Indiana

Education, From The Capitol To The Classroom

Should Teachers Count Off When Students Don't Show Work?

Elle Moxley / StateImpact Indiana

A math worksheet emphasizes the 'partial sums' method of solving addition problems.

A group of Indianapolis parents leading a statehouse push to withdraw Indiana from the Common Core say they wouldn’t have known Indiana’s academic standards had changed if not for the math homework.

“You wait to get the math papers and you wonder what they’re going to do this week because it’s just bizarre,” says Suzanne Sherby. “I definitely think the older kids learned in a much more traditional way, and the little kids just aren’t. It’s not part of the curriculum.”

Sherby told StateImpact her son’s teacher subtracts points when he doesn’t show work she says isn’t needed to solve the problem — for example, a question might ask students to draw objects then cross some out to solve a subtraction problem.

It’s true that the Common Core wants teachers using pictures and other aids to communicate the tenants of basic arithmetic to very young children. But one of the architects who helped write the math standards says kids who are ready to move beyond blocks and drawings — known as “manipulatives” — shouldn’t be penalized if they don’t show all their work.

“Any teacher that says ‘No, no, you must use the manipulatives to show you understand,’ doesn’t understand the Common Core,” says Doug Clements, a mathematics and early childhood education researcher at the University of Denver.

Clements says the Common Core is about getting kids to think conceptually about math — for example, making sure they understand the place values of ones, tens and hundreds. Teachers often do this using units called “Base 10″ blocks. But Clements says inevitably, some students will grasp the reasoning behind the cubes faster than their classmates.

Teachers might end up with “a group of kids or a whole class of kids that can skip the manipulative level or the expanded notation level because they understand it,” says Clements.

He says if a kid is doing the math in their head and can explain their thought process to the teacher, it’s time for them to move on with more advanced concepts within the Common Core. Clements says there’s no script within the standards that says kids capable of doing more advanced math need to continue using manipulatives.

“We got to spread the word that it may be a misconstrual,” says Clements.

Math teachers, what do you think?

Comments

  • Karynb9

    ISTEP “counts off” for students not showing their work in the “applied skills” section. You can answer a problem correctly and still not receive full credit if you didn’t show your work. As long as teachers in this state have to prepare students for a standardized test that requires work to be shown, even for students who have “mastered” the content and may be working a year or two above grade level in the classroom, then teachers in Indiana would be silly to NOT require students to show their work on classroom assignments.

  • http://icebrc.blogspot.com/ A View Through My Eyes

    Showing work is a vital part of the process of learning.

    I have two issues and I’m on my lunch break so I’ll be brief.

    1) While the article is directed at elementary learning, I teach HS chemistry and I care much less about their answers than I do their work. If they can show me they know the process then I know that they are capable of any problem similar to it. Besides, in this golden age of mobile technology they can acquire the answers to some of the most complicated chemistry problems in a matter of seconds (I have several to help grade faster).

    So yes, showing one’s work is part of the process of demonstrating learning.

    2) Following directions is an important and necessary skill. If a student leaves some aspect off of a problem is it because they do not know or understand that part? Or rather is it because, as the person quoted said, they are “beyond” that concept?

    Well, when you have over 160 students to keep track of their learning and abilities it is nearly impossible to identify a student’s intent behind what they did not write.

  • Reaction from a Consultant

    While Number and Operations in Base Ten is emphasized In the CCSS, the worksheet shown is a commercially made one that is part of a math textbook. Place value could be taught in this way or in other ways according to what the teacher chooses. A teacher using Best Practices would teach this particular standard in any number of ways to make sure students with different levels of understanding master the concept. As far as the use of manipulatives is concerned, modeling is a standard. As a classroom teacher of several different grade levels, it isn’t always easy to know if a student truly has mastery. Often they are overconfident or don’t want to take the time to visually or kinesthetically explore the concept. Good points are made below in the comments. The process is important and the ISTEP+ Applied Skills test calls for students to show work. Having said that good teachers differentiate and should enrich those students having true mastery and plenty of experience with modeling. This is not a Common Core State Standard issue but more of a methods issue. Many things are being blamed on the new standards that have more to do with textbooks and teacher presentation than they do with the new CCSS.

  • ferrarabar

    In the elementary grades I would like to see students learning good habits. Showing work is a good habit. I teach Honors Algebra to 8th graders – in general the ones that show their work are the ones that get the higher grades. I would prefer they showed the work, even if they can do it in their head. Then, when they make a silly mistake I still know that they know the process that was being taught.

  • I-man’s dad

    I am a person whose hands can’t keep up with my brain. I miss more problems showing my work than not. Inevitably, by the time I write something down, I’ve forgotten the idea I started with. I have argued with math teachers all of my life about this. The argument always comes back “you can’t do that without writing it down”. To a great degree, when I really have the concept, I’ve been able to. I’ve known others that are the same way and some even better. Don’t ask me for a rough draft of a paper or to diagram a sentence. I’m a performer, ready for the stage now. There aren’t a great many of us out here, BUT we are here! The best coaches know that if you’ve got somebody who CAN, you sometimes have to let them go.

  • April C. Holloway

    Just sharing my reflective thought on that article. :)))))

    Habit phrase: “Show your work.” (Translation: write down what I expect you to write)

    Maybe a better phrase to convey the idea is: “Record your thinking.” The latter phrase supports the 21st Century Learning skill of communication. If you’re brilliant and you work for NASA, you need to be able to record your thinking to convey your math to Lockheed (and vice versa). Blast from the past story below…. :))))

    http://articles.latimes.com/1999/oct/01/news/mn-17288

  • highshoolmath

    It is my understanding that the PARCC test will require students to show their work and use of manipulatives. If this is true it would be a disservice to students to not require them to do this on a daily basis. As a high school math teacher, we are charged with teaching the communication and notation aspects of mathematics – showing work is critical – in reading and writing mathematically, demonstrating mathematical knowledge and in helping to see structure and connections across concepts and content. I am less concerned about the answer than I am with the mathematical process. The answer will be the natural by-product of the mathematics used. Showing work can also help students to identify common errors and misconceptions and what areas they need to work on. This is essential when making the transition from operations with numbers to operations variables.

  • frustrated

    My second grade daughter uses Everyday Math Common Core Edition and it’s as if the teacher is following a script and there’s no exit. All children MUST show all work and move at the same pace. Last week our Everyday Math homework gave four double digit math problems under the instruction of “practice” so our daughter used mental math and answered the questions. Her argument at home was that she wanted something harder and was tired of doing it the “baby way”. Even though her answers were correct she was marked wrong and the teacher wrote, “I realize B can do these BUT the third grade teachers will INSIST she show her work.” Last year was the same, even though the school acknowledged she was good at math, she still had to do homework with tally marks. Why wasn’t common core written with an option for the top 25%? The school has tested her 4 times on a national test and she continues to score in the 99%, but each day she is tested with the class on subtraction problems under 10 i.e.:10-7. I doubt the school will listen to Mr. Clements and I have little hope for third grade.

    • http://icebrc.blogspot.com/ A View Through My Eyes

      This is exactly why I am not in favor for grouping students based purely on age. Grouping should be based on ability first. I was a product of the tracking era and I believe it is the only way to give proper attention to students’ individual abilities.

      “Differentiated instruction” is bull and is not a realistic solution for the variety of skill levels that may be in a classroom.

      • frustrated

        When I asked our school about the opportunity for harder math I was told the teachers do “differentiated learning” in the classroom. The reality is all the kids complete the same homework, move at the same pace and take the same tests. There’s nothing different about it!

  • minho

    Don’t show work

  • Orangesforluxembourg

    This is upsetting. As a child, until 10th grade, I prided myself on not needing any sort of help – no calculator, no scratch paper, no back of book- and I was always several grade levels above all of my contemporaries. While I managed to enter high school with the best math entry test levels in my county (without using any calculator or scratch paper on a test that allowed both), I was ousted from algebra 2 honors in 10th grade because of not showing my work. To me, to show work was to show that you needed to work outside of your head and that you didn’t get it enough. Actually sometimes I couldn’t understand how one could arbitrarily insert work when the solution appeared so naturally from the equation. Anyways after getting kicked out of the only math that was halfway compelling to me, I basically stopped caring about classes and formed a drug dependency. I would love to see the taskmasters take the inanity out of showing that one can perform calculations.

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