Book Review: "Good Questions: Great Ways to Differentiate Mathematics Instruction"

In an attempt to find and implement effective strategies to differentiate instruction in my classes, I purchased "Good Questions: Great Ways to Differentiate Mathematics Instruction" by Marian Small. I purchased the book from the NCTM (National Council of Teachers of Mathematics) web site.

The Good: The book does a great job giving examples of open questions and parallel tasks that can be used for student from Kindergarten up through 8th grade. The levels are grouped by k-2, 3-5, and 6-8. And, there are examples of both question types for all the groups across all of the "Big Ideas" derived from NCTM's Principles and Standards for School Mathematics. The examples themselves were of high quality and the advice for creating your own questions didn't require intensive planning labor.

The Bad: Like every other resource I've encountered, there seems to be an assumption that the right questions will transform all your students into active participants that will suddenly take charge of their learning. The author writes about it as if its a foregone conclusion that everyone will suddenly enjoy learning math and immerse themselves in the questions. There isn't any discussion about how to actually make it happen. I will use strategies because I like the concepts, but I have no delusion that I've solved my struggles with keeping students engaged while I work with individuals or small groups.

Overall: I do recommend the book because of the sound teaching strategies and plethora of example problems for elementary and middle school students. If you're struggling with apathy and lack of effort from students, I don't foresee this book providing the solutions to resolve those issues.

Organizing and Teaching with Spreadsheets.

ORGANIZING
Every year, one of the first things I do to get ready for the new school year is import student data into a spreadsheet. The spreadsheet serves many purposes throughout the year. I mail merge student names into a label document to print out labels for student planners and take-home folders. I record assignments of textbooks, calculators, locks, and lockers. The formulas feature makes calculating growth on test scores a breeze. And, as ridiculous as it sounds, it helps me answer the question that takes me off guard about three times a year, "How many students do you have on your team?"

TEACHING MATH
One of the best teaching strategies I've implemented in the past couple of years requires students to store collected data in spreadsheets. One of our class activities at the beginning of the year has students working in groups to measure each students' height, arm span, resting heart rate, exercising heart rate, wrist, neck, thumb, foot length, and stride length. The data is used for multiple purposes throughout the course of the year. We make scatter plots to determine relationships between different data. We use the data for five number summaries, box-and-whisker plots, frequency tables (line plots), stem and leaf plots, and histograms. We make circle graphs and bar graphs to demonstrate misleading graphs and displays of data. The spreadsheet software only makes a few of these graphs, but putting the data into a spreadsheet accomplishes a few critical objectives. One, the data is stored electronically under the students' profile and less likely to be lost. Two, students accomplish some of the technology curriculum by creating formulas, sorting data and graphing data using spreadsheets. And Three, students can easily reorganize the data to make it more readable for a specific application. I strongly recommend reserving the computer lab anytime students are collecting data. Even if you don't have access to the computer lab when you're using the data, any student can access the data on the classroom computer and share with the class.

Tammy Worcester has developed an extensive list of spreadsheet enhanced lessons for all grade levels. I would be remiss if I posted this blog without providing a link to her website.

DonorsChoose.org. Great Way to get Class Materials

Today, I submitted my first DonorsChoose.org grant for the school year. I submitted a need for a video camera and tripod for my classroom. I've had great success in the past with DonorsChoose.org grants. Over the past three years donors have bought some excellent technology for my classroom. Thanks to the generosity of various donors, my classroom has been equipped with a Bluetooth wireless keyboard/mouse, a XGA TV converter, a USB 1GB memory stick, a presentation remote, and a TI-Presenter. I haven't been awarded every request, but its certainly paid off to keep trying. DonorsChoose outright tells you that requests costing less than $400 have the best chance of being funded. This has proven very true in my experience. I have applied for other grant opportunities with no success. I will continue to try for these other grants, but I strongly recommend that every eligible teacher appeal to donors on DonorsChoose.org to get what you need for your classroom. I also recommend starting small so that you build momentum toward getting higher priced items.

Physical Education and Math

Had a great conversation today with one of our P.E. teachers. He was looking for a way to integrate fitness data with the math curriculum. We discussed ways students might electronically store their fitness statistics. (Heart rates, # push ups, # sit ups, running times, ... etc.) It was a fortuitous discussion because I have deliberated several times over the past year about ways to used data that is meaningful to students in teaching data analysis and graphing. I'm excited about the prospect of the 8th grade math department collaborating with the P.E. department to find ways to make math personal for the students.

I really enjoyed the conversation because it testifies to the climate of our school. We have an amazing professional staff and the professionalism is contagious. It looks like we're off to a great start this year.

Video in the classroom. Kids behind the camera.

I've been contemplating ways to enhance my teaching this year by using video. I'm determined to make video cameras a staple in my classroom this year. Nothing seems to excite students more than the prospect of being in pictures.

One idea I've been mulling over involves students acting out a script to teach a math concept. Even if they don't really understand what they're teaching, I think they could memorize a script and act out the scene. Videos should peak student interest. Acting activates multiple intelligences. And, content isn't compromised. I will post more as I develop a more concrete lesson plan and again as I execute the lesson.

I also intend to incorporate video into normal daily routines. There's something about knowing you're being recorded that makes you want to do your best. Not only will it encourage students to be at their best, it will also motivate me to be on top of my game as a teacher.

I certainly welcome any ideas about other ways that I can effectively use video in my math classes.

The Hiatus has ended.

I have returned to blogging after an extended break. As I get ready for school to start, I've decided to return to blogging. I'm taking a different attitude with my blogging this year. I became somewhat disappointed last year when I felt like no one was reading my Blog. I wasn't getting comments posted and took this to mean that I had no audience. While I would like to have an audience completely riveted to my every word, the real usefulness comes from the valuable self-reflection that goes into Blogging.

My first educational video.

I've finally done it. After putting together a few hours of uninterupted time, I finally managed to put together my first teaching video. It's no masterpiece, but I don't think its horrible for a first attempt. I've posted it to Teachertube.

Team Collaboration. Wiki Style.

Today representatives from the North Carolina Department of Public Instruction (NCDPI) visited our school to videotape our team's (Garry, Mike, and Curtis) collaboration meeting with the school's media and technology facilitators(Gina and Julia respectively). I felt that the meeting went exceptionally well.

This was our second collaboration meeting relating to our interdisciplinary unit on "Change". Before getting into the details of today's meeting, here is a little history on how the unit had developed up to this point. In October we were charged with the task of deciding on the theme of a collaborative unit that we would develop and implement as a team. This was the only required piece going into the first meeting. The key to selecting the them was deciding on a time frame in which the unit would be implemented. We decided to "kick-off" the unit early in the third quarter. (Late January) Garry shared that he would normally cover the civil war during that time period in his Social Studies class and his Science class would cover evolution. These both lent themselves well to the theme of "Change". The Math curriculum pacing guide (provided by our district) indicated that I would be covering linear equations early in the third quarter. It was only a small leap to tie in slope or "rate of change". Our theme was born. We selected "Change". Mike hit the ground running. He instantly tackled the theme with a contagious excitement. We met with Gina and Julia late in October to brainstorm lesson ideas that matched our curriculum with the theme. We came up with several tentative ideas at that time. Here a few of the key ideas:

Teach slope/rate of change (Math - Curtis)

Cost of Civil War -- Twist Notebook [Electronic Scrapbook Activity] (Social Studies - Garry)

Point of View journal entries related to Civil War (Social Studies - Garry)

Walt Whitman poetry -- Change reflected in art (Language Arts - Mike)

Red Badge of Courage novel (Language Arts - Mike)

Seminar [topic to be determined later] (Language Arts - Mike)

The first meeting began rather awkwardly. With the mandated interdisciplinary unit collaboration meeting, we were unsure what we were supposed to bring to the table. After the initial awkwardness, we plodded through and gained at least enough ideas to get us thinking about and preparing for the unit. Shortly after our first meeting, Gina created a wikispaces page that permitted everyone to collaborate online. This really improved our preparation for today's meeting.

It only makes sense to direct you at this point to the wiki so that you can see how the collaboration developed from random ideas to carefully selected activities. Please keep in mind that the wiki is a work in progress. I would like to acknowledge Scott Elias. I plugged his presentation

View Upload your own

when it was suggested that one of the student products for Social Studies would be created using Powerpoint or Photostory 3. It occured to me that students might benefit from these pointers before creating presentations.

Response to "Careful Now: 21st Century Edition" by dy/dan

This post is actually a comment that I left on dy/dan's blog entitled "Careful Now: 21st Century Edition". The comment ran on so long that I decided to post it here as well. (I also noticed a few typos that I wanted to clean up)

It was funny to see your post about 21st Century Classrooms and particularly making the transitions in Math classrooms. My own blogging for the past two days has traveled similar paths.

I’d like to first comment about Dan’s statement that the post reflects “the 21st-century-learning crowd’s total misapprehension of how students learn mathematics, particularly of how students who don’t understand mathematics at all learn mathematics.”

I think the 21st-century-learning crowd sometimes comes across this way because they’ve become accustomed to defending their positions against those who simply resist change. I’m sure there are some tech-nazis out there who insist that everything done without technology is a disservice to our students. But, most are level headed folks that encourage us to explore ways to enhance what we do using technology.

Judging from the staff development I’ve attended over the past few years, Math teachers must be the bain of the guest speaker’s existence. 95% of the sessions I’ve attended finds at least one Math teacher stating, “That’s great! But, how do I use that in Math?” There really isn’t a viable substitute for paper in Math. Not only is it difficult to write equations with fractions and exponents, there are the process steps of carrying the one and simplifying the fraction that require you to move around the problem to annotate steps you’ve taken. Interactive whiteboards, school pads, and notepads permit you to write with a “pen” just like on paper. But if its just like on paper, how is it “better”? At first, students might be more engaged because they’re playing with the new toy. When the new toy loses its new, we’re left where we started. All these items are wonderful tools and contribute to classrooms in amazing ways. As the “21st-century-learning crowd” we should never imply that teachers shouldn’t use handouts any more. And, as teachers we can’t assume that integrating technology into our classrooms means we have to use it for everything.

Jenny made an excellent point that there are aspects of other subjects, including English, that don’t lend themselves well to the use of technology. Math generally gets the most attention because it has fewer areas that can be completely taught using technology alone.

The similar Blog postings mentioned in the first paragraph are:

Does the School of the Future Buy Textbooks?
Interesting Discussion Regarding “21st Century Classrooms”.

Does the school of the future buy textbooks?

Part two of commuter conversations revolved around the concept of textbook free schools. We all found the idea rather intriguing. Like children at Christmas time, we began calculating the amount of funding that could be redirected toward enhancing the technology offerings in classrooms. It's certainly worth considering. Take for example a grade level of 225 students. Estimate textbooks at approximately $100 each. Textbook adoptions are revised about every five years. If a school purchases textbooks in the four core curriculum subjects (Math, Science, Social Studies, and English) they spend about $90,000 in a five year cycle for textbooks on one grade level. This is obviously an overly simplified scenario. Actual implementation of such a plan would require significant logistical planning, but it's certainly food for thought.

Interesting Discussion Regarding "21st Century Classrooms".

This morning I had a very interesting conversation on the way to work. I need to preface by saying that I'm very fortunate to work at the same school with my wife, Gina. She is an excellent Media Coordinator and wonderful teacher. She has been teaching for over 15 years and has been my mentor (unofficially of course) since I started teaching 5 years ago. Today, she and our Technology Facilitator traveled across the state with our principal to attend a meeting. Consequently, we carpooled to work this morning with Julia (the Technology Facilitator).

I'm not sure how the conversation started, but Julia told us about another district that was currently in the process of making every classroom a "21st Century Classroom". She defined "21st Century Classroom" as containing at least a data projector, a Smartboard, and a laptop. She related a conversation with one of their district instructional technologists in which he commented that they were finding it difficult to engage high school students using the Smartboards. This sparked an impromptu mini-brainstorming session within the van. Each of us speculated about possible reasons that high school students might not be engaged by Smartboard technology. Gina pointed out that turning your back to high school students to write on the Smartboard (As with the traditional white board) is generally a bad idea. Julia shared that she beleived that the teachers were not putting the technology in the hands of the students. I must say that I beleive both are correct.

Speaking from the perspective of a Math teacher who has taught using a Smartboard, these are two pitfalls inherent in the Smartboard that are not easily overcome. As Gina said, it's generally bad practice to turn you back on students (particularly high school students). If you don't write at the Smartboard, it becomes a $1000+ pull-down screen. The alternative puts students at the Smartboard. This is an improvement to turning your back on students, but I've found that having a student at the board does not engage the rest of the class. Even when my eighth graders are excited about the prospect of using the technology, the technology doesn't inspire them to focus on the content presented by their peers. I suspect this effect is considerably different at the elementary levels. Gina related a visit she had with a second grade class where a Smartboard was used very effectively with hands on activities for students who were highly engaged. The students were playing some type of educational game that they had obviously played before. The teacher's role in the activity was observation only.

The most effective lesson I've taught in eighth grade was rotational symmetry. I opened a powerpoint slide and inserted an image of objects that were rotationally symmetrical. I copied the image and pasted the copy beside the original. Using the rotate tool, I was able to specify the angle of rotation. Students could visually see that the original image and the rotated image were identical. This lesson was the exception rather than the rule. Most of the lessons I attempted using the Smartboard could have been accomplished equally effectively with an overhead projector. I acknowledge that some of this might be due to my own inexperience or lack of creativity. I welcome any advice on using Smartboards for engaging instruction.

There were more interesting comments during our commute, but I'll save that discussion for another post. This one has become far more longwinded than I had originally intended.

Vouchers for Private Schools?

The on-going argument for vouchers and/or tax credits for parents who opt to send their children to private school has been an ongoing debate for several years now. It really starts to boil around election time. Guess what? It's election time again and the same old rhetoric surfaces yet again. It amazes me that so many people cabbage on to the concept of paying for private education for their children and thinking they should no longer pay for public education because they're not using it. In fact, they continue to "use" public education even after their children enroll in private school. We don't, as a society, pay for public school so that our children can go to school. We pay for public school so that everyone's children can go to school. Should we get a tax credit because our house didn't catch fire this year? The fire department never put out a fire at my house. So, why should I have to pay for it?

Additionally, the biggest supporters of a voucher system usually seem to be the most vocal opposition to "tax and spend" policies. Vouchers and tax credits won't make public schools any cheaper to run. Where will we get the money for these tax credits and vouchers? The obvious answer is that government spending on education would increase and in turn taxes would increase to fill the void.

Finally, let's not delude ourselves. Vouchers and tax credits won't equal the playing field. Low income families still won't be able to afford quality private education. The tax credits and vouchers only increase the divide between the "Haves" and the "Have nots". The wealthy, (or even middle class) who can already afford private education, get help paying for private schools at the expense of those who cannot afford private school.

Sorry for the rant, but I've never heard an argument for vouchers that didn't seem rooted (at some level) in greed. The greater motivation should Social responsibility and doing what is right.

This rant brought to you by edspresso.com who posted EDITORIAL: Charter school moratorium.

Talking Math Communication

This Blog post is in direct response to Matt Christiansen's posting "Communication in the Math classroom" and the comment posted by selias22. I agree with selias22. "Dumbing it down" is a terrible idea. One of my greatest challenges with struggling 8th graders is getting them to think beyond the operations represented by symbols on their calculators. This will never change if I don't continuously model the use of math vocabulary. I often interupt my own discourse to check student comprehension of the math vocabulary I'm using. Once I detect that some students are struggling with a term, I revisit the term multiple times throughout the rest of the unit until comprehension is achieved.

Its critical that we realize our students struggle with vocabulary. They certainly won't learn concepts and applications if they can't comprehend the basic math jargon used to teach the concepts. Matt also makes a wonderful point about exercising patience regarding student writing in Math. Writing is a wonderful way to strengthen students' vocbulary and comprehension. Writing is a difficult skill for students and becomes doubly so when they attempt to articulate math concepts that they only understand on the most rudimentary level.

Reading Matt's post has reignited my thinking about strengthening students' math dialogue. I will definitely review my upcoming lesson plans to make sure that I'm applying math communication as a critical strategy in improving student achievement.

Excellent resource by Scott Elias on presenting.

Scott Elias' "Presentation on Presenting" provides excellent advice to teachers who find themselves struggling to keep students engaged with their slide presentations. The presentation provides excellent concrete guidelines and clear strategies to avoid the pitfalls of Powerpoint.

My school purchased data projectors for almost every classroom in the school this year. The 8th grade Math teachers have worked together to create powerpoint presentations to replace the normal notetaking practice. Regretably we have committed many of the faux pas that Scott wards against. I suspect that I will revisit his document many times in the coming weeks in an effort to clean up some bad presentation habits. It has been very defeating to spend hours creating presentations that my students insist on sleeping through. Thank you for the excellent post Scott.

As an aside, I think that I will post a before and after presentation once I've implemented Scott's recommended strategies.

Got started with a couple of my NCETC inspired initiatives today.

I created a wikispaces wiki page today. The URL is http://WMSMath.wikispaces.com. I chose to create a protected wiki since the purpose of the wiki is to provide a centralized location for Walkertown Middle School math teachers to share resources and collaborate. I may even need to part with a little cash and establish it as a private wiki. I'm a little concerned with posting some of the items that we've included in our powerpoint presentations this year. Some of our examples were copied directly from our textbook software. In the meantime, I think we will simply replace the copied examples with original creations.

The other project that I've begun working on is the video to teach slope. As I've stated in an earlier post, I was very impressed with Lee Lefever's "Wikis in Plain English" video that David Warlick showed in his presentation "The Art And Technique Of Wikis" at NCETC on November 28, 2007. I've decided to do my slope video using powerpoint. I've started developing some ideas and implementing the animations. It's going to be a lot of work, but I am hoping to have a quality finished product when I'm done. I will put a copy of what I've accomplished periodically on the new wiki page so that everyone can see the progress.

Wiki excitement

Today I shared the "Wikis in Plain English" video with my teammates and with the Math department. It generated considerable excitement. As a result, I am now in charge of finding a Wiki service that will let us create accounts for our students without requiring them to provide an e-mail address. Someone suggested at the North Carolina Educational Technology Conference (NCETC) that PBwiki provided this sort of service. I will probably begin there. Valerie, one of my colleagues in the Math department, suggested that we pool our resoures into a wiki. As a department, we have been creating and sharing powerpoint presentations for our notes on various topics. Additionally, we have collaborated and shared our projects and ideas. Valerie's idea is to build a wiki page listing all the topics we cover in our classes and import our resources into the wiki. I will post details once we start the wiki.

Indirect idea from Warlick's wiki session.

During David Warlick's presentation "The Art and Technique of Wikis" at the North Carolina Educational Technology Conference (NCETC) he showed a Youtube video that illustrated the use of wikis.   The video was done by Lee Lefever and is entitled "Wikis in Plain English." (See attached link)   This video is very cleverly done.   It occurred to me a couple days after the conference that I could make similar videos to help teach concepts in my classroom.   I've got to work out a few logistical issues, but I'm going to attempt a similar video on slope and linear equations.   I will post again when I've completed the video.

Video Link

Mockumentaries

I loved this idea that I got from the UNC-Greensboro presenters.   They played a video (vodcast?) spoofing Mad Money and using a staged call to explain the concept of Economic Profit.   I found myself actually anxious to hear the explanation.   I think this could be done on a small scale to teach almost anything. Imagine capturing students' attention by imitating pop culture icons.   Another powerful aspect of the video was that it wasn't explaining the concept to the students, but rather a third party.   It was very powerful that the audience is an indirect target of the information.   It would take considerable work for a single concept, but it may be worth it when considering that it could be used in multiple classes and in multiple school years.

Wiki projects!

One of my favorite tools that I learned about at NCETC 2007 were wiki's.   I thought that one excellent use would be for a teacher to start a wiki with a simple paragraph or page about a general topic.   Within the paragraph, many of the key words should be created as links.   These keywords are then assigned to students who would research the keywords and fill in the wiki with data related to that keyword.   I think this could be an amazing way to carry out a research project with students.   I don't have anything concrete for this yet, but I would like to create a sample page.   Most of the implementations for this idea so far relate more to subjects other than Math.   I might develop this idea for Science or Social Studies first.   As a second effort I would like to adjust the idea to fit Math somehow.

Gaming Fair

Another idea that I absolutely loved from David Warlick's presentation on video gaming. He stated that some schools had hosted a gaming fair. What a magnificent way to get students excited about a school event. Students were invited to bring in their gaming systems and they demonstrated to parents and faculty the many aspects of the gaming world that are foreign to many adults. This would also be a great event to springboard a PTSA meeting. There are lots of great resources available at David Warlick's wiki page for this presentation. Click on the attached link to visit the page.