I have typically given assessments with both calculator questions and no-calculator questions. I've reasoned that students ought to know how to do a few things without the use of a calculator. (maybe we should say technology now instead of a calculator) Now I've reevaluated my opinion. I've changed over to the idea that all my questions on any assessment should be allowing the use of technology. Why? That is a question I hope to answer for you.
1. Change the question if you think they can solve it with technology too easily. You will find it probably wasn't a good question in the first place. I like to change my "too easy with technology" questions to be reversed. Example: Change....Solve x^2-4x-12=0 to be this...Create a quadratic equation to have solutions of x = 6 and x = -2.
2. Technology is a great way to reinforce answers. My tests often have this as the directions. Solve using algebra, and verify your answer using technology. Justify your work. Or even simpler, solve in two ways.
3. No Calculator questions strip the students of their best and most visual resource: THE GRAPH. What No Calculator questions do is get students to forget that GRAPHING is a GREAT way to solve almost anything. Don't we want to encourage graphing? I don't mean graphing by hand either. I mean a really fast way to analyze a problem. Are we discouraging graphing because that is too easy? When we take that away from students that is a major loss for their problem solving skills.
4. My assessments are changing. I no longer have 30 questions on a test. I given less computational questions and more conceptual questions. I have fewer questions which will help my students focus in on the difficult ideas. They often have to show answers in multiple ways. I'm always asking them to explain WHY did you do something. The questions are a little more challenging and need to be able to use technology to solve.
5. Technology is NOT CHEATING! Solve this problem. 3x + 5 = 23 How about graphing? We have two lines and they are intersecting. This is a system. Maybe y= 3x + 5 and y = 23. Then find the intersection point. Is that cheating? I think the way to give this question is to ask students to solve this problem by graphing and algebra.
6. A student without technology is often asked to find an answer a certain way. It might even have only one way to solve it. I think this takes the creativity away from a student. It also causes them to be fearful of not making a mistake because they can't even check it with other methods.
7. What about the argument that we need to have our students get better at computational math skills? I AGREE. However, I don't think that a student with good computational math skills equals a complex math thinker.
8. I'm going to give more messy number problems. Technology allows us to give our students weird numbers. We should be doing that on most of our questions. Messy numbers actually will encourage them to understand what is happening. (By the way, have you ever been asked by a student if the answer was wrong because it had a decimal in it?)
9. Having students use or not use technology is not going to change their number sense during an assessment. I think we have to promote number sense in many ways during our classes. But I don't think we should force them into manual calculation during an assessment. I also don't think that a bunch of calculations by hand will change their number sense too much. It will probably just build the hate they already have for math.
How about you? What do you think about having "no calculator" questions on your assessment? I'd love to hear from you.
8 comments:
I agree with you 100% and I've made many of these changes to my assessments that you are talking about. Having said that, I keep coming back to the fact that many colleges and universities are not allowing calculators on tests (this is what I hear from many of my former students). I worry that my kids are not going to be prepared for that. Thoughts?
I understand the fear. I guess that I justify doing the best for the students that I think right now. I hope that their use of technology will give them good problem solving skills for when they get to those classes. I want to do my best for my students right now. However, I worry too.
I completely agree with you as well! I definitely think we can challenge students in other ways besides taking the calculator away from them. My classes consist of all skill levels, so I can't say to my advanced students you can't use it and to my struggling students you can. Therefore, I let them all use it and like you said, change the way I ask the question. The ONLY class I may have no calculator questions on a test is for Precalculus, in order to prepare them for AP Calculus and college courses. Until this changes, I do feel I have to prepare them for what's to come.
Well said. I don't agree (yet), but you make a good argument for it. You seem you have made it work so that the technology leads to greater understanding. I would be concerned that in a lot of classrooms, the ability to always have a calculator would mean less work for students and less understanding.
Thanks for your comment Jim. I loved the "yet" part of your comment. I think we are all evolving. I don't see this issue as you have to take it or leave it. But an issue than we can continually adapt our assessments to be more technology friendly. But I know that this issue is not going away.
Greetings to All,
I'm a teacher of Senior Mathematics (Years 7 - 12) in Australia. I found your post very interesting, but there are some points I disagree with. My main concern is twofold:
1) Technological solutions can show a limited degree of understanding - showing only that the student knows how to use the technology, not apply the mathematical concept. For example, many of the graphing calculators can also do direct solutions, using syntax such as solve().
2) If questions are designed such that a direct technological solution (such as using solve() or simultaneous solution graphing), it is difficult to determine the reason that a student was unsuccessful. Were they unable to use the mathematical technique? Were they unable to interpret the question context?
Finally, facility with solving mathematics on pen and paper has a (theoretically) greater potential of developing mathematical fluency.
This is an interesting view. I have always assumed no-calculator questions encouraged the students to prove they could solve it without help, but I really like the idea of changing the question to one that they can't answer with technology such as having them create a problem that has a specific answer rather than find the answer. With technology become such an important part of our world and students wanting to use it more and more, I do agree that telling them they are not allowed to could feed a negative view of math. I think it would be good to have questions that the students couldn't use technology to answer, but to design them in such a way that a "no-technology" statement is not needed.
:) Decimal answers are surely wrong and so are whole number answers when working out slopes. What year do your students start using graphing calculators? In my high school, a few students in Y11 and some students in Y12 use graphing calculators. Also our Y11 Algebra test is a non calculator test which causes a few upsets, especially to lower able students who relied on it to work out fraction problems and similar.
Does your high school use external assessments as well? If so, how dies your "asking conceptual questions approach" relate to assessments not created by you or your department? Sandra (Hamilton, New Zealand)
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