Solving the Fractions Challenge. Fractions are hard to teach and difficult for students to learn. At the same time, fractions are a pivotal topic in mathematics education.
Fractions are the earliest topic in school mathematics where educators agree that students fail and teachers struggle to instruct. This is why we chose fractions as the first area of endeavor for Conceptua Math. “Difficulty with fractions (including decimals and percents) is pervasive and is a major obstacle to further progress in mathematics, including algebra.” (National Math Advisory Panel, 2008.) This challenge is understandable as fractions present major conceptual leaps for students. Consider these factors:
Fractions can describe many different things, including parts of a whole, parts of a set, time, and length.
Sophisticated reasoning is required to evaluate any fraction. Students must analyze the relationship between two numbers in order to understand a single value, and recognize that the real value of a fraction is dependent upon the unit, or whole, of which it is a part.
Fractions operations can be multi-step and abstract. Addition and subtraction can require multiple steps, while multiplication and division are too abstract for many people.
Fractions present a plethora of new terms for students to master. Terminology like numerator, denominator, equivalent, common, uncommon, proper, and improper can confound students, especially students who are struggling with reading.
Provide concentrated time with our supplemental lessons. Instructional time is a key to success, and every instructional minute is precious. Using our lessons, students successfully complete as many as 90 problems in 30 minutes. Students experience success with instruction that unfolds logically and adapts to their level. The concentration of successful interactions builds synaptic connections and sets the stage for success.
Use visual models to progress from concrete to abstract. From the very first NCTM Standards to the current work in Singapore Math, educators have consistently agreed on the value of moving from concrete manipulatives, to pictorial representations, to abstract numbers. Our lessons start with the visual models and the language, and then lead students to understanding fractions and solving number problems.
Provide language-rich instruction and feedback. Math is largely about words! Yes, 3+4=7 is written in a universal language, but when you start talking about common denominators and equivalence, you need to help students make sense of these terms. Conceptua Fractions' lessons use visual models and spoken text to build this understanding in a meaningful way.
Differentiate instruction with formative assessment. For every main lesson in a unit of study, we have produced three supplemental support lessons for students who struggle! Every time a student fails a skills check, the software prompts them to raise their hand and ask the teacher for advice. You, the teacher, have instant access to student work and can make a re-assignment within 30 seconds!