I was a recent guest to Esmy Lozano (a reading tutor and online tutor coach) at Online Tutors Grow (on Instagram). Esmy was my tutoring coach and she and I still partner up on projects. We decided to do a mini-series on her Instagram Live where we talked about math. Why? She also gets students who need support in math, even though she is a reading specialist. I get students who need support in reading, and I am a math tutor. We decided we would compliment each other well, so we embarked on this journey together. She asked me to bring my expertise to express my thoughts about math fact fluency and the importance of it.
Having been in the classroom for 32 years, and now working as a full-time elementary math tutor, I knew it was vital to have knowledge of math facts. What I didn’t necessarily have was expertise (research-based field work) to state why this was so important. I had field experience, but I hadn’t taken notes and done the challenging job of putting it all together into a researched thesis. Thus, I went on a fact-finding mission and discovered a few important pieces of the puzzle.
As I was searching around for this information, I kept thinking to myself, “Why isn’t this an emphasis in the math books that are purchased and used by most school districts?” I knew I had only had one math book in my entire teaching history that had an emphasis on math fact fluency, and that was Saxon Math. I had never used another tool that was provided by my district that had math fact practice built into the program. When our school district pivoted away from Saxon Math (mostly because it was very rigorous and the lower elementary teachers didn’t like the structure of the lessons) our school district purchased a separate curriculum that we were asked to use. I honestly don’t remember the name of it anymore, but it had math fact fluency sheets and repetitive songs and verses that students were to use to remember their facts. We also had this huge number line that went around the room and we were to place dots on it to show the math facts of different groups. I remember it took me HOURS to put all of this together. (I am not exaggerating!) I hung it up, and used the program, but it didn’t have the impact that Saxon Math had provided for my students. Maybe it was because I wasn’t a huge fan, and my enthusiasm may have been a bit of production, rather than true love for that part of the math program. It just didn’t work for my kiddos like Saxon Math had done. Saxon Math had the math fact fluency built into the program, and it did a spiral review of concepts taught to the students, so you kept coming back to math concepts that were already taught at the end of each lesson. And, if you didn’t teach a lesson, it backfired on you because you had to have that information to move forward with the lessons. As a fifth grade teacher, I loved the structure and all of the features this program provided.
I had taught long enough and used enough math books that I was able to recognize the value of a strong mathematical program and unfortunately, we no longer had it in my district. It was now left up to the teacher to pivot from large group instruction to small group instruction, rather than large group instruction with small group support. We no longer had the math fact review in our math program, it was an add-on. With the switch to small group instruction, and having to have a mini-lesson and then meet with 4 or 5 small groups during the hour to hour and a half of math time, we simply could no longer use the teacher directed program the school district had provided. There wasn’t enough time in the day to fit EVERYTHING in!
I know that I am preaching to the choir when I explain this. Teachers all over the United States, and I am sure in other areas of the world, are confronted with too much to do, and too little time to do it! Yet, the powers-at-be like to keep adding to the LONG list of things teachers are supposed to fit into their very busy day. They are expected to teach an incredible amount of information in the school year, and sometimes, the teacher is forced to cut short or even cut out something they can no longer fit in. They are being told by their administration to teach in small groups because it is good for the kids. And, if a skill is not explicitly stated in the state’s math standards they may not touch upon it. And, some schools write their own math standards and get the state school boards to okay their standards. If the state says that students are to have mastered their math facts at the third grade, that standard may not actually show up past that grade level. The teachers are expected to teach what is written on the approved standards, so they may be forced to skip something like math fact practice or provide time for their students to work on them independently. But, what happens to the students who cannot teach themselves while the teacher is doing small group instruction?
I had this problem throughout the end of my teaching career in public schools. What I described literally happened to me! I valued the need for my students to learn their math facts, but I simply couldn’t fit everything into our day! So, I would provide time into our school day for students to practice their math facts while I was working with 4-6 kids at a time (with my class sizes ranging anywhere for 18-24, 25, or 26 kids). But when the students were not able to conceptually understand the math facts, they simply didn’t make progress. The intention for them is to practice, but it is like learning a new language but not understanding it. Perhaps they will learn a few math facts, but without direct instruction, guided practice, repeated independent practices and then applying them to actual skills based problems, the students are not going to be very successful. And, how can a teacher actually monitor what the 18 kids who are doing independent practice are doing as they are teaching 4-6 kids in small groups? You may be fortunate to have a paraprofessional in your classroom, but many teachers do not have that luxury.
I did research on math fact fluency in preparation for my interview with Esmy Lozano from Online Tutors Grow (Instagram), and found some interesting facts. I found a study that was done by Austin T. Baker and Josh Cuevas, both from the University of North Georgia. It was entitled, The Importance of Automaticity Development in Mathematics. It was printed in The Georgia Educational Researcher (2018). So, let’s dissect this idea article and the ideas of automaticity in mathematics as it relates to math fact fluency.
The authors quoted several other researchers and I will do the same. This idea of fluency can sometimes be difficult to explain to a parent, but most of us would say, “Your child can do something without thinking.” (That is my idea of what fluency is!) Here is a direct quote from the article, “”The definition of automaticity provided by Stickney et al. (2012) is the ability to deliver a correct answer immediately from memory without conscious thought, as opposed to relying on calculation. And in the related research is another term called fluency. According to Lin and Kubina, (2005) fluency requires students to be both fast and accurate when solving basic math facts. Automaticity is a piece of fluency. Fluency is the end goal and considered true mastery of the concept when reached. Now connect these two terms to mathematics and we develop the idea that students will develop automaticity first, then fluency, and by doing this, they will develop a pattern of sustained success in the mathematics career (Cumming and Elkins, 1999; Lin and Kubina, 2005; Stickney et al., 2012; Woodward, 2006).””
The article went on to discuss the importance of automaticity. It basically said, if a student is not able to quickly and automatically retrieve their math facts they spend time trying to come up with the answers to the smaller facts. Then they get lost in the steps of longer algorithms (steps it takes to solve a math problem) because they are trying to think about the math facts, rather than the longer math problems they are trying to solve. This can lead to confusion and lower understanding of the math they are learning.
Another quote from the aforementioned article caught my attention. It stated, “”According to Woodward (2006), decades of research show that academically low-achieving students as well as those with learning disabilities exhibit considerable difficulty in developing automaticity. Research on elementary aged students indicates that students with learning disabilities are more likely to rely on counting strategies than direct retrieval when working with single-digit fact problems. Failing to reach automaticity results in students relying on different counting strategies. Whether it is a student with a learning disability or a student without, the results are very similar. The students begin to fall behind at the elementary level and continue this pattern into secondary level.””
And, this problem isn’t only in relation to addition and subtraction. It affects multiplication and division math facts. When students don’t have the understanding of the mathematical concepts, then telling them to learn their math facts isn’t going to work. They need to conceptually understand what it means.
The research paper went on to discuss a research project where they did a study about how students were using their skills to solve math fact problems and they discussed their findings. If you want the full findings, be sure to read their full article. I would like to quote their discussion of the findings. It is as follows: “The findings from this study are consistent with other research provided by Burns et al. (2014) and Stickney et al. (2012). Students are continuing to struggle with single digit multiplication problems and this is not only affecting them now, it is also putting their success in the future in jeopardy. Developing automaticity is a building block for the success of students in the math classroom. Just as students cannot read with understanding without first learning the correct process for sounding out words and memorizing their sight words, math students cannot “read” math without learning their basic math facts. Those basic facts do not just include multiplication facts, it also includes single digit addition, subtraction, and division problems.”
And they went on to discuss the reading and math relationship even further by stating: “The relationship between learning to read and learning math is more similar than one might think…This is called fluency. According to Pikulski and Chard (2005), ‘Reading fluency refers to rapid, efficient, accurate word recognition skills that permit a reader to construct the meaning of text. Fluency is also manifested in accurate, rapid, expressive oral reading and is applied during, and makes possible, silent reading comprehension.’ Reading fluency is important because it bridges the gap between word recognition and comprehension. Similarly, basic multiplication facts would be analogous to word recognition. Better word recognition leads to better reading comprehension. Learning the basic multiplication facts would lead to a better understanding of more complex math concepts. Before any comprehension can take place, whether in reading or in math, automaticity of sight words or math facts must be achieved to improve comprehension.”
This article led me to ponder what else it means to be fluent in math facts. My previous school district had always provided me with the reading fluency benchmarks. We had all kinds of charts we were expected to follow. We had the benchmarks for the beginning, middle, and end of the year tests we gave, but not once in my entire 32 year teaching experience at this district did we EVER get a list of math fact fluency benchmarks. I actually did a Google search for those, and I found them! I found a pdf when doing a search, and I found a document entitled, Required Fluencies in the Common Core State Standards for Mathematics. I teach in Nebraska, and we use the Nebraska State Standards, and I had never seen this chart before. It laid out the required fluencies for each grade level. It looked like this for K-6:
|K||Add/Subtract within 5|
|1||Add/Subtract within 10|
|2||Add/Subtract within 20 |
Add/Subtract within 100 (pencil and paper)
|3||Multiply/divide within 100|
Add/subtract within 1000
|4||Add/subtract within 1,000,000|
Multi-digit decimal operations
When I look at this list I feel overwhelmed! This is the math fluency they want our students to be proficient in, but this is a very SMALL portion of all of the skills students are required to master at each level as well. How is a teacher supposed to do this, all the while teaching in small groups, and being held accountable for all of the standards for their state, plus deal with all of the other details of their normal day? It is an incredible feat to be sure!
I have been teaching long enough to remember a time where things were much simpler and we had a curriculum that was much more manageable. Our powers-that-be have moved things down to lower grades and increased rigor and expectations, but to what end? Has this REALLY made the difference it was supposed to make? I will be the first person to say it has not. Giving teachers more to do, increasing the complexity of the curriculum doesn’t make a lot of sense when our kiddos are not cognitively ready to tackle those mathematical ideas. And, we can barely find the time to make sure our kiddos are mastering their math facts.
I do not have a simple answer,but I know that what we are doing is not working. I do have some things we can ponder:
What if we got parents to buy into the fact that they need to support the learning that is going on in school? What if the parents took the time to help their child learn their math facts?
What if we reexamined what is going on in our classrooms? How is instruction taking place, and is it really best practice to teach all elementary grade levels in a small group, thus leaving students to self-teach themselves rather than getting that all-important teacher-led instruction?
What if we reexamine our curriculum and state standards, and consider the grade level appropriateness of what we are teaching our students. Is it really important for a 5th grader to learn the sheer number of state required standards? Isn’t less sometimes more? Can’t we think about teaching less but going deeper rather than teaching more and just skimming the surface?
Maybe some of these changes would support the importance of automaticity with math facts thus creating fluency with our students. And remember, I have only discussed math. I haven’t even been talking about all of the other subjects kids are learning in our schools.
I hope this has given you and others some things to ponder.
It is my hope this blog post will lead to productive and thoughtful conversations about the importance of supporting learning for your child. Being an active participant with your child’s learning is vital for their success. I hope you see the importance of math fact fluency and how a full understanding of those facts will support your child not only in the elementary grade levels, but beyond.
For more information about Tutoring with Sheryl and how she supports her student learners, be sure to visit https://midwesttutor.com or https://linktr.ee/sheryluehling.