Science behind Lymboo Math's "Enhanced Learning"

Lymboo Math is rooted in the findings of the best research in cognitive and pedagogical sciences. Insights into effective learning and retention strategies have shaped the structure and content of Lymboo Math. As a result, Lymboo Math promotes independent learning, fosters critical thinking skills and ensures long-term retention of knowledge.

Differentiated & Adaptive Learning + Mastery Learning + Interleaved & Spaced Learning = Enhanced Learning

Differentiated Learning
    Students in differentiated classrooms have better learning experience than those who are not and are more excited about their work. [1]

Differentiated instruction, is the process of "matching a student's level of existing knowledge, readiness, and interests with teaching and learning methods to achieve his or her maximum growth as a learner." [1] Therefore, differentiation is an organized, yet flexible way of proactively adjusting teaching and learning methods.

An important part of differentiated instruction is determining what students already know so as not to cover material students have mastered. The goal of pre-assessment or diagnostic test is to determine a student’s knowledge and readiness prior to study.

Lymboo Math Implementation

Lymboo Math students begin the program with a comprehensive diagnostic test designed to gauge their existing knowledge. A comfortable starting point ensures the early successes that are so crucial to building self-confidence. A confident child is motivated to be a self-learner and will eventually succeed in the program.

The student performance on diagnostic tests (and subsequent periodic assessments) allow teachers to know their students and their needs, in order to tailor effective teaching and learning strategies and interventions to maximize student achievement. Lymboo Math's consistent program review and diagnosis of whole-class and individual student performance provides ongoing feedback to not only teachers, but students and parents as well!

Adaptive Practice
    Recent studies have shown that adaptive learning can increase student achievement rates by 15%! [2]

Children are virtuosos as learners and they have an immense appetite for knowledge. They also have diverse instructional needs. While a diagnostic test sets the stage for an effective teaching and learning strategy, adaptive practice endeavors to transform the learner from passive receptor of information to a collaborator. [2] An adaptive learning system adjusts to the student's learning needs, which result in a better and more effective learning experience.

Lymboo Math Implementation

Lymboo Math is a personalized and adaptive learning program that keeps pace with a child's learning requirement. The objective of Lymboo Math program is to provide them the tools they can use to become independent learners, and eventually excel and thrive.

The comprehensive and rich curriculum and the unique practice structure, combine to make Lymboo Math the most effective math enrichment program on the web. The program provides students with ample opportunities to master the concepts, and keeps track of their strengths and weaknesses. Comprehensive tracking mechanism ensures that students never miss a concept and weaker concepts are brought back in to practice when required.

Mastery Learning
    The average mastery learning student was above 84% of the students learning through conventional instruction. [3]

Every child can learn if provided with appropriate learning conditions. Learning for mastery or mastery learning, as coined by Benjamin S. Bloom, when adopted in classrooms has shown to reduce achievement gaps between varying groups of students. In Mastery learning, "the students are helped to master each learning unit before proceeding to a more advanced learning task" [3] in contrast to "one-size-fits-all conventional instruction".

Lymboo Math Implementation

Lymboo Math curriculum emphasizes gradual learning to promote deeper understanding of math concepts and to build proficiency. Students learn the basic concepts first. Once students attain mastery of a topic they progress to advanced topics along strict prerequisites-based curriculum. The curriculum introduces various mathematical concepts from different perspectives to help students gain valuable insight and appreciate math.

The hallmark of mastery is the ability to comprehend a problem and recognize and apply the skill(s) necessary to solve it. To accomplish this Lymboo Math incorporates problems from four different categories: basic, applied, critical thinking, and problem solving.

Lymboo Math basic problems help the student grasp the fundamentals of a math concept. Students learn them well through daily practice assignments. All the assignments are timed and students are required to demonstrate proficiency – as measured by LyQ score – before progressing to the next topic.
Understanding & Applying

Lymboo Math introduces concepts from multiple perspectives to help students recognize underlying patterns and solidify their understanding. The curriculum is replete with word problems, which train the students to comprehend a real world problem and map it on to the math realm.

Analyzing, Evaluating, Creating

The critical thinking and challenging problems in Lymboo Math curriculum enable students to hone their skills of careful reasoning and analysis. Students are challenged to extend their prior knowledge and independently come up with smarter solutions, faster!

Interleaved & Spaced Learning
    Students using interleaved practice performed 43% better on tests than those using focused practice! [4]

Mastery learning emphasizes gradual learning and students must demonstrate proficiency in a concept before proceeding to advance topics. While this process promotes mastery, it does not directly address long-term retention of knowledge. Insights from recent research in Cognitive Psychology [4] has shown that interleaved & spaced practice increases the ability of students to learn and retain all kinds of knowledge. Interleaved practice, sometimes also known as spiral review, involves working on multiple skills in parallel. Block learning, on the other hand, focuses on mastering a single skill at a time.

Researchers have shown that interleaved practice forces the brain to bring the appropriate knowledge into working memory for every practice problem. This causes the pathways for those memories to strengthen and allow for better retention. Additionally, recalling multiple skills forces the brain to focus more intensely and this leads to better retention.

Interleaved practice also magnifies the Spacing Effect. Students' performance on tests was found to be superior when they practice mixed skills spread over multiple sessions instead of just a single session. [4]

Lymboo Math Implementation

The unique structure of Lymboo Math provides continuous reinforcement of learned math concepts throughout the program. While daily practice assignments provide ample practice to promote mastery of a concept, it's the periodic and progressive spiral review assignments that ensure long-term retention. This combined methodology makes it less likely for students to forget what was learned, and also diminishes the need that those concepts be retaught in later years.

The composition of review assignments, by their very nature, enhance context-switching skills and reinforce a child's understanding of math concepts.

Daily Assignments
Daily practice assignments provide the rigor and the discipline necessary to thoroughly understand and learn a concept.
Unit Spiral Reviews
While daily practice assignments promote mastery of a skill, it's the periodic unit review assignments that 'cement' the learned concepts and improve short-term retention.
Stage Spiral Reviews
Stage review assignments challenge the students to recall a variety of concepts learned over a longer period of time, thereby promoting long-term retention.

[1] Differentiated Learning
  1. , Start where they are: Differentiating for success with the young adolescent, Pearson Education Canada, 2008.
  2. , Differentiated instruction: The effect on student achievement in an elementary school, Eastern Michigan University, 2007.
  3. , Differentiated assessment strategies: One tool doesn’t fit all, Corwin Press, Thousand Oaks, 2005.
  4. , Fulfilling the promise of the differentiated classroom: Strategies and tools for responsive teaching, Association for Supervision and Curriculum Development, Alexandria, VA, 2003.

[2] Adaptive Practice
  1. , Adaptive learning environments and e-learning standards, Electronic Journal of eLearning, 2004.
  2. , Cognitive scaffolding for a web-based adaptive learning environment, ICWL, 2003.
  3. Adaptive Learning. Wikipedia.

[3] Mastery Learning
  1. , Flip your classroom: Reach every student in every class every day, ISTE, 2012.
  2. , Closing achievement gaps: Revisiting Benjamin S. Bloom’s “Learning for mastery.", Journal of Advanced Academics. 19, 8-31. 2007.
  3. , Developing talent in young people, Ballantine Books, 1985.
  4. , The 2 sigma problem: The search for methods of group instructions as effective as one-to-one tutoring, Educational Researcher, 1984. PDF
  5. , Taxonomy of educational objectives, 1956.

[4] Interleaved & Spaced Learning
  1. , Why interleaving enhances inductive learning: The role of discrimination and retrieval, Memory & Cognition, 2013. PDF
  2. , Interleaving helps students distinguish among similar concepts, Educational Psychology Review, 2012. PDF
  3. , Using spacing to enhance diverse forms of learning: Review of recent research and implications for instruction, Educational Psychology Review, 2012. PDF
  4. , The effects of interleaving practice, Applied Cognitive Psychology, 2010. PDF
  5. , Tests enhance the transfer of learning, Journal of Experimental Psychology: Learning, Memory, and Cognition, 2010. PDF
  6. , The shuffling of mathematics practice improves learning, Instructional Science, 2007. PDF