The “Dichotomies Underlying Difference Stances in Mathematics Education” chart interested me a lot. I think both of sides are important, and I do not think that math teaching is either conservative or progressive. Even though understanding, sense-making, and exploratory are significant, fluency, absorbing and applying facts are also crucial. A student is not expected to do multiplication or division effectively if he or she is not able to memorize multiplication chart fluently. Also, some of the math concepts required by other subjects may be too hard for the students to understand at their current level, so the only way will be to present the topic and have them understand latter in advanced math courses. Another point that stopped me is that “rather than trying to cover a larger number of mathematical topics in a given time, Dewey advocated the development of high quality mental processes and a scientific attitude”. My inquiry topic is on how to foster mathematical thi
Thanks for this thoughtful unit plan, Yijia!
ReplyDeleteRationale: Very good
Project: Good idea. I think you will need to find some really intriguing examples for students to explore though if you are to hold students’ interest for a two week project. If it’s just plugging numbers into a conversion equation (F to C, for example), there may not be enough to keep them interested. On the other hand, if they need to be able to derive that relationship, and work it in both directions, that might be more interesting — and even more so if they have to add degrees Kelvin into the mix. Similarly, if they are looking at currency conversions, you might want to ask them how to go in both directions, how how to convert among three or four currencies (in all directions) etc.
Generally, it will be helpful if you can offer the students guidance towards worthwhile and sufficiently interesting/ challenging topics that will get them thinking about linear relationships in real life.
Assessment: OK. Where does the project fit in with this assessment plan though?
Unit elements: Hmmmm — there are some topics that are given too short a time, and others that are given too much time here! For example, the fourth lesson, ‘return quiz and discuss about the progress’, would only take about 10 minutes, but you only have 4 substantive lessons to teach everything about linear relationships — and it will take your students longer than that to learn this unit!
Does this topic include lines (their slopes and intercepts), intersection of lines, transforming linear relationships into the slope-intercept or standard form, etc.? If so, there are not really equations to solve, as these are relations (y=mx+b), not equations in one variable. I am not quite clear what your overall sense of the unit topic is, and you should check your perception with your SA to make sure you are covering the topic thoroughly!
Lesson #1: Activity: This activity is a very simple one (y= 2x). It’s a reasonable start for exploring linear patterns, but it is certainly not enough for a whole lesson (or a 20 minute activity!) I also think it’s not necessary to give candies out for this simple activity, and the scenario with the candies does not allow for much variation to explore different kinds of linear relation patterns (like, say, y= .5x + 7, or y = (-8)x - 3). Don’t shortchange your students by oversimplifying the math or assuming they need to be bribed with candy!
Example: What is the example? You haven’t provided it here.
Generally, this is a good topic with lots to explore, but you have only given the very simple candy example here, so I don’t have a sense of where you are going with this. It sounds to me like you are trying to oversimplify things, but your students will be ready to take things further, and will likely be bored with just y=2x.
Lesson #2: The example from the textbook on air temperature (which you haven’t given, but which I can…extrapolate!) seems like a good one to explore, especially with the proviso that you can’t extrapolate air temperature into space! Perhaps you could start by extrapolating to a more reasonable altitude, then try out the ‘space’ example.
ReplyDeleteActivities: The water use question is a good one. I suggest you put together 3 or 4 similar questions on a variety of interesting topics and get students to work in groups on one of them, using research to create linear relations that describe the situation they are working on. Good integration of sustainability topics with math.
Lesson #3: Good! The example of the cruise ship’s fuel consumption is a good one. Which relationships are you planning to have your students make tables and graphs of? Can some of them include a b (a constant that changes the y-intercept)?
The activity drawing a picture using linear relation equations and Desmos or GeoGebra (and/or pencil and paper) is a fun one, and students can also create a puzzle for another group (giving them a set of equations and having them graph them to draw a surprise picture).
Overall: Good start on a unit overview. You have some interesting examples (but need more), some interesting, involving activities and a good flow. I see the need for more work with your SA to make sure that you really are covering the topics included in this unit, and to make sure your estimates of timings for each of the lessons in the unit makes sense.