The Need to Make Homework Comprehensible
By Matt Larson, NCTM PresidentNovember 15, 2016
Whether you are an elementary, middle level, or high school teacher, you are likely to have had parents say to you that they can’t help their children with their math homework. At the secondary level, the difficulty is often the content itself; at the elementary level, however, it is often a function of parents’ unfamiliarity with the instructional strategies that we use today to build conceptual understanding.In recent years, as new standards and instructional strategies have been implemented at the school and classroom level to build students’ conceptual understanding in addition to helping them meet traditional procedural fluency goals, parental concerns about math homework, particularly at the elementary level, have increased. Social media provide a new vehicle by which parents rapidly share examples and express their concerns about math homework and instructional strategies that they find confusing or unnecessarily complicated.A recent report from the Fordham Institute, Common Core Math in the K–8 Classroom: Results from a National Survey, found that 85 percent of teachers reported a decline in parental reinforcement of math learning at home because parents do not understand the way that mathematics is being taught in school. This is an overwhelming percentage!This issue is not new. Mathematics homework has long been a conundrum for students, teachers, and parents alike (see NCTM's Homework History Research Brief and Clip). Today some teachers, schools, and school districts are going so far as to limit or even ban homework in certain grades. To some degree, this is part of a historical cycle in the United States: homework falls in and out of favor every 15 to 20 years. Clearly, however, for many parents today, it is a hot topic that we need to address more effectively.Despite these calls to reduce or ban homework, most math teachers continue to assign it because we recognize that success—whether in mathematics, music, or athletics—depends on at least two common components: practice and perseverance. Too many adults, and students for that matter, tend to view success in mathematics as dependent on a talent that someone either is or is not born with. Several highly regarded researchers, including Carol Dweck and Jo Boaler, have demonstrated that this simply isn’t the case. Each and every student can learn more mathematics in the same way that an athlete improves his or her running time or a musician masters the technique required to play a piece of music—by receiving appropriate and effective instruction in a supportive environment, by responding to feedback, and by expending effort—trying again and again, while using different strategies—in short, by engaging in meaningful practice.
However, as the Fordham Institute report recommends, we need to make the practice that goes home as straightforward and comprehensible as possible for parents. And we need to recognize that while we may discuss multiple solution methods in class, the goal is not for students to practice and master multiple methods; rather, it is for students to practice and develop proficiency with their preferred, well-understood, and most efficient method. Making homework comprehensible means, in part, that we need to be responsible for the types of tasks that we send home. Many of the instructional and homework tasks that frustrate parents reflect instructional strategies used to develop student understanding of underlying mathematical concepts. For example, in the fourth grade, an open array model for two-digit multiplication can illustrate partial products, place value, and the distributive property. However, sending home practice that requires students to solve multiplication problems by using an open array may not be advisable, because this approach is likely to be unfamiliar to many parents.Finally, we need to show parents the solution strategies that we are using in the mathematics classroom. Evidence suggests that once parents are shown, engaged in thinking about, and come to understand the strategies in use, their support increases. NCTM has a number of resources that can support parents in understanding school mathematics today, including the recent publication It’s Elementary: A Parent’s Guide to K–5 Mathematics, which offers clear explanations of many of the instructional strategies that parents may not have experienced when they were in school themselves.As mathematics teachers, it is our responsibility to share with parents the instructional strategies that we use in the classroom and make the practice that we send home comprehensible so that parents can engage with their children in constructive ways and support their mathematical learning.
A little late to this ocnversation...
Phil Daro once suggested that homework should be used largely to help students' develop confidence that they can successfully do mathematics independently, and that this is especially important for students who struggle with mathematics. Worth considering. It requires some additional thought about the kinds of tasks students are doing for homework.
As a persuasive and responsible mathematics teacher we know the importance of homework in mathematics. Perhaps,most students devote more time in mathematics than in other many subjects.Doing mathematics largly involves doing homework.One of the importance of homework in mathematics lies in its role of individual attempts made by each students to solve problems(routine or non-routine).Most of the homeworks are done by students at their homes.We know that homeworks can be effectively, timely and meaningfully done under the guidance of teacher or superior elders or parents as mentioned by Vygotsky's sociocultural theory. The task of most available scaffolding to do homeworks for students at their homes can be provided by their parents if they can be supported with appropriate resource materials which could help them to understand school mathematics (at least to some extent as needed by them). As mentioned in president's message, appropriate resources could be developed to support parents so that they would be in positions to support their children at least to some significiant extent.For this, there should be live and frequent interactions between schools and parents.If this could be done to some remarkable extent, popularization of mathematics can go ahead simultaneously.Such situation needs to be followed by huge changes in school mathematics curriculum which lend itself to various needs and demands.
Well stated, Matt! I think part of the challenge is ensuring that teachers are aware of the purpose behind developing multiple solution methods to engage students with different learning styles. Too often I see teachers trying to get ALL their students to learn ALL the solution methods, or hear them saying things like, "This is the way we are supposed to do multiplication now." When we can make students, teachers, and parents all aware of the importance of teaching/learning mathematics in a way that effectively balances conceptual understanding and procedural fluency, we're on our way to effective mathematics instruction.
Family Math Nights are excellent opportunities to share with parents new content and strategies that are being used in mathematics.
I agree that assigning homework that is incomprehensible to parents doesn't make sense but sending home meaningless drill sheets can be just as frustrating for the parent and child. Developing a relationship with parents is critical if you want to bing them on board with new and innovative ideas in math.
I had to go to You-Tube to get the gist of the idea of using an array to multiply 2-digit numbers. The student has to add four numbers which are each a product of 2 simpler numbers. This a probably a better method than the old pencil & paper system, especially when all work is done on a laptop.
The question is: Is the student going to always do multiplication this way? What if he/she forgets how to set up the problem using the array?
"To some degree, this is part of a historical cycle in the United States: homework falls in and out of favor every 15 to 20 years. Clearly, however, for many parents today, it is a hot topic that we need to address more effectively."
The swing this time includes inovations using technology. This study by SRI_Education showed that by boosting teachers reach into the home using a tool to support their individual homework assignments students learned more. If parents know that their child's teacher will be responding to the homework in new innovative ways they may become more connected. https://www.sri.com/newsroom/press-releases/rigorous-sri-study-shows-online-mathematics-homework-program-developed
However, sending home practice that requires students to solve multiplication problems by using an open array may not be advisable, because this approach is likely to be unfamiliar to many parents.
I have a real problem with this statement especially coming from the president of NCTM. So, because Parents don't understand we should stop asking the children to understand on their homework? No. This issue is all about parent education. Every classroom teacher needs to think and plan education events for their parents starting at the beginning of the year and continuing throughout the year. We have parents doing 19th century math and children doing 21th century math. Of course there is a disconnect.
What I mean is we should not send home practice and "DICTATE" the specific strategy that students are required to use. I certainly agree that we should expect to have students do things parents may not have experienced themselves in school. I have long been an advocate that we need to use instructional strategies that are current, up-to-date, research-informed, and at times unfamiliar to parents.
"And we need to recognize that while we may discuss multiple solution methods in class, the goal is not for students to practice and master multiple methods; rather, it is for students to practice and develop proficiency with their preferred, well-understood, and most efficient method."
YES! This is something that I continue to try and help teachers and parents understand. We want students to try these methods that we introduce, but it is not expected that they master all of them. The goal is for them to discover a strategy that makes sense to them and will allow them to be successful.