As I was traveling for the entire past month (33 days away from my bed!) I had to watch from the sidelines as everyone nabbed deals left and right. But now I'm home and I get to seek out the deals that everyone has been boasting about finding! Today I browsed the dollar bins of Target and found a few worthy buys.

Top Left: Scissor Bin. Teaching geometry results in a good amount of cutting out shapes. Last year I got a couple diner style baskets for scissors and protractors but the scissors would be easier to grab standing up. Now there's a free basket for something else, like the markers.

Top Right: Dry erase markers and pom poms. In a few #made4math posts (starting here) people attached pom-poms to dry erase markers so kids would have built in erasers. I'm planning to give everyone a page protector with a piece of graph paper inside. Hopefully we'll use them throughout the year to do a variety of things and I'll get to try some of the white boarding activities I hear so much about.

Bottom Right: Since many of my students forget pencils, I supply golf pencils. The kids hate that they are short; I love that they come pre-sharpened, are way cheap and that the kids dislike them so much that they leave them behind. However, there's the drawback of no erasers. 16 erasers for $.99 is a great deal, I may even leave a few out rather than hiding them away in my drawer for only the most desperate of erasing situations.

Bottom Center: Silly erasers. They are hamburgers and hot dogs. I have a basket of random little prizes that I give out when we play review games.

Bottom Left: Sticky graph paper! Not sure exactly what I'll use it for, but it was too cool to pass up.

Center: Self inking "Great Work" stamp. I have a gold star stamp for A's on the first attempt, and a funny little clock guy that says "take you time" for kids who need to resubmit. This one can be for improvements. Love that it's self inking.

Less than $20 for the haul, which is impressive since there are 10 dry erase markers in that pack. Too bad I don't trust kids enough to give them refillable markers (love love love my AusPen markers).

## July 30, 2012

### Made for Math: fiddle toy

At PCMI one evening activity was to make a rhombic dodecahedron flip cube. It looks as crazy as it sounds! I didn't make it to the event (can't remember if I was at soccer or letting my brain recuperate/catching up on twitter) but I got the materials and made my own last night/this afternoon.

The template is here. Print on cardstock, attach contact paper and cut them all out.

Score the interior lines (only way to get crisp folds), fold up and tape (they gave me clear contact paper to use as tape, easier to cut to size).

My next steps were: tape together in ways that would lock it closed, stare at the design, ask my brother for help (who looked at me like I was crazy) and finally decide that after midnight was not the time to think about how to make this work.

By the time I got around to puzzling over this again, @roughlynormal had come to my rescue and posted these instructions (pdf) with pictures!

And the final result is:

I don't know yet if I will let my students play with this one all the time, but I do think that having some small flip cubes (made of 8 cubes, tape in the same spots) around is a great idea. I have a terrible time sitting still, I can't even watch tv without something to occupy my hands (there is silly putty on my coffee table for days I don't feel like crocheting). I would like to encourage students to find quiet ways to fiddle and use their extra energy so their brains are free to focus. Do you have a favorite fiddle toy for you or your students?

The template is here. Print on cardstock, attach contact paper and cut them all out.

Score the interior lines (only way to get crisp folds), fold up and tape (they gave me clear contact paper to use as tape, easier to cut to size).

Yes, those are lady bug scissors. I've had them since I was learning to write my name (it's very shakily there on the name tag in all caps). |

My next steps were: tape together in ways that would lock it closed, stare at the design, ask my brother for help (who looked at me like I was crazy) and finally decide that after midnight was not the time to think about how to make this work.

By the time I got around to puzzling over this again, @roughlynormal had come to my rescue and posted these instructions (pdf) with pictures!

And the final result is:

I don't know yet if I will let my students play with this one all the time, but I do think that having some small flip cubes (made of 8 cubes, tape in the same spots) around is a great idea. I have a terrible time sitting still, I can't even watch tv without something to occupy my hands (there is silly putty on my coffee table for days I don't feel like crocheting). I would like to encourage students to find quiet ways to fiddle and use their extra energy so their brains are free to focus. Do you have a favorite fiddle toy for you or your students?

## July 17, 2012

### Google Forms

In the past couple days I've built a google form, learned the differences between multiple choice and check boxes, gotten some submissions, re-written the questions and linked entries from one spreadsheet to another so the final product is somewhat user friendly. While the initial process was complicated, I now feel rather confident that I can use Google Forms and I'm looking forward to using them with my classes throughout the year.

That's where you come in:

Have you used Google Forms at school? How did it work? What types of forms are useful? What pitfalls should I watch out for so next time this doesn't take so many steps?

My hint: if you use checkboxes, make the text for each box concise! Everything next to the box will show up in your spreadsheet and it's hard to scan. The extra line underneath the question is a great space to put all the wordy stuff if your options need explanations.

Can't wait to hear your ideas!

That's where you come in:

Have you used Google Forms at school? How did it work? What types of forms are useful? What pitfalls should I watch out for so next time this doesn't take so many steps?

My hint: if you use checkboxes, make the text for each box concise! Everything next to the box will show up in your spreadsheet and it's hard to scan. The extra line underneath the question is a great space to put all the wordy stuff if your options need explanations.

Can't wait to hear your ideas!

## July 14, 2012

### PCMI: Week 2

Another mind dump after another busy week!

"It was not enough to teach better mathematics, I also had to teach mathematics better." -Steven Reinhart in

*Never Say Anything a Kid Can Say*

No grades on papers! This came from articles, other teacher's experiences and my own experience. The most convincing arguments came from @Mythagon - she shared that she puts comments on papers and grades in the gradebook (including the online one that students can access) and when students ask what grade they got she has them look over their work and figure it out. It's not about hiding the grade from students, but about directing their focus to the comments and finding their errors. It also hugely changed the conversations students have after she passes back papers. I start out every year with great intentions on this front and waver as the year goes on. Maybe this year I'll be consistent!

If you're implementing the Common Core (as most every state is) then it would be a great idea to check out c-TaP and see if you can get a "tool-kit" (facilitator) to come to your district. They've been working really hard over the past couple weeks to put together some awesome PD that has the goal of establishing teachers as professionals. Their work started before PCMI and will certainly continue afterwards, but it's been great hearing about the plans they have and they've been working harder than all of the other groups, hands down. For more info, I refer you to @Mythagon.

There was an excellent presentation on Google Docs. I'm excited for all the options of ways to use forms, docs and presentations with my students. I hope we've reached the point where it's reasonable to ask everyone to do out of class assignments that require the internet, I'll find out after my beginning of the year questionnaire. This teacher had her students journal in a google doc, which would be an awesome way for me to comment back, but I don't see how it's feasible for my exit ticket style journaling to happen online. Someday everyone will come to school with a device, but that's certainly not next year.

CME Project books are awesome. I found out you can order chapters separately, so now I'm wondering if I can convince my school to buy a chapter a year if we don't have money for new books. Smaller books sound better to me anyway! There's also a large online resource at cmeproject.edc.org, if you ask for a login there are implementation videos, tons of teacher created worksheets and more. Just use the "contact us" link in the top right of the page.

I'm planning to implement Standards Based Grading next year as well as transitioning into the Common Core Standards. Yesterday a group of us got together to discuss that process, but I discovered that it's all very individualized and I'll need to sit down to make my standards lists and hash out the details myself. In the meantime I'm asking for personal successes and failures from anyone using SBG. If you have a favorite blog post or resource on SBG I'd love to see it, and to be less selfish I'll put it on the #matheme page as well. Comment here or tweet with #matheme and I'll be sure to update the page.

## July 7, 2012

### PCMI: Week 1

Apologies in advance for the mind dump. This is a conglomeration of notes I highlighted (love that aspect of Notebook) and ideas bouncing around my brain.

Teachers need to assert themselves as professionals: we need to demand respect, have a stronger voice (any voice in some cases) in legislation, defend ourselves to the average citizen and remind ourselves that we are the experts.

Implementation is everything. In the TIMSS video study they discovered that while US teachers use problems that lend themselves to investigation, use of the practice standards and making connections, the problems in the study were *all* implemented as procedural tasks. I know that every teacher in the US doesn't fit this mold, but enough do that we need to think about doing more than just getting great texts/problems out to people, but also to have PD and teacher prep programs that very explicitly address this issue. How do we break down making connections problems to make them accessible without losing the richness? Making connections problems are supposed to be ones that students don't know how to solve immediately.

I rarely assign projects to be done in groups since that frequently ends up with an imbalance of effort among students. We did the broken square activity (I've used it before and don't know where it originated, but this link seems as good as any other) which got us to wondering "How do you design tasks that need to be done in a group and couldn't be effective if completed individually?"

At my training in Carnegie Learning several years ago the instructor told us to ask students "What questions do you have?" rather than "Anyone have any questions?" Students respond to those two prompts in dramatically different ways (to the extent it surprises me every time I remember to ask the first way). Next year I want to really focus on having students ask questions, and to extend the type of questions I get beyond clarifications to ideas they are wondering about. The #rethinkgeo crew has been contemplating ways to keep a running list of open questions that we may eventually be able to answer.

Good teachers don't ask "What am I doing tomorrow?" but "What are the students doing tomorrow?"

The National PTA has guides to the Common Core. The CCSS aren't meant to be a list of separate topics, they are chunked for a reason. When I make my SBG standards list I should retain some of the organization.

Instead of homework being practice every night, have different types and label them! Explain, explore, practice, read, study...

Teachers need to assert themselves as professionals: we need to demand respect, have a stronger voice (any voice in some cases) in legislation, defend ourselves to the average citizen and remind ourselves that we are the experts.

Implementation is everything. In the TIMSS video study they discovered that while US teachers use problems that lend themselves to investigation, use of the practice standards and making connections, the problems in the study were *all* implemented as procedural tasks. I know that every teacher in the US doesn't fit this mold, but enough do that we need to think about doing more than just getting great texts/problems out to people, but also to have PD and teacher prep programs that very explicitly address this issue. How do we break down making connections problems to make them accessible without losing the richness? Making connections problems are supposed to be ones that students don't know how to solve immediately.

I rarely assign projects to be done in groups since that frequently ends up with an imbalance of effort among students. We did the broken square activity (I've used it before and don't know where it originated, but this link seems as good as any other) which got us to wondering "How do you design tasks that need to be done in a group and couldn't be effective if completed individually?"

At my training in Carnegie Learning several years ago the instructor told us to ask students "What questions do you have?" rather than "Anyone have any questions?" Students respond to those two prompts in dramatically different ways (to the extent it surprises me every time I remember to ask the first way). Next year I want to really focus on having students ask questions, and to extend the type of questions I get beyond clarifications to ideas they are wondering about. The #rethinkgeo crew has been contemplating ways to keep a running list of open questions that we may eventually be able to answer.

Good teachers don't ask "What am I doing tomorrow?" but "What are the students doing tomorrow?"

The National PTA has guides to the Common Core. The CCSS aren't meant to be a list of separate topics, they are chunked for a reason. When I make my SBG standards list I should retain some of the organization.

Instead of homework being practice every night, have different types and label them! Explain, explore, practice, read, study...

### Math Practice Standards

The last week of June I attended an excellent course at the EDC via DSAC which is a part of the MA DESE about the math practices in the CCSS. Does every profession have such ridiculous acronyms? Crazy jumblings of letters aside, it was a great week. The course was specifically designed for high school math courses beyond Algebra 1, so it was ideal for me as I continue to teach Geometry and start up with Pre-Calculus next year. Each day was focused on examples of a particular math practice. Since I took the course for credit I wrote a reflection each evening about my current and future use of the math practices. Since life is busy (I'm at PCMI!) I'm sharing excerpts of those reflections here with you. I really hope that you are thinking deeply about how to incorporate the practice standards in your classroom. New standards mean nothing unless you, the teachers, make sure students need to use them (more on that in my next post- reflecting on my first week at PCMI this year).

The Standards for Mathematical Practice are:

The Standards for Mathematical Practice are:

## 1. Make sense of problems and persevere in solving them.

## 2. Reason abstractly and quantitatively.

## 3. Construct viable arguments and critique the reasoning of others.

## 4. Model with mathematics.

## 5. Use appropriate tools strategically.

## 6. Attend to precision.

## 7. Look for and make use of structure.

## 8. Look for and express regularity in repeated reasoning.

I try to encourage students to use all of the standards for mathematical practice, although I do so implicitly. A goal for the upcoming year is to post the standards and explicitly ask students what methods they are using or which method they could apply to a problem when they are stuck. This level of metacognition should help students be able to better help themselves.

In Geometry, I try to invoke the ideas of mathematical practice 3 outside of formal proofs and the chapter on conditional statements so students recognize that justification is a part of all mathematics, not specific to two column proofs. A phrase that I utter in class so often that by the end of the first month students can already anticipate it is: “defend your answer.” I introduce it the first few times as imagining that they are lawyers and need to present evidence to the jury beyond reasonable doubt to convince the class that their answer is correct. Asking this of students moves the focus from the answer to the method of solving. When we are in the middle of discussing a problem and a student yells out an answer I redirect them to the step we are on and refuse to confirm or deny their number. In the future I would like to make my reasoning for focusing on the process rather than the product clearer to students- every student quickly realizes that I do focus on the process, but they don’t necessarily realize why.

I am not yet sure which of the contexts in Pre-Calculus will lend themselves best to MP3, but at the very least I will make sure to include questions that require interpreting results to justify why the solution makes sense. And throughout the course students will be required to justify their solutions using the laws of algebra. I look forward to finding other opportunities for proof, analysis and critique in my classes.

One way I plan to support my students in using Mathematical Practice 7 next year is by increasing their familiarity with structures that they should already know. For example, I will be teaching two sections of Honors Pre-Calculus. For that class I assigned a summer project where students have to graph a few examples of the families of functions they have studied so far. After attending class today I wish that I had specified including a table of values for at minimum the parent functions. Since I neglected to assign it over the summer I will plan to have students work with perfect squares, perfect cubes, powers of two and any other important sets of numbers that students should quickly recognize. Knowing these numbers by heart makes it so much easier to notice when a set of numbers is one less or one more than a perfect square or seems to be increasing like an exponential function.

Math Practice 8 seems to apply differently in Geometry than in Algebra based courses. However, we do use this process on a regular basis. In class I ask students to draw a model and take some measurements, then make a conjecture based on the data everyone produces. I try to do this in some form for every theorem we introduce, so students have the opportunity to at the very least gain intuition, but in the best cases they get to experience the thrill of discovering a new property.

Another thing I learned in this class is how very hard it is to sit and work for 8 hours! Students at least get to change rooms and subjects a few times a day, but it still is draining to be asked to think for long stretches of time (especially the first week of summer!). Our instructors anticipated this and provided candy and play dough to keep us on a sugar high and give us something to play with other than our phones.

## July 1, 2012

### Cross Country Collaboration

Way back in February and March Shireen (http://mathteachermambo.blogspot.com) and I did an online project with our students. Somehow, I never blogged about it, but better late than never!

Goals: students experience remote communication (learn about types of tech and how to collaborate) and long term projects (pacing self and partner).

Methods: Each Geometry student in MA was paired with a student in TX. We provided them with each others name and gmail address. The pair had to work together on google docs to choose a topic and brainstorm key ideas and vocabulary. Then, using an online resource of their choice, come up with a teaching or practicing tool. They were given a timeline with a portion of the project due each week. MA provided computers in class (if they finished classwork early they could work on their project).

Issues: Both schools had vacation during the timeline (oops!). It was a lot of grading (50 pairs with 4 submissions each). Not all MA students had access to computers outside of school. One MA student didn't know how to use the programs and was resentful that I didn't explicitly teach her (it's a bigger concern that a 16 year old in 2012 has never used PowerPoint). Typical issues of one student not doing their part or waiting until the last minute and having tech issues.

Successes: Students generally enjoyed the idea of working with someone across the country. They liked google docs (and the teachers loved the way it tracks contributions). Students are now proficient in at least one type of presentation/quiz technology. Each student became an expert in a particular topic and we have a database of materials to offer to future students. All MA students now have professional gmail accounts (TX students had school gmail accounts already).

Next time: I would only have two deadlines: outline and final project. I had some students use google forms to leave peer feedback so that would be a good intermediate step rather than two teachers having to grade 50 projects twice! Since I plan to use google docs with kids starting in the fall the tech issues should be minimized. Overall I thought it was a great project that exposed students to many of the great resources available online that they don't necessarily get introduced to otherwise.

Goals: students experience remote communication (learn about types of tech and how to collaborate) and long term projects (pacing self and partner).

Methods: Each Geometry student in MA was paired with a student in TX. We provided them with each others name and gmail address. The pair had to work together on google docs to choose a topic and brainstorm key ideas and vocabulary. Then, using an online resource of their choice, come up with a teaching or practicing tool. They were given a timeline with a portion of the project due each week. MA provided computers in class (if they finished classwork early they could work on their project).

Issues: Both schools had vacation during the timeline (oops!). It was a lot of grading (50 pairs with 4 submissions each). Not all MA students had access to computers outside of school. One MA student didn't know how to use the programs and was resentful that I didn't explicitly teach her (it's a bigger concern that a 16 year old in 2012 has never used PowerPoint). Typical issues of one student not doing their part or waiting until the last minute and having tech issues.

Successes: Students generally enjoyed the idea of working with someone across the country. They liked google docs (and the teachers loved the way it tracks contributions). Students are now proficient in at least one type of presentation/quiz technology. Each student became an expert in a particular topic and we have a database of materials to offer to future students. All MA students now have professional gmail accounts (TX students had school gmail accounts already).

Next time: I would only have two deadlines: outline and final project. I had some students use google forms to leave peer feedback so that would be a good intermediate step rather than two teachers having to grade 50 projects twice! Since I plan to use google docs with kids starting in the fall the tech issues should be minimized. Overall I thought it was a great project that exposed students to many of the great resources available online that they don't necessarily get introduced to otherwise.

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