My Numeracy students are now about a month into their ALEKS experience. I started all students out on the third grade standards level (the lowest ALEKS goes), and on average, my students scored around 50% mastery on their initial diagnostics. At this point, some of the students have completed level 3 and are onto level 4, and many others are close to completing the level. There are the stragglers too, of course. I'll do more detailed stats later on. The goal I've set with students is that they should try to complete 3 entire levels by the end of the year (i.e. 3 years of growth in math ability). I was skeptical at first, but after seeing how the students interact with the program, I have much more hope. ALEKS is not a creative, fun, snazzy program. Essentially, students get a sample problem to try. If they don't know how to do it, they read an explanation and try again. When they get a certain type of question right 3 or 4 times in a row, without asking for help, the concept is added to their pie chart. Periodically, they are re-assessed by the program, and concepts they no longer know are pulled back out of their pie chart.

I have been impressed by how self-reliant the students are being. They are managing to read the explanations and figure out the problems on their own. Some students are really getting into it, and are bragging to each other about how much of their pie they have completed. They have also figured out that getting a problem wrong, or clicking on the "explain" button causes the program to require more correct problems to add the concept to the pie. For that reason, they are actually trying harder to get the problem right the first time. The immediate feedback has been very helpful for the students. My favorite moments are now at the end of class; sometimes, when I tell students they need to log off, a few will be like "oh wait, let me just get this one last problem so I can add it to my pie".

Right now, I am just assessing them on time spent on ALEKS - not on the actual amount of progress being made; it seems to be effective enough, and the whole point is to allow students to work at their own pace. We'll see if I need to modify that policy in the future.

On a different note, we have been working on bar modeling to solve word problems every class for 15-20 minutes. I assigned the first problem set as homework last week, and I graded them this weekend. They were quite bad. It's always a bad feeling when you realize your students are a lot farther behind than you thought. I've pushed ahead into more complicated problems, but I just realized that many students are still having trouble with the basics. That's ok.. we'll just cycle back to the beginning and have another go at it.

In Algebra 2, we've started in with the basic idea of logarithms, using the Big L notation I wrote about in an earlier post. I think it is working well. We have been focusing on the similarities between roots and logs: in a root, the index tells you the exponent, and you are looking for the base. In a log, the subscript tells you the base, and you are looking for the exponent. Last year, many students had trouble in power expressions determining when to use a log or a root; I think they will have a much better understanding of it this year.

Graphing Tangent and Cotangent

1 day ago

## 6 comments:

We used your "Representational Fluency" functions worksheet for Algebra II in class today, and it was

veryeffective. Thanks!Hi Hanna,

I'm glad it helped! I love me some good representational fluency!

Let me know if you come up with any good modifications of additions.

We've used the worksheets on Translations and Transformations too (still working on the last one), and these have been immensely helpful in breaking up a very dense chapter in the textbook. The distance between where the students are and what the textbook does is pretty huge, and we'll be looking for a new text at Asilomar this year. Meanwhile - thanks for making these great materials available! I'm nervous about seeing the copy count for this month, though... Have likely gone over the limits of the Math Dept copy budget.

Glad you're back and writing again. Have a restful break.

Your graphs are done in Sketchpad, no? How do you do the open/closed circles at discontinuities in the graphs of piecewise functions?

No, I do them in the Grapher app that comes with OS X. Unfortunately, I haven't found a program yet that does open/closed circles well. I actually do them by hand - just create a tiny circle object, and copy and paste it around. I just save some parent graphs, and then retool them as needed for further examples. You may want to look into GeoGebra to make graphs also. It's free, anyway. If you ever find a good solution to this, please let me know!

Thank you so much!

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