Mike started a good conversation about assessment. My definition of assessment is the process of gathering information on a student. What you are gathering should give a overall picture of what the student knows about a particular unit or outcome. Types of assessments can be summative assessments such as unit tests and term assignments, or formative assessments such as quizzes, homework, and the completion of daily work. Only summation assessments are for marks because formative assessments are designed to help students master the outcomes. I believe that evaluation is the process of a teacher assigning a grade to all the evidence that has been gathered. Student input should be welcomed in designing rubrics and setting due dates, but overall the teacher uses their professional judgment to assign a grade. Exactly what you are assessing is determined by the outcomes that the students are trying to achieve.
In Thursdays class much of the conversation centered around assessing students work who do not have good computer skills, and recognizing that for some students in takes more time. Luckily for me I do not have to assess computer skills, as I am a math teacher. Certainly a students math skills, and computer skills are not mutually exclusive but when assessing a students work I try to mark fairly, with an emphasis towards mathematics competency. In fact when I use the computer lab with the math class it is often an exploratory activity whose sole purpose is to aid in future discoveries. As such, the work that we do in the lab is purely formative. Students that can demonstrate an ability to problem solve with technology usually seem to demonstrate the same ability without technology so the techies are not at a disadvantage. The line becomes a little more unclear in my Applied Math 20s class. Here students use a graphing calculator every day. My focus over the last few years has really shifted away from evaluating the students ability to use the calculator, to the students ability to do math. Before I used to teach calculator now I teach math. Although many of my questions require the use of the calculator, my assessments require a high level of cognitive demand. Rather than asking a traditional regression question and having the calculator do all the work, students are required to think and extend beyond what is written on the screen. Students have to collect really world data, and perform the appropriate regressions that make sense. I seldom use the variables x and y and prefer variable such as height and time, or population and year. These variable have more meaning, and extrapolating with real world variables is more useful and easier to understand. Stats Canada has a lot of real world data that can be easily incorporated into meaningful lessons. The essence of algebra is not x!
Students who are not tech savvy should not be punished in a math class, but there are certain procedures that they have to become familiar with. In a similar fashion students who are tech savvy should be allowed to demonstrate their technological ability, but they should only be assessed on their mathematics ability. Math teachers should not be tempted to overuse technology and have students making videos, and electronic presentations. Let’s leave video editing and PowerPoints to the technology (and English :)) classes, and let the technology teachers assess those products in relation to the ICT framework.
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Interesting, Paul. Do you find that the calculator or certain software helps when students compare, for example, changes in the values of slope or intercept? Do you find that students like being able to see in seconds the effects of varying m or b? I think technology has it's place in the math classroom, but I, like you, want students to understand the mathematics. What is annoying is to hear a student say, "the calculator said so." You are right about the essence of algebra... it's not x... it's "y!"
ReplyDeleteSounds like you have good handle on assessment/evaluation & calculator/technology use in math, Paul (although I can think of some useful ways to use presentation software, etc in math). One of many issues with applied math was that it often seemed (in some classrooms)to be more about what buttons to push to get a result than about the math concepts. Graphing calcs/software can be a great aid to animate, discover, inquire and analyze... but the focus, as you state, should be the math!
ReplyDeleteI am starting to feel sorry for poor x, once the darling of math, it is now the unwelcome guest... :-)
Assessment will always generate scads of conversation - probably because of its ambiguous nature. That is, how do we know if we are assessing fairly or accurately? If a student earns 100% on all unit tests and suffers from examphobia (an inability to write or perform well on exams), is that student no longer a 100% student. Just look at what the provincial exam does to the marks of many a student. Authentic assessment (or assessment by triangulation) is a fair more practical approach to getting, as you have so eloquently stated, an overall picture of what the student knows.
ReplyDeleteTo me, technology and math are intricately related. Math is a form of technology. It is a human creation which assists us on many levels whether it's physics, engineering, etc.
ReplyDeleteI like how you are getting your students to "think beyond what is written on the screen." That taps into students' right-brain/creative thinking, which is what separates us from the calculators.
This, though, leads to another assessment problem: Students need to communicate their thinking to the teacher, beyond just the correct answer on their calculator. So is the teacher assessing their math skills or their communicative language skills? I struggled with this issue when I taught grade 4: My math tests were tied so closing to reading skills: The better readers were able to understand the problems, and the better writers were able to share their understanding on paper. Was I really assessing math skills or ELA skills?
This is where technology can assist, as students can use multiple ways of expressing their math understanding, even if they are not the strongest writer/drawer/speaker.
I wish I had calculus teachers like you in university! I never understood what a parabola was until a teacher recently told me to imagine a giant salad bowl. It's great when skilled teachers are able to make concrete what appear to be very abstract ideas.