Modifying Tasks
It’s important for students to be exposed to high cognitive tasks in the classroom because the tasks hold the possibility of engaging students in the reasoning and problem solving skills, and ultimately the tasks provided for the students decide what the students learn. Any LCD task can be altered to require higher levels of thinking with just a little planning done by the teacher. These alterations help students to make sense of mathematics and learn relationships between mathematical concepts.
Modified Task Example
Original Task (LCD):
Task K
Solve.
38 + ___ = 81
Modified Task (HCD):
38 + ___ = 81
Please solve this problem using two different strategies, and explain your thinking on paper using thought bubbles and pictures/diagrams if needed. Then, write a story problem that corresponds to the equation.
Explanation: In the original problem, the student can perform a memorized strategy to produce the correct solution without thinking about the process or the conceptual ideas of addition or subtraction. By simply asking the student to explain their work, we are asking them to reflect on the strategy they have executed and the reflect upon the underlying concept, which leads to a greater understanding on their end. They are engaging in their work and developing a deeper understanding of subtraction and addition concepts. By making explaining their work and writing a story problem, they are making connections among the representations, which helps them make sense of the math.
Task K
Solve.
38 + ___ = 81
Modified Task (HCD):
38 + ___ = 81
Please solve this problem using two different strategies, and explain your thinking on paper using thought bubbles and pictures/diagrams if needed. Then, write a story problem that corresponds to the equation.
Explanation: In the original problem, the student can perform a memorized strategy to produce the correct solution without thinking about the process or the conceptual ideas of addition or subtraction. By simply asking the student to explain their work, we are asking them to reflect on the strategy they have executed and the reflect upon the underlying concept, which leads to a greater understanding on their end. They are engaging in their work and developing a deeper understanding of subtraction and addition concepts. By making explaining their work and writing a story problem, they are making connections among the representations, which helps them make sense of the math.