10,000 Kicks: Practice in the Mathematics Classroom

  • 10,000 Kicks: Practice in the Mathematics Classroom

    By Tim Hickey July 18, 2016 —

    “The best way for a student to get out of difficulty is to go through it.” —Aristotle

    “I fear not the man who has practiced 10,000 kicks once, but I fear the man who has practiced one kick 10,000 times.” —Bruce Lee

    “Mastering a skill requires a fair amount of focused practice. . . . It’s not until students have practiced upwards of about 24 times that they reach 80-percent competency.” —Robert Marzano, Debra Pickering, and Jane Pollack in Classroom Instruction That Works (2001, p. 69)

    “There is a consistent progression to the lessons of . . . champion teachers. . . . It’s best described as I/We/You. . . . Others use the terms direct instruction, guided practice, and independent practice.” —Doug Lemov in Teach Like a Champion: 49 Techniques that Put Students on the Path to College (2010, p. 71)

    My name is Tim Hickey. I teach math, and I give my students worksheets. In a way, it feels like confessing a sin to say it. Modern edu-culture frowns on the worksheet for its inability to engage students and its inauthentic, out-of-context existence. And yet, the best teachers I know give their students worksheets. Why? I would point to three reasons.

    First, practicing math problems provides students with the opportunity to improve their math skills. This simple, common sense statement is rooted in historical pedagogical tradition (see Aristotle quote above), evident in other arenas of life (see Bruce Lee), and supported by leading educational researchers and authors (see Robert Marzano and his colleagues as well as Doug Lemov). So I give worksheets. Let me be clear that students need an overall balance between out-of-context practice and authentic, applied problem solving. But the latter cannot happen without the former. I have written in my past five blog posts here on the value of project-based learning and integrating technology into the mathematics classroom, and I believe passionately in the value of both to engage students and enrich their lives. But, to use a basketball analogy, you’re more likely to make a free throw in a game if you’ve spent hours doing it in practice.

    Second, teachers are busy. We have a perpetual list of a thousand things to do, and if we can get through a few hundred in any given day, then the job is well done. That is just the reality of teaching. Giving my students a worksheet gives me the chance to get through my day with my sanity intact. Not every lesson can possibly be 3D printing and real-world modeling, nor should it be. Giving worksheets every day is lazy; however, giving them strategically is practical and pedagogically sound. We all know that many teachers burn out early in their careers. If giving the occasional worksheet allows a great teacher to stay in the classroom longer than a handful of years, then that is a net win for students. I would note that I have crafted some of my best future lessons on days when I have carved out planning time for myself because I just gave a worksheet in class that day. The long-term gain was worth the short-term expediency.

    Third, practicing math problems fosters joy and inspiration in students. Seriously. The better one is at math, the more fun it becomes. To be sure, students can practice in a variety of ways. For instance, the attached Black and Gold worksheet requires students to work together on product rule and quotient rule. And I do believe that highlighting to students the specific ways that they have improved their math skills (e.g., “You’ve worked so hard at dividing fractions this year, and it’s really paying off!”) is crucial, because fostering metacognition in students is key to developing their growth mindset. But some form of practice for students is required in the mathematics classroom.

    Worksheets provide practice, practice leads to improvement, and improvement is fun and inspiring. So go ahead and give that worksheet. Your students will be just fine, and so will you.

    2016-05 Hickey picTim Hickey is a Nationally Board Certified Teacher and the math department chair at Monticello High School in Charlottesville, Virginia.

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    Constantino Jose Machado de Sousa - 6/3/2017 4:22:25 PM


    '' Every nation will be unhappy as long as it does not educate its children '' ... and '' being educated is the only way to be free. ''
    "The interdisciplinary study room from elementary to university Professor Paulo Freire, located at the Polyvalent State School II, Getúlio Vargas neighborhood in Bagé - RS, coordinated by Professor Constantino de Sousa, presents to all lovers of knowledge his established methodology of teaching partner Individualizing. '' Teaching is based on lessons and informal discussions where students can help one another. Living and learning together is an important part of the already successful studies in our teaching laboratory.
    Our method of teaching is called Logarithmic Learning, which means that if a student can solve a problem, he explains it to another and then these two to two others, these four to four others, and so on. Thus "N" students learn to solve problems in (logN) '' in base 2 '' STAGES. ''
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    What is the Earth Charter?
    The Earth Charter is a statement of fundamental ethical principles for building, in the 21st century, a just, sustainable and peaceful global society. It seeks to inspire all peoples to a new sense of global interdependence and shared responsibility aimed at the well-being of all ...
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     RUA IBRAIMA VAZ, 50 (PO Box, 126)

    ZIP CODE. 96415-540 / Bagé / Rio Grande do Sul / Brazil
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    Email: constantinosousa@uol.com.br



    John Golden - 7/23/2016 12:04:39 PM
    I think about this a lot and am glad you shared your thoughts. I've never done martial arts, but my son who found it challenging just got his first dan in TKD. He went from not being able to repeat what people did to knowing long complex forms. I think what we are practicing matters. Practice a kick to make it fluent and automatic. There aren't many topics in math that are similar to me. I want my students to practice number sense, representation, problem solving and communication. Finding work that is meaningful to them. Many or most worksheets fall short on these things. But the structure of a worksheet is helpful, and more so the less the students are ready for autonomy. ... So I'm still learning.

    Cindy Morris - 7/22/2016 5:03:11 PM
    I'm interested in the Black and God worksheet requiring students to work together on the product and quotient rules. I do not see the attachment mentioned.

    Natalie Perez - 7/20/2016 4:40:52 PM
    I have seen worksheets used in both a strategic, "learn from you mistakes" manner and in a horrific "do the following 50 problems silently" manner. The worksheet isn't the problem, it's how the worksheet is used in class that makes it either an asset or detriment to a student's experience with mathematics. Seems like you are using them in a good way.

    Brian Lawler - 7/18/2016 6:24:12 PM
    The logic of practice is sound when the goals of mathematics education are assimilation and performance. For me, these are the exact goals why most of the society is turned off from mathematics. This focus is strongly on getting children to know and perform the discipline, instead of a stronger (if not total) focus on the child's mathematical activity. Or, to be more careful with my words, what we as mathematicians would name as mathematical in our observations of the student.