I've been looking through the CME Precalculus book and I think its wonderful.

I was just given precalc to teach, and while I've taught Alg1, Alg2 I've never seen, or can't recall ever having been taught or asked to consider the way some of the stuff in this textbook is presented.

I think some of the ways they have introduced things is very interesting, ie complex numbers as an introduction and standard used throughout as a means of working with Trig identities. I've never seen it before, and I understand what is happening mathematically; I also know that I'm not sure how to teach it.

The work CME provides is a good start, but only for students really prepared for that level of material. My students lack many of the skills and the confidence which comes with them, to drive the discourse. In my school we've discussed the issue of students cramming for assessment, without really learning the material and we agree it is an issue that needs to be fixed. We've been working on this issue, and slowly it is being addressed, but this is a systemic issue - not one fixed easily.

As I've been working through the material, I've though how great it would be if a textbook publisher was clever enough to take advantage of the potentials of social media and how it could be a great resource, for the educators who perhaps haven't seen this material (in this way) or for whom such mathematics was 20+ years ago.

If there were a weekly/biweekly chat, a chat room or a means of connecting with other teachers using this material I know it would make me even more strongly interested in using it. (granted this might require engaging the teaching community in a more personal way than most textbook manufacturers currently do it). Recruiting and advertising should occur fairly locally as many teachers who aren't very -social media savy do speak with other teachers at least locally.

One more thing.... Textbook manufacturers MUST consider making and perhaps offering resources (as in free, gasp) to help teachers remediate key skills in mathematics, especially at the secondary level, though not exclusively. Had I known I was teaching this class, I would have actually spent much of the summer looking at the curriculum. (which I do recognize is not universally standardized, which makes a social media solution better than a one-size fits all)

I know that there are many teachers who use no textbook at all. I actually went 90% of the way there in Alg1 and Alg2. I also know that there are teachers who go page to page in the book. (and by way of full disclosure I think I know one of the contributors).

I'm not yet ready to make really good decisions about how to teach this. A popular addition to many textbooks is the student goal section. I bet teachers would like to see the "necessary skills list" in addition to a series of activities or examples as good as those explaining the necessary content.

I've got friends in the #MTBoS who help with this, for me. Textbook manufacturers needs to plan on enticing teachers like me as well as ones for whom that hashtag thing is a mystery, or just plain silly.

I was given a recommended pacing and curriculum (which was simply all the (+) standards) and told to"go" partway through the marking period.

Already I see concerns with the curriculum. Vectors with Logarithms? Complex with matrices?

## Wednesday, November 27, 2013

## Sunday, November 24, 2013

### Sequence and Series Cards

I made a set of sequence cards over the summer and while I knew then that I wanted to use them to help students with sequences I didn't know exactly how I planned on using them. I shared them on twitter with a few ppl, but got no suggestions on how to use them.

On Friday as I had just completed working with Arithmetic and Geometric sequences with 2 of my classes I decided that I wanted my students to work on writing explicit and recursive equations, so I had the students break themselves into small groups (3-4 students max) and I gave each group 1 (of the 5) sets of 8 equations.

Here is where it got fun. First, the students cut out the cards and placed them face-up on one of the desks. Then I had them choose 1 card to give away (group 1 to 2, 2 to 3... 5 to 1). So they gave away their hardest sequence. Then I let 1 person from each group take 2 cards from another group (this time 5 from 4, 4 from 3, ...) Now that the cards were exchanged, and a little attitude distributed to the groups we were ready.

I gave the groups 10 minutes to find both kinds of equations for each of the sequences. The time limit assured that it was unlikely that 1 of the students could do this while the rest of the group watched (I hate that ).

I took a set of cards myself and shuffled them. After the 10 minutes had passed I started randomly choosing sequences and rolling a die to choose which rule I wanted (explicit or recursive). If a correct answer was given the group picked a representative to throw a bean bag for a chance to get up to 3 points for the upcoming quiz.

Next time I need to find a way to make sure more groups get a chance to play (the first hour I did this, one groups got 4 chances to throw the bag and 2 groups didn't get called on at all). I will do this by limiting the cards in my own shuffled deck (12 instead of the full 40 cards). I will also make sure to keep the warm-up to just the 5 mins its supposed to take and spend less time on the previous day's homework so the time for this activity is greater.

Still, it was a great lesson.

On Friday as I had just completed working with Arithmetic and Geometric sequences with 2 of my classes I decided that I wanted my students to work on writing explicit and recursive equations, so I had the students break themselves into small groups (3-4 students max) and I gave each group 1 (of the 5) sets of 8 equations.

Here is where it got fun. First, the students cut out the cards and placed them face-up on one of the desks. Then I had them choose 1 card to give away (group 1 to 2, 2 to 3... 5 to 1). So they gave away their hardest sequence. Then I let 1 person from each group take 2 cards from another group (this time 5 from 4, 4 from 3, ...) Now that the cards were exchanged, and a little attitude distributed to the groups we were ready.

I gave the groups 10 minutes to find both kinds of equations for each of the sequences. The time limit assured that it was unlikely that 1 of the students could do this while the rest of the group watched (I hate that ).

I took a set of cards myself and shuffled them. After the 10 minutes had passed I started randomly choosing sequences and rolling a die to choose which rule I wanted (explicit or recursive). If a correct answer was given the group picked a representative to throw a bean bag for a chance to get up to 3 points for the upcoming quiz.

Next time I need to find a way to make sure more groups get a chance to play (the first hour I did this, one groups got 4 chances to throw the bag and 2 groups didn't get called on at all). I will do this by limiting the cards in my own shuffled deck (12 instead of the full 40 cards). I will also make sure to keep the warm-up to just the 5 mins its supposed to take and spend less time on the previous day's homework so the time for this activity is greater.

Still, it was a great lesson.

## Monday, November 18, 2013

### Testing day MADE for MATH

Today I'm giving my Pre Calculus students a test (on matrices and rational expressions) and while going through my standard testing procedure checklist I rattled off my warning speech. I made the first part up about 10 years ago and added a second part to it a couple years back. The students find it amusing and each trimester many of them try to memorize it.

Here goes...

Here goes...

*You may “look down in concentration”*

*Or up for inspiration*

*You may not, however, look to either side*

*Or behind you out of desperation*

*To do so means I will draw a pretty circular illustration (on the top of your page)*

*And you get to deal with your parents’ frustration*

*And consternation.*

*Alternatively, if you are struggling with stressful perspiration*

*And are led into plagiaristic temptation*

*You may find yourself on academic probation**And suffer familial humiliation.*

I had not planned to post this, but the students in my 3rd hour class insisted and I figured it might make a quirky made for math Monday posting.

## Friday, November 8, 2013

### It took me too long to figure out MTBoS #5

That my job should be all about getting kids from utter frustration, feeling like they just can't do it, to convincing them that they can (even if it appears to me that its unlikely). If I don't at some point make a student have to look at math differently, not just a student, but every student, then I'm not what I want to be as a teacher.

It's at that point, when math looks strange is where growth in our subject occurs.

The difficult, woefully ill prepared, students give us this opportunity the most. I know I need to get better at engaging them. I want them to know, I want them to see and experience what I see in Mathematics. I'm trying different things with different groups of students. We'll see what comes of it.

Thank you, to the whole #MTBoS. I'm better than I was and I will be better than I am. I joke with my students that when I retire the tech in my classroom will be so magical that I won't ever want to leave. I know that the real magic is the kids. You all have helped me see that. If I'm following you, please know it is because I'm in awe.

For the peeps doing the chats I attend, know you're among the very best. #statschat , #precalcchat , #MSMathchat , #Alg2chat .

It's at that point, when math looks strange is where growth in our subject occurs.

The difficult, woefully ill prepared, students give us this opportunity the most. I know I need to get better at engaging them. I want them to know, I want them to see and experience what I see in Mathematics. I'm trying different things with different groups of students. We'll see what comes of it.

Thank you, to the whole #MTBoS. I'm better than I was and I will be better than I am. I joke with my students that when I retire the tech in my classroom will be so magical that I won't ever want to leave. I know that the real magic is the kids. You all have helped me see that. If I'm following you, please know it is because I'm in awe.

For the peeps doing the chats I attend, know you're among the very best. #statschat , #precalcchat , #MSMathchat , #Alg2chat .

### Station activity -sequence and series. Afterwards

The NSPIRE activity was definitely the most problematic. Students struggled with how to manipulate the activity as well as how to get started, though interestingly enough one group told me they thought this one was their favorite because the calculator sort of walked them through the activity and all they had to do was observe and discuss.

The teacher led activity included 4 sequences to discuss and figure out. I was surprised how difficult it was to hint and cajole a small group 3-4 students, through the material. I know that at times we all want to just scream out the answer is 4 (or whatever) but it really is much more tempting with a smell group sitting there looking truly lost. Fibonacci's sequence was the first one, with n^2 and n^2+1 beefing the second and a hybrid fraction geometric and arithmatic for the last. I wish the second one had been first and that I had primed them by asking them to use blocks to build out each of the terms in the sequence.

There was a worksheet station in which students were required to I'd each set of numbers as arithmetic or geometric or neither and in hindsight I wish I had left that worksheet for the lower groups, but had a more accelerated one for groups ready for more of a challenge.

I had two groups in which members browsed on the IPADS, thus making it difficult for the next group to get started right away. Fortunately given my proximity to that station I know which students were not on task and write ups and phone calls will address the issue (both students, have previously been addressed about being off task previously).

I still think the teacher led station could be reworked so that I am not tied down and busy the whole time. I do have write-ups from the students, but its not the same as actually observing where students struggle.

The teacher led activity included 4 sequences to discuss and figure out. I was surprised how difficult it was to hint and cajole a small group 3-4 students, through the material. I know that at times we all want to just scream out the answer is 4 (or whatever) but it really is much more tempting with a smell group sitting there looking truly lost. Fibonacci's sequence was the first one, with n^2 and n^2+1 beefing the second and a hybrid fraction geometric and arithmatic for the last. I wish the second one had been first and that I had primed them by asking them to use blocks to build out each of the terms in the sequence.

There was a worksheet station in which students were required to I'd each set of numbers as arithmetic or geometric or neither and in hindsight I wish I had left that worksheet for the lower groups, but had a more accelerated one for groups ready for more of a challenge.

I had two groups in which members browsed on the IPADS, thus making it difficult for the next group to get started right away. Fortunately given my proximity to that station I know which students were not on task and write ups and phone calls will address the issue (both students, have previously been addressed about being off task previously).

I still think the teacher led station could be reworked so that I am not tied down and busy the whole time. I do have write-ups from the students, but its not the same as actually observing where students struggle.

### Station activity - Sequences and Series - Before

I like the concept of station activities. I truly do, but preparing one is nothing less than an exercise in frustration and just darn tiring.

Admin decided that since stations work so well in ELA that math should be doing them regularly as well. I know people have blogged about this topic before Julie at I speak math being the quintessential example. But the department chair (and presumably the administration) have made it clear that station activities should look a certain way. ie. technology enhanced station, a teacher led station (forget about being able to help stuck groups).

enough complaining...My goal here is to actually blog before and after and see hwo I do at predicting how things will go.

The unit we are covering in Algebra 2 is sequences and series. our stations include 1) identifying arithmatic vs geometric sequences (and differences and ratios) 2) finding the sum of an infinite geometric series (on the NSPIRE) 3) a teacher led station on "neither" sequences such as squares and Fibonacci and the two I worked on 4) having students find the rule for sum of angles of a regular polygon and # of triangles formed from a vertex of a regular polygon (both done through the use of geogebra and IPADS) and 5) a hands on station in which students will tie knots in a rope and measure how the length changes.

Students will rotate in small groups around the stations interacting with the activity and, hopefully, the mathematics which ties all of these mini-lessons together. At the end they will turn in a single page which has a space for work from each station as well as a short response question at the end.

I already know that the NSPIRE activity will likely be a problem. I've found that the students frequently find the NSPIREs complicated and manipulating the buttons and sliders is not as easy as it *should* be.

I'm hoping that being tied the whole time to a single lesson isn't frustrating as I know that normally I would prefer being able to move around the room assisting or just observing.

Check back later for the details on how things went...

Admin decided that since stations work so well in ELA that math should be doing them regularly as well. I know people have blogged about this topic before Julie at I speak math being the quintessential example. But the department chair (and presumably the administration) have made it clear that station activities should look a certain way. ie. technology enhanced station, a teacher led station (forget about being able to help stuck groups).

enough complaining...My goal here is to actually blog before and after and see hwo I do at predicting how things will go.

The unit we are covering in Algebra 2 is sequences and series. our stations include 1) identifying arithmatic vs geometric sequences (and differences and ratios) 2) finding the sum of an infinite geometric series (on the NSPIRE) 3) a teacher led station on "neither" sequences such as squares and Fibonacci and the two I worked on 4) having students find the rule for sum of angles of a regular polygon and # of triangles formed from a vertex of a regular polygon (both done through the use of geogebra and IPADS) and 5) a hands on station in which students will tie knots in a rope and measure how the length changes.

Students will rotate in small groups around the stations interacting with the activity and, hopefully, the mathematics which ties all of these mini-lessons together. At the end they will turn in a single page which has a space for work from each station as well as a short response question at the end.

I already know that the NSPIRE activity will likely be a problem. I've found that the students frequently find the NSPIREs complicated and manipulating the buttons and sliders is not as easy as it *should* be.

I'm hoping that being tied the whole time to a single lesson isn't frustrating as I know that normally I would prefer being able to move around the room assisting or just observing.

Check back later for the details on how things went...

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