multiple teachers with sets of 4, 6, and 10-sided dice to make practice problem generation fast and easy. I also want to make sure that teachers are aware of issues unrelated to class content that might keep students from showing what they know using certain long-familiar techniques.
No requirement to assess fluency. I do it on my own (including timed tests). We don't use a numeracy screener. We use Reflex and daily practice, but I am considering Facts On Fire (Brian Poncy) to include writing the equations on the way to memorization. (Third grade)
When Indiana revised the standards in 2023, they came out with substantial tool titled "Indiana Frameworks," which is a series of Google Docs that unpacks every standard. It is very nice for onboarding a new teacher, and is a one-stop-shop for all state assessments, academic vocabulary, vertical alignment, etc. It is just cumbersome to get to.
For part of the conversation, there may need to be a coming-to-terms with what fluency means.
Here is a link to the 3rd grade math standard where multiplication facts would traditionally be a non-negotiable with most teachers. If this links doesn't work, sign in with any Google account and refresh the link.
If you scroll to the clarification statements section, there is a lot of information. Like I said earlier, it is nice to have this to onboard new teachers.
I find that both new and vet teachers are often confused over the term fluency as it is described in a few ways, and furthermore, they are confused on what assessment of the standard should look like. Fortunately, Indiana has easily accessible item specs for their ILEARN, so a problem can be cross-referenced here.
When I coach teachers, we often have to come to terms with what we consider "fluency" and how that is measured and reported to accurately give us an understanding of how students are performing on benchmark assessments.
This is incredibly helpful, and thanks for acknowledging what I was kind of trying to get at with the original question—that a lot of teachers don't get this kind of clarity, and the term "fluency," if not specified and measured, can mean a lot of different things to different people.
Two things to add as I am looking at other's comments:
1) At one point, there was a clarifying statement in that third grade standard which said "we do not consider the use of timed tests as an indicator of fluency." That is no longer in the document.
2) The reason the state is publishing this information in Google Docs is for quick policy shifts and change of recommendations. IDOE reps discourage teachers from printing those documents because anything could change and there isn't log of these changes that is accessible to teachers.
I teach 4th grade in Southern Oregon. My district has quietly deprioritized math fact fluency. The line for math facts disappeared from our report cards years ago. It doesn’t come up in professional development. Leadership treats fluency as a nice-to-have, not something essential.
The one tool we’re officially encouraged to use is Fluency Flight, an online program bundled with our curriculum. As far as I can tell, there’s no research behind it. The results reflect that. Some of my students spent nearly 10 minutes a day on it last year and still count backwards on their fingers to subtract. My own daughter has been fluent in all her facts since early 3rd grade and is now in 4th grade. She’s still getting problems like 6 minus 1.
I stopped using it and instead switched to Brian Poncy’s Facts on Fire. Five minutes a day. Systematic instruction and timed practice! It’s been a game changer. After just three months working through our multiplication packets, I went from 2 out of 23 students at benchmark to 18 out of 23 with facts mastered.
The best part is that my students are now flying through multi-digit multiplication and division. Everything has become SO much easier because the foundational knowledge is finally automatic.
Math facts should be treated like phonics or sight words: essential content that every child has a right to be taught using the most effective and efficient methods we have.
That usually means systematic instruction and lots of low-stakes, high-success timed practice.
Sure, we should still include activities to build number sense. But these can and should can be done in tandem with timed memorization techniques.
The point is to have the facts stored in long term memory. If kids get stuck on any method that doesn’t lead to automatic retrieval, then we need to help them move past it.
And no—our numeracy screener does not include a timed fact component.
Thank you, this is really helpful! I've never heard of Fluency Flight but now I will look into it. And interesting that math facts used to be a line on the report card...hmmmm. I might circle back to you and ask you a few questions if you're interested.
Daniel's comment prompted me to look at my second grader's report card. Fluency within 20 is not even on it - whether memorized or derived. All the lines regarding addition/subtraction refer to using strategies within 100. I looked up the district's 1st grade card - it has a line for "adding / subtracting within 20. Within 10 fluently." Which explains a lot in hindsight - why the first grade teachers do seem to focus on fluency practice, whereas (at least with my older two kids) the 2nd grade teachers did not. Looking at the 3rd grade card - it does have "fluently multiply within 100" - and I know there is a fluency focus in third. For second grade, the CA standards explicitly say "Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two
one-digit numbers." They hit on both strategies and memorization. But our district isn't tracking EITHER for second grade apparently. (High performing district - but lots of after-schooling goes on.) I knew it was a standard based report card, so I assumed it was there. But it is not!
I went back and looked at 3rd grade and found it does exist there on the report card. I suppose students are assumed to have mastered it then? It is absent on 4th and 5th.
I coach our middle school teachers to include fact fluency practice in 6th and 7th grade, but it is in the context of support block which is targeting students who need support with foundational skills, so there is no assessment of facts per se.
We assess math facts. First we make sure kids are getting targeted subitizing (heavily researched important part of fluency) and targeted instruction on relationships and strategies at the students fact level based on the best fit fact trajectory level. We keep timing but we follow the IES recommendations on fluency intervention which does not recommend format of timed tests used in the past. They recommend timed activities (which can include games) and student reflection on efficienct strategies. We give timed assessments but it is on fact type in focus (with a review of previously mastered levels) and the timing is per fact not per whole set of questions. This helps us to pinpoint which facts students stop need to work on and which facts they already have down that they can use to help them with the facts they don't (i.e. if a student knows 6 + 6 we can help them use it for 6 + 7).
A really important thing some spokespersons for SOM keep on neglecting is that these strategies don't just live with basic facts. They extend throughout the number system and concepts. Stop when we take time to make sure kids are strategic (have part whole relationships, have number relationships, have inverse relationships down at each fact level) we are not only supporting fluency for whole number operations but also fractions, etc as well as algebraic reasoning.
I work for a private non-profit organization in Idaho. Our state is hostile to research and hostile to educating in general. We are lucky at our org that we are encouraged to look at the research as a small team and make decisions together.
The “multiple strategies” method is not mutually exclusive to also checking for fluency. Fluency can develop through conceptual understanding, which leads to better long term outcomes.
How are you defining fluency? If fluency has a component of memorization/automaticity, that may not be achieved with strategy use. A child who uses count-on to solve 7 + 5 (e.g. 7, 8, 9, 10, 11,12) is not be practicing/retrieving the declarative sentence "7 + 5 is 12." A child using the make-10 strategy to solve 7 + 5, is practicing 7 + 3 + 2 --> 10 +2 = 12, again - this is NOT practicing the declarative fact of 7 + 5 = 12. (The facts being recalled/practiced here are 7+3 =10 and 10+2 = 12. ) Strategies ARE useful, especially when used with larger numbers, but just because they are useful for generalization doesn't mean they are useful for automaticity (which is when a prompt results in a recalled - not derived - response). A strategy is a procedure, a fact is a declarative sentence. Two completely different things. Assuming strategies will result in memorization makes no more sense than assuming memorization will lead to strategy use. Both are valuable. Both are needed. If you want ALL students to have both, both need to be developed with intentional support and structure from the teacher.
The process of 7+ 3 + 2 is what gets kids to automaticity, similar to how having them sound out phonemes (sh - oo-k, shook) gets them to automaticity with reading words. It is part of the process. I agree that intentional and structured teaching needs to happen. But there are multiple ideas happening here. Part whole, inverse operations, and connecting facts. Facts that are learned with connections are not only stronger but they also translate to procedural fluency beyond basic facts.
No requirement to assess fact fluency here. I don't know that I assess myself in the way you're describing because it's obvious if you just spend a few minutes with my students at the start of the year that they need more practice with math facts. I do spend a lot of time teaching and facilitating fact fluency practice in a yearlong progression with my students and do a lot of informal assessment to guide how we work through that progression - the goal is to do focused practice on all fact families, all four operations throughour the year.
Good to know—do you do any timed practice?
Define timed practice? I do high-volume practice where I emphasize to students that the goal is to retrieve facts from memory. I don't explicitly time or track number of facts per minute, etc. The timing stuff takes a lot of time and I work through a progression so the timing/tracking feels like a lot of effort when we're going to move on to the next step in the progression soon.
All of this is in draft form but if you want to see the current resources I've put together they're here: https://drive.google.com/drive/folders/1-JyND334mPap-oNb0ssOXgTsf3bcliCH
Thank you!
I think this issue can be oversimplified. Yes, knowing math facts is crucial, but how kids get to memorization is important too. If kids are simply asked to know the answers quickly, we can miss gaps in foundational number sense. In the early grades, kids to need learn derived strategies for solving the ones they don’t know. For example, to solve 9+7, they can add 1 to 9 to make 10 and the add 6 more. This strategy comes after kids are fluent with combinations that make 10 and 10+ facts. Speed and accuracy are important, but so is flexibility. If a child forgets a fact, they need an efficient way to solve it. At first they can learn counting strategies, but then they should move on to derived strategies like the one mentioned above. I have observed students get stalled out on programs like Reflex because the program is simply assessing whether they get the right answer quickly. I watched one of my students get very fast at counting on his fingers, but the program did not teach him what to do next. Once I explicitly taught him derived strategies and had him practice, he mastered his facts in a couple months. He had been doing reflex for two years up until that point. It’s not as simple as going through flash cards. We do want memorization eventually, but we also want to build number sense. It’s like those babies that are taught to “read.” They really just memorized the whole word, but the aren’t actually reading. You can drill and drill math facts with young learners so they appear to have memorized them, but then they forget over time without foundational number sense. Math Fact Fluency by Jennifer Bay-Williams is a good resource for teachers.
Hi Abby, thanks for this comment. In your state or district, is there a requirement to assess fluency in any way? And then is anything done with that information?
I’m no longer in the classroom. I’m a private tutor of students in multiple districts. There are no district fluency assessment requirements that I’m aware of. My daughter’s school uses Reflex, but they don’t use a separate assessment.
We require fact fluency and assess it in 1st through 5th grade (district requirement). We send home information to parents about what their child still needs to learn and a set of 2 to 3 facts for a student to practice that week. The fluency goals are part of the teacher's and the building's yearly goals. We set aside at least 15 minutes each day for fluency practice. This is our first year with the requirement. We assess both untimed and timed, each assessment is used in a different way.
Parent here, commenting on an old issue about timed fluency tests. One of my kids has both dysgraphia and has now 99% recovered from a dysfluency of speech. His 3rd grade teacher did daily timed testing of math facts (starting with addition and subtraction in the fall, ending the year having added multiplication and division facts. All very good with me as a teaching method.
HOWEVER! History repeated itself. (My extreme nearsghtedness was discovered in 3rd grade because I was inaccurately copying math problems from the black board.)
The method that teacher used to test fluency was to write the problems on the board before school started and pull down the projection screen. At the bell, he would raise the screen and give students 3 minutes to write down and solve 10 problems at the beginning of most school days. In spite of his disabilities, my son was completely fluent with math facts. (Dice-centric tabletop role-playing games FTW!), but could not copy the problems from the board fast enough or accurately enough to do them all in the allowed 3 minutes because of his dysgraphia. When I drew this to the teacher's attention, the teacher tried doing oral math facts with the whole class instead. That became problematic because of my son's speech issues, and the speech & language therapist asked the teacher to stop.
My son was finally able to (and allowed to) demonstrate his fluency by using a computer learning program on the computer, so that he only had to type the answer. Using that process, he got over 200 math facts correct in 3 minutes, which convinced the teacher not to include any of the handwritten scores in his math grade. He did miss 1 problem in the first effort to do this, but it appeared to be a typo, (3 digit answer rather than 1) not that he typed a wrong answer.
I am 100% in favor of practicing and testing for fluency on math facts (and spelling, and science vocabulary, and ...) in the classroom. I have gifted multiple teachers with sets of 4, 6, and 10-sided dice to make practice problem generation fast and easy. I also want to make sure that teachers are aware of issues unrelated to class content that might keep students from showing what they know using certain long-familiar techniques.
Thanks for this comment!
Our district in Virginia (28K students) uses the software Reflex for all 4 operations. Reflex uses timed exercises. It is used in Grades 2-5.
I’m not familiar with Reflex but now I will look it up!
No requirement to assess fluency. I do it on my own (including timed tests). We don't use a numeracy screener. We use Reflex and daily practice, but I am considering Facts On Fire (Brian Poncy) to include writing the equations on the way to memorization. (Third grade)
Great to know—what state are you in?
South Dakota, but I work at a tribal school
When Indiana revised the standards in 2023, they came out with substantial tool titled "Indiana Frameworks," which is a series of Google Docs that unpacks every standard. It is very nice for onboarding a new teacher, and is a one-stop-shop for all state assessments, academic vocabulary, vertical alignment, etc. It is just cumbersome to get to.
For part of the conversation, there may need to be a coming-to-terms with what fluency means.
Here is a link to the 3rd grade math standard where multiplication facts would traditionally be a non-negotiable with most teachers. If this links doesn't work, sign in with any Google account and refresh the link.
https://docs.google.com/document/d/1RV4JUV44uUHX0PGajQUpAkzGmw_s3tVZc3gYAGi1sds/edit?tab=t.0#heading=h.x7gogfdl3ixs
If you scroll to the clarification statements section, there is a lot of information. Like I said earlier, it is nice to have this to onboard new teachers.
I find that both new and vet teachers are often confused over the term fluency as it is described in a few ways, and furthermore, they are confused on what assessment of the standard should look like. Fortunately, Indiana has easily accessible item specs for their ILEARN, so a problem can be cross-referenced here.
When I coach teachers, we often have to come to terms with what we consider "fluency" and how that is measured and reported to accurately give us an understanding of how students are performing on benchmark assessments.
This is incredibly helpful, and thanks for acknowledging what I was kind of trying to get at with the original question—that a lot of teachers don't get this kind of clarity, and the term "fluency," if not specified and measured, can mean a lot of different things to different people.
Two things to add as I am looking at other's comments:
1) At one point, there was a clarifying statement in that third grade standard which said "we do not consider the use of timed tests as an indicator of fluency." That is no longer in the document.
2) The reason the state is publishing this information in Google Docs is for quick policy shifts and change of recommendations. IDOE reps discourage teachers from printing those documents because anything could change and there isn't log of these changes that is accessible to teachers.
I teach 4th grade in Southern Oregon. My district has quietly deprioritized math fact fluency. The line for math facts disappeared from our report cards years ago. It doesn’t come up in professional development. Leadership treats fluency as a nice-to-have, not something essential.
The one tool we’re officially encouraged to use is Fluency Flight, an online program bundled with our curriculum. As far as I can tell, there’s no research behind it. The results reflect that. Some of my students spent nearly 10 minutes a day on it last year and still count backwards on their fingers to subtract. My own daughter has been fluent in all her facts since early 3rd grade and is now in 4th grade. She’s still getting problems like 6 minus 1.
I stopped using it and instead switched to Brian Poncy’s Facts on Fire. Five minutes a day. Systematic instruction and timed practice! It’s been a game changer. After just three months working through our multiplication packets, I went from 2 out of 23 students at benchmark to 18 out of 23 with facts mastered.
The best part is that my students are now flying through multi-digit multiplication and division. Everything has become SO much easier because the foundational knowledge is finally automatic.
Math facts should be treated like phonics or sight words: essential content that every child has a right to be taught using the most effective and efficient methods we have.
That usually means systematic instruction and lots of low-stakes, high-success timed practice.
Sure, we should still include activities to build number sense. But these can and should can be done in tandem with timed memorization techniques.
The point is to have the facts stored in long term memory. If kids get stuck on any method that doesn’t lead to automatic retrieval, then we need to help them move past it.
And no—our numeracy screener does not include a timed fact component.
Thank you, this is really helpful! I've never heard of Fluency Flight but now I will look into it. And interesting that math facts used to be a line on the report card...hmmmm. I might circle back to you and ask you a few questions if you're interested.
Daniel's comment prompted me to look at my second grader's report card. Fluency within 20 is not even on it - whether memorized or derived. All the lines regarding addition/subtraction refer to using strategies within 100. I looked up the district's 1st grade card - it has a line for "adding / subtracting within 20. Within 10 fluently." Which explains a lot in hindsight - why the first grade teachers do seem to focus on fluency practice, whereas (at least with my older two kids) the 2nd grade teachers did not. Looking at the 3rd grade card - it does have "fluently multiply within 100" - and I know there is a fluency focus in third. For second grade, the CA standards explicitly say "Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two
one-digit numbers." They hit on both strategies and memorization. But our district isn't tracking EITHER for second grade apparently. (High performing district - but lots of after-schooling goes on.) I knew it was a standard based report card, so I assumed it was there. But it is not!
I went back and looked at 3rd grade and found it does exist there on the report card. I suppose students are assumed to have mastered it then? It is absent on 4th and 5th.
I coach our middle school teachers to include fact fluency practice in 6th and 7th grade, but it is in the context of support block which is targeting students who need support with foundational skills, so there is no assessment of facts per se.
We assess math facts. First we make sure kids are getting targeted subitizing (heavily researched important part of fluency) and targeted instruction on relationships and strategies at the students fact level based on the best fit fact trajectory level. We keep timing but we follow the IES recommendations on fluency intervention which does not recommend format of timed tests used in the past. They recommend timed activities (which can include games) and student reflection on efficienct strategies. We give timed assessments but it is on fact type in focus (with a review of previously mastered levels) and the timing is per fact not per whole set of questions. This helps us to pinpoint which facts students stop need to work on and which facts they already have down that they can use to help them with the facts they don't (i.e. if a student knows 6 + 6 we can help them use it for 6 + 7).
A really important thing some spokespersons for SOM keep on neglecting is that these strategies don't just live with basic facts. They extend throughout the number system and concepts. Stop when we take time to make sure kids are strategic (have part whole relationships, have number relationships, have inverse relationships down at each fact level) we are not only supporting fluency for whole number operations but also fractions, etc as well as algebraic reasoning.
Thank you for this comment! Is this your school or district, or coming from the state? And if yes, what state?
I work for a private non-profit organization in Idaho. Our state is hostile to research and hostile to educating in general. We are lucky at our org that we are encouraged to look at the research as a small team and make decisions together.
💯
There is no numeracy screener until grade 3 and then it's an adaptive multiple choice assessment to predict state test outcomes.
In California, right?
Yup. Bay area.
The “multiple strategies” method is not mutually exclusive to also checking for fluency. Fluency can develop through conceptual understanding, which leads to better long term outcomes.
How are you defining fluency? If fluency has a component of memorization/automaticity, that may not be achieved with strategy use. A child who uses count-on to solve 7 + 5 (e.g. 7, 8, 9, 10, 11,12) is not be practicing/retrieving the declarative sentence "7 + 5 is 12." A child using the make-10 strategy to solve 7 + 5, is practicing 7 + 3 + 2 --> 10 +2 = 12, again - this is NOT practicing the declarative fact of 7 + 5 = 12. (The facts being recalled/practiced here are 7+3 =10 and 10+2 = 12. ) Strategies ARE useful, especially when used with larger numbers, but just because they are useful for generalization doesn't mean they are useful for automaticity (which is when a prompt results in a recalled - not derived - response). A strategy is a procedure, a fact is a declarative sentence. Two completely different things. Assuming strategies will result in memorization makes no more sense than assuming memorization will lead to strategy use. Both are valuable. Both are needed. If you want ALL students to have both, both need to be developed with intentional support and structure from the teacher.
Just gonna post this https://www.nctm.org/Standards-and-Positions/Position-Statements/Procedural-Fluency-in-Mathematics/
The process of 7+ 3 + 2 is what gets kids to automaticity, similar to how having them sound out phonemes (sh - oo-k, shook) gets them to automaticity with reading words. It is part of the process. I agree that intentional and structured teaching needs to happen. But there are multiple ideas happening here. Part whole, inverse operations, and connecting facts. Facts that are learned with connections are not only stronger but they also translate to procedural fluency beyond basic facts.