##### Research

*The National Research Council*

In 2001, the National Research Council, which is the principal operating agency of the National Academy of Sciences, released the findings of an eighteen month mathematics based study. The purpose was to synthesize research on pre-kindergarten through eighth-grade mathematics learning to find what it means to be successful in mathematics and, based on these findings, provide research-based recommendations for teaching, teacher education, and curriculum development. This study identified five crucial components each student needs to use while learning in order to develop mathematical proficiency. These components are conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition. Rooted Facts was developed with these components.

*Conceptual Understanding* occurs when a learner understands the mathematical concept being taught and the relationships the concept has. Rooted Facts breaks the principles of multiplication into smaller, learner-friendly chunks. This significantly increases a learner’s opportunity to know, and understand, the why behind a multiplication fact. This also helps learners recognize the relationships multiplication facts have with each other, which further increases knowledge acquisition.

*Procedural Fluency* is an individual’s ability to carry out mathematical procedures, such as multiplication, quickly, accurately, and efficiently. Not only does Rooted Facts improve student fluency after the use of the program, but learners also increase their procedural fluency during its use as students begin to recognize the various relationships between multiplication facts.

*Strategic Competence* occurs when a learner is able to identify, create, and use different strategies to reach an answer to a mathematical problem. Because Rooted Facts teaches students various chunking techniques to identify the correct answer to a multiplication or division problem, the student also develops a variety of strategies to identify answers.

*Adaptive Reasoning* is an individual’s ability to reason why their chosen answer is correct. Rooted Facts is designed to have this ability develop naturally. For the first four lessons, as students follow the teacher’s direct instruction, students automatically develop a deeper understanding of their taught multiplication and division facts. On the final lesson, lesson five, students are given the opportunity to investigate, explore and discuss all the multiplication items presented on the final Multiplication Guide. By providing this opportunity on the final lesson, this decreases the chance of student misconceptions so when these ideas are presented there is a much higher chance of student success.

*Productive Disposition* is a person’s ability to see themselves as capable of solving mathematical concepts. Because this product was developed in a way that increases the likelihood of any student being able to learn the multiplication facts, regardless of perceived disability, Rooted Facts can improve any student’s belief in their ability to solve problems using mathematics.

*Memory Development*

Memories are the most essential component of learning. Memories store information for us and allow us to recall this information when necessary. In order to develop a memory the brain first uses its sensory functions (such as sight, hearing, speech and touch) to gather information. The brain then analyzes this information through other functions of the brain (including language and reasoning) to organize the information and determine its usefulness. If this information is deemed useful it can then be transferred and stored in our long-term memory.

By focusing on the formation of memories we become better equipped to provide effective instruction. When a teaching method engages multiple functions of the brain (including sight, hearing, speech, touch, language and reasoning) there is an increased chance learning will occur. Rooted Facts is a teaching technique developed to teach both multiplication and division. Rooted Facts utilizes each of these functions of the brain (sight, hearing, speech, touch, language and reasoning) during instruction to improve the likelihood memories will develop.

*Improving Retention*

Memories are the most essential component of learning. Memories store information for us and allow us to recall this information when necessary.. Once a memory is developed it can then be strengthened. When a memory is strengthened it becomes easier to retrieve and lasts for longer periods of time. Memories can be strengthened through recency (how recently the information has been used), frequency (how frequently the information is used), and memory connections (the amount of connections to other memories).

By focusing on the strengthening of memories we become better equipped to provide effective instruction. When a teaching method incorporates recency, frequency, and connections to other memories there is an increased chance of longer retention and quicker retrieval. Rooted Facts is a teaching technique developed to teach both multiplication and division. Rooted Facts utilizes each of these concepts (recency, frequency, and memory connections) during instruction to improve the likelihood memories will be retained.

##### Testing Results

*Click on a link to open the full report*

Elementary Launch – This information provides research from use at a K-5 elementary school.

Middle School – Math Remediation Classroom – This information provides research from use at a middle school math remediation classroom.