RESEARCH




Rationale
Research Tied to Rationale:
As I have been teaching fourth grade, I started to see that the knowledge of math facts was crucial for success in fourth grade math lessons. There was no time for doing facts on a paper, referencing a
multiplication chart, or counting on fingers. The students were expected to know facts immediately for their new, current lessons. After reviewing data from my two fourth grade classrooms, I averaged the students’ multiplication timed test scores and ranked each student in order from highest to lowest averaged scores.
* 8 out of 23 students received a 75% or less on two multiplication checkpoints
*students were relying on pictures and manipulatives to do multiplication and division
*many students in my class were struggling with two by two digit multiplication because they didn't know their one digit by one digit multiplication
*12 out of 23 students answered fewer than 30 multiplication problems correct on a three minute timed test
I started teaching one by two digit and two by two digit multiplication and the students were getting the one by one digit multiplication problems wrong, so that resulted in the whole problem being incorrect. Students don’t like to take the time to figure out every single fact when the problem is 67 x 94. The students would get frustrated when it took them 10 minutes to do this problem, and other students a very short amount of time because they knew their multiplication facts. After I noticed their test scores and their overall attitude about multiplication, I knew it was something that needed to be worked on within the classroom. I would tell the students to practice their facts at home with flashcards, but the results of our three minute timed test every month showed that they weren’t really practicing. After talking with teachers at my school and my CADRE associate, I knew that I needed to focus on multiplication automaticity for about 12 of my students. It was my hope that they would become automatic by the time we got to the end of fourth grade.
Setting individualized goals really tends to get my students motivated so I thought with a program like Rocket Math students would be more motivated to pass their goal everyday. They also love being able to track their progress on our monthly three minute timed tests so I knew that they would enjoy seeing their growth through Rocket Math daily.

Students first took a writing probe test. They were asked to copy as many numbers as possible in one minute. Depending on how many numbers they were able to write, a corresponding goal was set for the number of problems the student should be able to complete on the placement probes and one-minute tests.

The students circled their individualized goal number on this provided sheet. This showed them how many problems they should get correct one the one-minute tests.

This is an example of the progress-monitoring single-digit multiplication timed test that we took every two weeks.

Students first took a writing probe test. They were asked to copy as many numbers as possible in one minute. Depending on how many numbers they were able to write, a corresponding goal was set for the number of problems the student should be able to complete on the placement probes and one-minute tests.
Strategies
Research Tied to Strategies:
For years, educators have emphasized the importance of creating a sense of automaticity when it comes to basic mathematical skills. Many researchers even conclude that establishing fluency in basic
multiplication facts serves as a foundation for application of mathematical concepts later in education (As cited by Codding, Chan-Iannetta, Palmer, & Lukito, 2009 in Smith, Marchand-Martella, & Martella, 2011). Despite the many reasons to improve fluency in basic multiplication facts, investigations of different curriculum programs to improve multiplication automaticity are ongoing. A substantial amount of time, effort, and money is put into mathematics education each year because mathematics is one of the core academic subjects taught in the United States. Fluency of basic mathematical facts is important in daily life along with later math education and reaching automaticity in basic multiplication facts is the first step to becoming a successful mathematician. Without mastery of basic multiplication facts, students spend so much time trying to perform a range of complex tasks to reach the correct answer that it often leads to errors in procedure (Woodward, 2006). Lack of fluency can impact the ability for students to acquire more complex skills and conceptual understanding by increasing the amount of time consumed in learning (As cited by Wong & Evans, 2007 in Rave & Golightly, 2014). It is important to ensure practice time at the elementary level because students who have not achieved fluent automaticity of basic facts by the end of fifth grade, will not have frequent, structured, opportunities to adequately develop that automaticity in later grades (Steel & Funnell, 2001).
In Rocket Math, students learn two facts and their reverses on each worksheet in a carefully controlled sequence which enables mastery at an individualized pace. Cooke and colleagues found evidence in practicing math facts to automaticity, “suggesting that greater fluency can be achieved when the instructional load is limited to only a few new facts interspersed with a review of other fluent facts (1993, p. 222). By focusing on a very small set of new target facts, no more than two facts and their reversals, instruction on this target set can continue until the student can retrieve the answers to automaticity. One strength of the Rocket Math program is the use of immediate peer provided feedback. When students do not know an answer in three seconds or less, they are given the answer by their peer. By doing this, the student is reminded of the answer and then gets more opportunities to practice “remembering” the fact’s answer. This technique is effective for two reasons. The time allowed for students to answer the fact ensures that they are using memory retrieval rather than using strategies to figure out the answers. Second, if the students fail to remember the fact, they are immediately told the answer and asked to repeat it.(http://www.rocketmath.com/p/about-the-program.html) It becomes clear to students that the point of the task is to “remember” the answers rather than continue to derive them over and over. Rocket Math allows students to establish a mastery learning paradigm, where small sets of facts are learned to high levels of mastery, before adding any more facts to be learned (Crawford, 2000). The learning is occurring during the “practice” time. Correspondingly because the timed tests are only over the facts already brought to mastery, students are quite successful. Students see their success in small increments because they are able to track their own progress. When students are seeing progress towards their goal, they are establishing a direction for their learning (Marzano, 2001). Under these circumstances, students are successful and enjoy graphing their progress on regular timed tests. One minute timings then assess when students are ready to move to the next set of facts. (http://www.rocketmath.com/p/about-the-program.html) Goal checking is also a process of self assessment and self evaluation, which creates more confidence and an improvement of attitude (Bystrom, 2010).
Building mathematical fluency is important for many reasons. First, mastering basic multiplication facts is essential to higher order skills, such as problems that are completed in algebra and calculus, which require automatic recall of basic facts. Second, when students build multiplication fluency, they are more likely to feel comfortable participating in class discussions about mathematics because they are more motivated and put forth more effort. Third, students who are able to respond automatically typically have less anxiety and are able to maintain the skills longer. The use of Rocket Math will work to build mathematical fluency at an individualized pace and therefore will reduce anxiety in students when it comes to mathematics. Lastly, students who are not fluent in basic multiplication skills tend to rely on time consuming strategies that prevent them from completing problems in an efficient manner (Smith et. al, 2011). While contemporary methods of math instruction have begun to de-emphasize the importance of fluency and have focused more on problem solving and concept development, there is a lack of focus on memorization of basic multiplication facts (Smith et. al, 2011). Unfortunately, this lack of focus on multiplication memorization through fluency building in general education has led to negative effects on students’ mathematical success in higher education (Smith et. al, 2011).
References:
Bystrom, A. (2010). The Impact of Daily Multiplication Fact Review. Retrieved July 16, from
http://scimath.unl.edu/MIM/files/research/Bystrom_AR_FinalDraftLA.odf
Cooke, N. L., Guzaukas, R., Pressley, J. S., Kerr, K. (1993) Effects of using a ratio of new items to review items during drill and practice: Three experiments. Education and Treatment of Children, 16(3), 213-234.
Crawford, D. (2000). The Third Stage of Learning Math Facts: Developing Automaticity.
Retrieved from http://www.rocketmath.com
Marzano, R. J., Pickering, D., & Pollock, J. E. (2001). Classroom instruction that works: Research-based strategies for increasing student achievement. Alexandria, Va: Association for Supervision and Curriculum Development.
Rave, K., & Golightly, A. F. (September 06, 2014). The Effectiveness of the Rocket Math Program for Improving Basic Multiplication Fact Fluency in Fifth Grade Students: A Case Study. Education¨†134¨†4, 537547.
Smith, Christina R., March and Martella, Nancy E., Martella, Ronald C. (2011). Assessing the effects of the rocket math program with a primary elementary school student at risk for school failure: A case study. Education and Treatment of Children¨34(2), 247-258.
Steel, S., & Funnell, E. (2001). Learning multiplication facts: a study of children taught by discovery methods in England. Journal Of Experimental Child Psychology, 79(1), 37-55. doi:10.1006/jecp.2000.2579
Woodward, J. (2006). Developing automaticity in multiplication facts: Integrating strategy instruction with timed practice drills. Learning Disability Quarterly¨,29(4), 269-289. doi:10.2307/30035554