Voices From the Field: Numerical Fluency

Since we released our Numerical Fluency (NF) materials last June, franchisees and Center Directors throughout the Mathnasium system have noticed immense benefits as they’ve used the curriculum to cure finger counting for students of all ages. The new curriculum helps fill in gaps in students’ math foundations, and take their confidence and performance to new heights. Last month, we surveyed frequent users of the Numerical Fluency program for their honest thoughts and feedback; here’s a rundown of the results!

A Welcome Addition

^{[1] [2]}While most centers had a method of assessing a child’s numerical fluency prior to the NF launch, the formality of the Assessment and the associated curriculum was a welcome improvement from the card games and WOBs that comprised many solutions. Center owners Vane and Ginger Lucas (South Tulsa, Broken Arrow, & Owasso, OK) tell us that “the NF program is a profound improvement. Its beauty lies in the ability to break down skills specifically so you can focus only on what the student needs. This saves time and places effort where it needs to be.”

^[3]Those who didn’t have a NF system in place quickly saw the value of such a program once they started to use it. Back then, “I didn’t see not having an NF program as a barrier to working with any students. Honestly, I didn’t know what I didn’t know,” says Michael Fisher (CD, St. Charles & Algonquin, IL).

The Introduction

^[4]In order to gain access to the NF curriculum, center owners and directors had to get up to speed on the new materials, reading applicable sections in the Operations Manual and completing the training modules on Mathnasium University. This was more important for NF than any other new material because of the new methods employed when evaluating mastery. For instance, the Y/S/N rectangles may appear confusing to the untrained eye, but become very intuitive once training is completed. Most respondents found these resources extremely useful. “They were very helpful and we require all new staff to take the NF training course prior to working with students,” says Carlos Rodriguez (CD, Lake Forest, IL).

^{[5] [6]}“The courses were helpful in the beginning, but we found them even more useful when we had been working with NF for a short period of time. We would go back to the training and review areas again just to make sure we understood,” center owners Michael & Joanna Ammer (Crystal Lake & South Elgin, IL) tell us. “Having the hands-on experience makes it so much easier to follow what the training is trying to deliver.”

NF in Action – Demonstrated Progress and Increased Confidence Across Multiple Age Groups

^[7]While there were several great suggestions for improvement, all those polled reported remarkable gains in most, if not all, students on the NF track. “Every student who has used the NF curriculum has improved their math skills and knowledge significantly,” reports John Shaw (Assistant CD, Mesa, AZ). “Most of the older students are quickly able to extend their new knowledge to more advanced topics.”

Carlos Rodriguez has noticed that the NF materials “help reduce students’ reliance on and eliminate finger counting, so they can move on to a better ‘number sense’ understanding of the relationships between numbers.”

^[8]“It’s fun to watch their confidence increase as students learn to not use their fingers when counting,” says Lindsey Grant (CD, Arcadia, AZ). “It also creates a positive experience for kids when they complete an astronomical amount of pages on their first day…. it really helps the whole process go much more smoothly.”

“After our initial exposure to NF, we felt that many students would benefit from the program,” Michael and Joanna Ammer tell us. “We made a decision to give every student in grades 1 to 5 the NF Assessment, and we’re so glad we did.”

^[9]“For the younger students especially, I can really see the value of the NF program. So many of them come in working slowly because they don’t have their basic facts down solid. I have one 2^nd grader who would routinely miss half the problems on her timed facts tests at school. Now she gets all of them right!” reports Susan Cooper (Wichita Falls, TX).

Michael Fisher reports, “After completing NF, we assess them again in regular material to see what improvement [completing NF] has on the outcome of the regular Assessment before they have a chance to work on the regular material.” In fact, many franchisees reported having students who improved on their Level Assessment based only on the knowledge and confidence gained by completing the NF program.

^[10]For Ruby Yao (Fort Lee, NJ), one particular 4^th grade NF student stands out. “She started out very uncomfortable with math. After one month into NF, she progressed to regular Mathnasium worksheets. After three months, she is smiling, testing ahead of her class, enjoying her Mathnasium sessions and volunteering to solve problems! We’re also using the NF Addition/Subtraction Assessment and materials with a couple of first graders—for these younger students, the only limit is their ability to concentrate.”

The bulk of our respondents utilize NF materials primarily with elementary-age students (between the ages of 6 and 11), and occasionally with those in middle school. However, the huge gains reported by those who have successfully used the materials with much older students are also worth highlighting.

Vane and Ginger Lucas report that an estimated 80 to 90% of students enrolled in their centers complete some portion of the NF curriculum. “Counting is so prevalent in the students we encounter, even high school students. Their number sense is weak and the lack of strong fundamental skills causes them much heartache in their upper level math due to frequent mistakes in addition and subtraction.” The Lucases have made taking the NF Assessment “non-negotiable” and use it with all students.

^{[11] [12]}Franchisees David and Jennifer Krull (Almaden, CA) also cite remarkable progress in NF students from first grade to high school. “We just started an 11^th grader in Algebra 2 with the NF materials. His was an extreme case of finger counting. He couldn’t do subtraction without counting backwards. (For example, for ‘9 minus 7,’ he would start at 9 and count backwards 7 times.) He’s been a great sport about it and is enjoying the feeling of finally understanding numbers.”

While Michael Fisher primarily uses NF materials with students up to 4^th grade, he recalls a high school sophomore who had remarkable success with the materials. “She struggled with subtraction. After she completed the material, her subtraction problems disappeared and she was able to better absorb the rest of her learning plan. I do keep this in the back of my mind while assessing all students in all grade ranges.”

Challenges and Recommendations

^[13]Several franchisees expressed concerns about students and parents responding negatively when told that focusing on NF was essential for overall success. A few noted that having a structured NF program makes the idea of revisiting these basic concepts more palatable for parents. Mila Gleason (Cottonwood Heights, UT) says, “I think the NF materials make us look more like ‘math experts’. For example, in 5^th and 6^th grade, teachers always tell parents what students are missing [regarding their grade level work]. No one’s telling them that their kid has been finger counting.”

“We feel immense pressure to get through the NF curriculum as quickly as possible. Parents really struggle when you tell them that you need to teach their 10-year-old how to add 8 and 7,” Mila continues. “Even if they know these skills are critical, they still want you to work on fractions with kids that age. And we tell parents all the time, ‘If you can’t add whole numbers under 12, how can you add decimals and fractions?’ They believe you when they leave after the consultation, but they soon forget. Now, we keep parents updated frequently on the progress kids are making on NF, and we tell them when we’re moving on to grade-level concepts. We really emphasize that this is important, and we really need to get it done.”

Vane and Ginger Lucas add, “We explain to the student (during the verbal Assessment) and to the parent (during the Post-Assessment meeting) that this is critical and helpful. We also ask every high school student at the end of the NF process if it was helpful. To date, every single one has responded affirmatively.”

Many of you pointed out that NF is a bit different than other curriculum frameworks in our system, and may require some special considerations for instructors and their training.

Lindsey Grant feels that “Maybe a bit more emphasis on the bigger picture and goals of NF would help Instructors better understand its importance. Also, kids working on NF pages can be easily overlooked if they are churning out pages but still using fingers when an Instructor is helping another student. The importance of keeping a vigilant eye on them cannot be overly emphasized.”

^[14]As our respondents implemented the NF materials in their centers, they experienced a variety of challenges. “NF students require a little more attention to ensure they’re using the right methods [and not resorting to counting],” says franchisee Dan Aloi (West Hartford, CT). “Proper staff training and talking to students about the purpose and goal of the program has worked out well.”

^[15]“The biggest challenge so far has been ensuring consistency when students work with Instructors who are at different stages of understanding and mastering NF [through training and practice]. Seeing the NF Mastery Check page as training is only one piece of delivering successful NF instruction,” says Betty Wang (CD, Kenilworth, IL).

To a person, the survey respondents noted that while NF students might require more attention in the near-term, the long-term benefits more than made up for this upfront investment. While a few were concerned about what to do with students who didn’t grasp all the material the first time around, there were some great suggestions proposed as well, in many cases utilizing the games, WOBs and other system materials that have been around before this program.

“Figuring out what to do when a student still struggled with NF after working through the pages has been a fine line to walk,” adds Lindsey Grant. “You can’t just have them keep doing the same pages, but it’s not beneficial to move too far ahead while they are still struggling. We have found that splitting the Mathnasium Hour into 20 pages of Section 3 as a warm up (a mixture of the NF pages they still find difficult after two tries, and WOB E), 20 pages of Section 2 (pages assigned based on the regular Assessment), and 20 minutes of homework has skyrocketed student performance across the board. They are more engaged in all facets of their Mathnasium Hour and start closing both skill and fluency gaps.”

The Ammers believe that “one of the keys to this program is to slow the kids down when they’re working on NF. We have seen many kids blast out 10 pages in between Instructors working with them. Almost always, these are the kids that have to go over the material again. However, the new Workout Plan released with Team Teaching is really helping with that issue.”

What’s The Verdict?

On average, survey respondents rated the NF materials an 8.8 on a scale of 1 to 10. (One franchisee loved it so much she gave it an 11!) “I rate it an 8.5. The materials are great and the outcomes are wonderful, but I would add another level to NF to assess basic understanding for students above the 3^rd/4^th grade level so we can gauge their fluency without using math problems that may seem overly simple to them,” says Michael Fisher.

“We would give it a 9, as there is always room for improvement,” Vane and Ginger Lucas tell us. “We feel very strongly that any student with issues in this area, regardless of age, benefits tremendously from this curriculum. We strongly advise Center Directors to use this Assessment with anyone who cannot answer 7 + 8 + 9 or 14 – 6 with effortless recall.”

“Overall, we give it an 8,” reports John Shaw. “HQ has provided an excellent start, but we feel the program should be augmented. Most of our NF students fly through the materials in as little as two weeks. Although our students master the materials in this time frame, they are still unable to perform slightly more advanced topics, such as multiplication, upon program completion. It would be a nice addition to include multiplication and division facts.”

“I love it. I give it a 9,” Lindsey Grant concludes. “Having an Assessment and plan in place to help kids overcome their fluency roadblocks gives me tremendous peace of mind that they are getting the help that they need. Once the students have their 10s, doubles, and single-number decompositions memorized… they are unstoppable! (And I find great joy in telling them so!)”