“Mom, Dad, can you help me with my math homework?” For some parents, this question elicits fear, as these parents are openly willing to admit that they never liked math. And then for other parents, they are all too eager to share their own way to derive an answer to math problems that appear to be of concern to their children during homework time.
A parent’s eagerness to help with math homework can quickly be stifled when the child’s response is: “I don’t get what you’re doing. That’s not the way my teacher taught it in class.” What is an appropriate parental response in such a situation? And why would a child ask for help if it is obvious that there is something that he/she understands of the concept? The child apparently knows enough to immediately recognize that the parent's approach is different. What is it that a child is actually requiring of his/her parent?
In classrooms across the country, students are experiencing math in ways that are vastly different from the way in which many of their parents experienced math. In these classrooms, the authoritarian model of teaching no longer exists. An authoritarian instructional method places the teacher at the center of instruction. Math teachers who instruct according to this model typically stand before a class of passive students and demonstrate a particular procedure that can lead to a correct solution for certain types of problems and mathematical expressions, and then, the teachers expect students to replicate the procedures when given a set containing similar problems.
Thankfully, the authoritarian model of classroom instruction is increasingly being replaced with more student-centered models, in which the acquisition of knowledge is understood and practices that fully support deep learning are employed.
In student-centered math classrooms, students are expected to observe problems and decipher that which is being asked of them, and then, they determine pertinent knowledge that they have acquired through previous math experiences that allows them to arrive at reasonable solutions. This expectation encourages students to develop flexibility in the way in which they express numbers and in the ways in which they are able to carry out mathematical operations. They create unique algorithms based on their individual observations, sense of number, and understanding of mathematical big ideas. Their approaches are shared, and students’ methods are questioned and critiqued by their peers in order to ascertain accuracy concerning the interpretation of problems, efficiency of processes, and the reasonableness of solutions. Students talk about math; they share their ideas, regardless of their solutions. Students learn that an algorithm with an incorrect solution may yet be meritorious because of the sophistication of a student’s thinking. And errors also provide discussion of thought which inevitably leads to the clarity thereof.
So what is it that your child needs from you when he/she asks you for help? Your child really seeks to be engaged in a discussion of the idea. Your child wants to be guided by your queries: your curiosity in knowing exactly that which he/she has gleaned from the day’s lesson. In other words, your child refuses to be a passive learner. Instead, he/she is choosing to be questioned, rather than provided answers; and real understanding, rather than shown a procedure that offers no connection of big ideas.
Because student-centered classrooms are learning communities, students approach their studies in mathematics in much the same manner as real mathematicians. Thus, students are asked to expect challenges, but most important, they are asked to consider their responses to challenges. When faced with a challenge, students are asked to examine and reexamine a problem to fully comprehend its aim. After their thorough examination, students are asked to consider possible strategies that would meet the aim as well as the essential information that is to be incorporated in their process. As students construct their algorithms, they are also responsible for being able to articulate the importance and/or connection of each step as it relates to the one preceding it. And finally, students are expected to consider the reasonableness of their results.
As these expectations reveal, student-centered classrooms press students to be active and develop their attention to detail, increase their level of stamina (or commitment to grappling), improve their ability to identify connecting ideas, and grow their ability to communicate their thinking verbally and through the construction of coherent algorithms. Even at homework time, your child wants and needs to be engaged at a level that considers the development of these qualities. Such engagement illuminates the concepts under investigation, making mathematical tasks about thought, rather than simply about “doing.” Sometimes, encouraging your child to return to their classroom learning community the next day with a well formulated question is perhaps the best way to see that he/she is engaged in this way.
The instruction of mathematics is changing, and this change is precipitated by a changing world. A world where thinking or ideas are the most valuable commodities will be the reality of today’s students. With parents embracing this truth by their support of curricula and pedagogy that promotes thinking and creativity, students will be prepared to effectively compete.