Math Classrooms: Deep-Six the Worksheet.

Worksheets have a large environmental and financial cost. Worksheet curation is a major time cost; teacher time that is better spent on lesson planning. Worksheet practice often doesn’t match a student's readiness level. It is time to deep-six the worksheet!

Let me first preface: Students need practice and repetition. In fact I would argue that practice and repetition are even more important in a math classroom than most other subjects. Math is a skill that needs to be practiced daily. To learn to hit a baseball spend time in the batting cage. For math classrooms the worksheet has served as the batting cage. I am in not arguing that we remove practice from our classrooms. I am arguing that we can improve the batting cage.

Let’s first talk about the financial costs of printing worksheets. The average classroom size for the state of Oregon, where I live, is 28 students. Most teachers teach at least five classes per day. If a teacher prints one worksheet per student per day that’s 140 pieces of paper daily. And that’s assuming only one piece of paper per student per day.

28 x 5 = 140

Students attend school 180 days a year. That brings our total to 25,200 pieces of paper.

140 x 180 = 25,200

My local UPS store charges $0.11 for a one sided black and white copy. We will assume our school can do the copies cheaper so we will use $0.10 to calculate the average cost of $2,520 per year per teacher. (I should note that this is an estimated accrual cost that covers paper, toner, and machine usage.)

25,200 x $0.10 = $2,520

Now remember this calculation assumes only one photocopy per student per day. An unrealistically low number. Other estimates put the annual average per teacher closer to 50,000 sheets of paper pushing the annual costs closer to $5,000. Are there better solutions that cost less? The short answer is yes. But first let’s continue discussing other problems with the worksheet because costs are not the strongest justification for deep-sixing the worksheet.

“Worksheets cause learning lag with their implicit bias that favors certain student groups more than others.”

Consider a learning matrix that compares the level of engagement with the the depth of learning. The idea of a learning matrix is to help teachers be cognizant of the scope of learning opportunities that happen in the classroom. Student learning is best achieved when activities are both engaging and have a high depth of learning. (The green area). Creating activities in the green zone is very challenging. To keep the depth of learning high requires that each activity be a strong match for a student's readiness level. A mismatch creates either boredom or frustration which not only affects the depth of learning but also student engagement. However, a strong match to a student’s readiness does the opposite. The psychology of flow suggests that enjoyment and therefore engagement increases when challenges match a student's skill readiness.

“the average [textbook] was created for the average student. The average student that doesn’t exist”

The problem with worksheets is that they have an implicit bias that favors certain student group readinesses more than others. Overall this creates a fairly low depth of learning with a fairly low engagement. Why? Simply the average worksheet, or textbook for that matter, was created for the average student. The average student that doesn’t exist. Think about it this way. Average is a statistical distribution. For some students this artificial average hits the mark perfectly and for those students the depth of learning might be quite high. But for most students it does not. This creates a fairly low depth of learning for the majority. But there is something else even more unfortunate that typically happens.

Learning Matrix with a sample average distribution.

According at a national survey by the Bill & Melinda Gates Foundation only 8% of High School teachers strongly agree that students enter their class prepared to do on-grade-level work.

America’s Teachers on the Teaching Profession: Bill & Melinda Gates Foundation

So what happens is teachers overwhelmingly spend most of their time targeting struggling students. Notice 51% of teachers stated that curriculum and instruction was designed specifically for struggling learners. Average and advanced students receive far less targeted instruction.

National Teacher Survey, Duffett of Farkas Duffett Research Group

“Students need practice and repetition”

All students need to practice, even advanced students. Unfortunately, in many classrooms the traditional worksheet model for practice becomes a tool specifically designed for struggling students. So you might be thinking, why not just give different students different worksheets? Struggling students would be given one worksheet and advanced students another. This seems like a reasonable approach. This type of approach is way to differentiate by content. (There are of course, other ways to differentiate.)

National Teacher Survey, Duffett of Farkas Duffett Research Group

There are a few difficulties with this type of approach. For one, it significantly increases the number of worksheets needed because a teacher cannot always predict how many are needed. Secondly, it increases the time required to prepare for each class and teachers are already overworked. Thirdly, differentiation is extremely difficult to do. 83% of teachers in a national survey reported that they found differentiation to be difficult. The result is that most teachers don’t do it, or don’t do it very often.

I taught in the classroom for 17 years. I have seen many variants regarding differentiated learning and I am strong believer in Carol Ann Tomlisons’ approach to the differentiated classroom. However, the amount of practice time needed to learn math is unique and creates a unique problem. Specifically, differentiation by content becomes extremely difficult. Attempting it comes with an enormous time cost. A time cost that teachers should be using to prepare higher impact learning activities. This is why the worksheet must be deep-sixed.

Technology can replace the traditional worksheet. I founded Ardor Education with this belief and priced it $14.99 a month for all classrooms and all students so it would costs significantly less than printing worksheets.

“When student learning becomes more individualized engagement and learning both increase”

Instead of printing worksheets, students practice math on their own mobile device or a school supplied device (iOS, Android, Chromebook). Ardor automatically differentiates content by skill level. The problems are procedurally generated based on individual performance so every problem closely matches a student's readiness level.

Real-time feedback helps eliminate bad practice habits. When a student gets a problem wrong Ardor will show them how to solve it. I have seen too many students do their homework only to return the next day and realize they did it all wrong. Unlearning can be sometimes even more difficult than learning.

When student learning becomes more individualized engagement and depth of learning both increase. When a student practices at their own skill level there is less boredom and frustration. A teacher will see the results immediately which gives them time and flexibility to adjust lesson plans to help both struggling and advanced students equally. When teachers are not curating worksheets or grading they have more time to create engaging classrooms. Deep-six the worksheet. Give technology a try.

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Matthew Thornton

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Teacher turned software developer and education advocate. Founder of Ardor Education Inc. Worked in Education for over 17 years.