According to Doug Rohrer of the University of South Florida,
In most mathematics textbooks, each lesson is followed by a set of practice problems comprised almost entirely of problems corresponding to that lesson. Thus, with this format, most or all of the problems relating to a given topic are massed into one practice set and not distributed across multiple practice sets.Excel Math takes a different approach. We know that students learn not chapter by chapter or even concept by concept, but learning takes place over time as concepts are integrated and reviewed across multiple lessons through spaced repetition. In Excel Math, we've created a unique Spiraling Process to ensure that students are tested on concepts only after they have been introduced and reviewed multiple times. In addition, the spiraling process reintroduces math concepts throughout the year so the concepts become embedded in a student's long-term memory. In this way, concepts build upon themselves. Remediation is built into the process, so even slower learners are able to succeed with lots of spaced repetition (an integral part of Excel Math lessons). Brainteaser stretches are included throughout the lessons along with creative problem solving and word problems that integrate literacy with math.
No wonder Excel Math classrooms show amazing test results. One teacher from California wrote:
“I cannot express how impressed I am with your program. Our STAR results are outstanding and I am convinced without EXCEL we would be struggling to meet our goals. The spiraling piece that is built in…is what makes this so effective. If I ever move schools and my district does not provide this program, I would purchase it with my own money. Thank you for a wonderful program.”If the unique spiraling process weren't enough, test scores of students using Excel Math are going through the roof! As a teacher from Texas called to say:
“I just had to call you! We used your curriculum for the last two years and our scores were phenomenal. Would you believe, this year both 4th and 5th grade got 100%! The parents love it because it’s consistent. It’s just an awesome program and very teacher-friendly. 7 out of 15 students were commended in my class in TAKS! So, hip…hip… hooray!
And in the studies cited by Doug Rohrer, these results have been shown to work because of the spaced repetition and distributed format of the very intentional spiraling process. As Doug Rohrer points out:
Read more from Doug Rohrer and others at http://www.psychologicalscience.org/observer/getArticle.cfm?id=1953In contrast to the massed-blocked format, a very small number of textbooks use a distributed-mixed format. With this arrangement, a small proportion of the problems within each practice set relate to the immediately preceding lesson, and these practice problems are mixed with the other practice problems.
This distributed-mixed format is exactly what Excel Math uses. Not only does Excel Math repeat math concepts introduced earlier, the concepts are reintroduced and reviewed at regular intervals and then tested after the student has had a chance to learn them over a period of several weeks:
|Excel Math's unique Spiraling Process showing spaced repetition|
In a separate report, Dr. Will Thalheimer gives an overview of research findings on the spacing effect and related learning factors based on more than 100 articles published in journals in the fields of memory, learning, and instruction.
Dr. Thalheimer’s review of this research shows that spacing learning over time produces substantial learning benefits. In his review, Dr. Thalheimer found that spaced repetitions are generally more effective than non-spaced repetitions. Excel Math incorporates the benefits of spaced repetition in its unique spiraling process. Read more on spaced learning and vocabulary at http://www.phase-6.com/what-is-phase-6/scientific-background/spacing-learning.html.
Dr. Thalheimer found that spacing is particularly beneficial if long-term retention is the goal. And of course, long-term retention is the goal in elementary math classes. He discovered that spacing helps minimize forgetting. Real learning doesn’t usually occur in one-time events. Read more on his blog at http://www.willatworklearning.com.
Take a closer look at how Excel Math incorporates a distributed-mixed format with spaced repetition in its spiraling process. Coins are introduced in Lesson 43 of Second Grade Math:
|Excel Math Lesson 43 Student Worksheet|
Then coins are reviewed again two lessons later in the Guided Practice section of Lesson 45:
|Excel Math Lesson 45 Student Worksheet|
After being reintroduced for several weeks, coins are included once again in the Homework section of Lesson 106. This shows just a glimpse of the spiraling process and spaced repetition of concepts found in Excel Math:
Here's what a dual immersion teacher had to say about the unique spiraling system in Excel Math:
“We like Excel because the concepts spiral and increase in difficulty throughout the year. New concepts are introduced every few days in First Grade, instead of daily. We also use _____ program and, while the children like the colorful pictures, it is a very difficult program to use in the classroom, because there is no chance for practice and each page is a new concept taught in isolation."Projectable Lessons.
NOTE: The researchers quoted in this post have not reviewed nor endorsed Excel Math. The teachers who have used Excel Math with their students have endorsed it wholeheartedly!