Teachers Talk

A recent blogging assignment in my grad class was this:
Blog: Your choice. What about your thinking or practice do you want to share with the world at large. This can be a record of something you’ve done, a particular activity to share, work from this course to share, or an opinion piece on an issue of the day (Khan Academy, standardized testing, Michigan education funding, ...)

They wrote interesting pieces, and I love hearing teachers' voices about that which they care most.  Four of the teachers have public blogs, so I'll point to theirs with this post. Leave them a comment, encourage them to keep blogging! Those who were blogging on Blackboard, I'll quote more extensively.  Post a comment here for them on how they should export and continue their writing!


Bill: Credo about what it takes to teach mathematics.
Also see: Bill's take on the 3 Act Story (I'm quite interested in this as a structure.  Here's a short urli.st of blogposts I've found on it.)


Eric: Textbooks. "The secret to being a lazy math teacher?  Good textbooks!..." Good hook!

Also see: HS grading

Melissa: only assignment she missed all course! Plenty to read at her blog, though.
See: Her description of her lesson planning process.

Ted: quick take on the public's perception of teachers and Summer Vacation.

Also see: his outstanding concept map for linear intercepts. (Not a blogpost, but wowser.)

Amy: Traditional Teaching
Taking this class has really got me thinking about the way that math is traditionally taught, and the way that I teach math. It has opened my eyes to the importance of teaching students how to problem solve and think critically. This has caused me to feel uncomfortable in my classroom for the past week or so. I feel that I want to make some changes, but yet it seems so overwhelming. The math department I work in is very concentrated on "everybody doing the same thing." This includes assessments and lessons. Also, the time that it takes to develop new tasks for student also is a daunting task.

So, as I reflect about changes I want to make for next year. I am thinking about making small changes. I think my first focus is going to be on formative and summative asssessments. Providing more opportunities for mastery rather than completion. I would also like to incorporate reflection on a daily basis to get students thinking about their problem solving and being able to put their thoughts into words.

In the future, I would like to work towards having more discovery and problem solving activities related to the concepts in my classes.

Erin: the switch from Michigan's High School Content to the Common Core State Standards
I have to complain for a minute about the switch from Michigan standards to the new Common Core standards. I have no problem with switching to common standards, I have no problem with the content of the standards, and I don't even have a problem with standardized tests based on the standards. My problem is this...

We are supposed to begin teaching to the new standards this year with testing based on the new standards to begin in 2 years, however, in the meantime, we are still being tested on the Michigan standards. That doesn't make any sense. The standards really are different in some ways and we are in the process of designing our curriculum based on the new standards. We have to be careful for the next two years that we also teach the HSCEs becuase that will be on the MME.

Someone tell me why we are rolling out the new and testing the old. Is testing really that important that we can't miss 2 years? Perhaps at least we can remove some of the consequences in the meantime so that we can develop a coherent curriculum without fear of the government taking over our schools.

Monica: Differentiation
When I took my Curriculum Development Class, we focused on Understanding by Design and Differentiated Instruction. Prior to that class, I had believed that differentiated instruction was synonymous with individualized instruction. And it wasn’t until the last 4 weeks or so that we started to talk more and more about what DI was, and how to adapt lessons and differentiate them.

First, some things I learned about DI:

• Quality differentiation begins with a growth mindset, moves to student-teacher connections, and evolves to community.  In a growth mindset students persist in the face of setbacks and see their effort as a pathway to mastery. Students embrace challenges, learn from criticism, and are able to find inspiration and motivation in others’ success. Rather than plateauing with skills and knowledge, students with a growth mindset reach higher levels of achievement.
• Quality DI is rooted in meaningful curriculum (not fluff!)
• DI is guided by on-going assessment which is used not for grades, but for instructional planning and providing feedback.
• and DI addresses students’ readiness, their interest, and their preferred method of learning.

Different methods of differentiating instruction include using

• Choice Boards--like a tic tac toe, where you have 9 activities listed, one in each box, and have students choose whichever 3 activities they’d like to do, as long as they make a tic-tac-toe. These activities should be rooted in the same learning objective, but address different learning types (multiple intelligences).
• Cubes or Think Dots--cubes would be using a net for a cube and having one question on each of the six sides. Think dots follow the same idea, but the students would roll a die or number cube, and then do the problem underneath the number they rolled on a worksheet (the worksheet would have 1 through 6 on the top, and the 6 problems listed under it—rather than making the cubes, now you just make a worksheet, and use a number cube).
• Sternberg’s Tri-Mind--list three different sets of directions to address the same objective. One way of addressing the objective would be analytical, one way would be practical, and another would be creative. There are tests, similar to multiple intelligence tests that students can take to see of the three they prefer.
• You can also have two similar worksheets, where one is more advanced and the other is more basic, depending on the level of the student. Students don’t know they have different leveled activities, but this is a great way to address the “just-right” problems for students on a case-by-case basis. You can make more than a basic and advanced, setting up four or five levels, but remember, differentiation is not individualizing.

In this class, I wish we would have learned earlier what differentiation was all about, and how to differentiate activities. This was most beneficial part of the class for me, and I wonder why “stuff like this” hasn’t been around longer. I feel that DI addresses issues that have been around in schools longer than solutions have, and this is something that should be included in all undergraduate teacher prep classes now (which I’m hoping it is)!

Monica's digital decimal differentiation designs are available at Scribd or by email from me.  There's quite a bit of work done on tic-tac-toe, tri-mind and cubes.

Closing Thought
Powerful stuff when teachers start sharing on Twitter or writing for sharing.

So why don't you join the conversation, you?










Photo credits: Search Engine People Blog, Cliff1066 @ Flickr

Differentiation

Differentiated Instruction can get a bad rap because it has a name.  So people give their spin on it, and then people can trow rocks at specific ideas and say, "see, I knew it was bad."  But at the heart of it, we know our students are diverse, and have different ways they learn best as well as different ways to express understanding.  One size fits all does not fit me, and if it did, it would not fit you.

Coach Ginsburg has two recent posts about this, and they're both quick worthwhile reads.  I whole-heartedly agree that differentiation needs to be practical and sustainable.  Making three different activities for multiple days a week is neither.  Choice and optional levels of support might be feasible.

Our student teachers have been thinking about this and I thought I'd just share what they wrote.  This is in response to reading an article of their choice.  The bibliography is at the end.  As you will be able to tell, there are some pretty sharp prospects in this bunch!

Cartoon from Cornered.  Photo from herzogbr@flickr.

Differentiation Ideas - Fall 2010

Class Discussion:
Question: The idea is good - individual attention and opportunities. But what about the gifted? How do you grade students that are working on different levels of work? If one makes a video and one a test? How do you grade fairly?

Discussion: Mastery learning. Compare with the objectives. With extensions ready, the students can work on ungraded material. They want to be busy. Extra credit even, if it's necessary.

Question: I like choice: but how do I explain the objective for each project?  How do I set it up?

Discussion: that’s what I see rubrics doing. They convey how to evaluate your work; clearly, concisely... this is what it looks like.

Question: How could we implement this in our classroom?  Everything is as a whole, everything is at once and it’s just too fast for some students. Makes me not to want to do the clicker, but they want that, too. They’ve mostly been doing clickers and notes.

Discussion: Are there ways to provide different levels of support for during the clicker questions? Hints? Though that can annoy people who’ve already clicked in. Without individual work, it’s hard to differentiate. Work on the questions first? Don’t enable clickers until after work time. Our cooperating teacher (CT) wants this quick.


Individual thoughts
Bre Betz- I have already seen this differentiation a lot in my classroom. We have a complete class of lower level students who this greatly effects. We also have a few “gifted students” in our room. For these students, I think that giving them some kind of extra credit or an extension into higher level math on certain problems is a really good idea. If they are not challenged very much they will eventually loose interest. On the other hand, one of our “gifted students” actually takes this idea into his own hands. Once in a while he will try and go further with a question in the book, usually he doesn’t quite make the correct assumptions, but at least he is trying and thinking outside the box.

Autumn Langlois- I love the idea of differentiating in the classroom. I also love the idea of giving the students choices as much as possible. My goal is to have two homework assignments per class. This would include the normal one that i would have handed out to every student and the other for the gifted. Those that just want a challenge can also chose the harder one. But the catch is once you pick up the harder one you can not go back and get the easier one. I love the idea of pulling students out to look at the material more deeply but in the school that I am in now, I do not see that as a possibility. The gifted article also hit the nail on the head when they started to talk about how schools are putting a lot of emphasis on the lower level students when the upper level students deserve just as much of a challenge as they are getting. Scary but true. The article really opened my eyes and I will be more aware of what I am saying to those that always have their hand up in the air.

Stephanie Bares- I was always unsure on how to help the gifted students with out giving them extra problems of the same thing. These students need a challenge and I was afraid if you gave them too much that they would ask why don’t other kids have to do this but it seems that they actually look for a challenge. the students also do not want to be pointed out as the real smart student they want the challenge to be there for anyone one so they are not that one special person. I like the differentiated task that Mrs.Baker in the article “The Gifted student” did. I liked it because students that were not gifted still could work through it and the gifted students still felt there was a challenge and also were able to share with others there ideas which in turn may of help others. I would hope I could make activities that would be able to include everyone like that one.

Jacob Dunklee- One way that I like differentiation in the classroom is to assign the same homework assignment to all students, but have extra, more challenging problems for the gifted students to work on after they are done; and for these problems give them extra credit and maybe a little treat if they complete so many of them. I also would offer more support to the struggling students by getting together in small groups to work on the homework together. I would try to at least pair them up with one of the students that in the gifted category or are able to understand the topics and explain them to others. This would allow for everyone to get something out of the instruction without killing myself by making up three different assignments for every lesson. As a teacher we can only take on so much extra work on top of everything else. But if we put in the time in the first few years of teaching it would be easier because we would have most of the assignments saved because of technology in this day and age so the extra work load would decrease eventually. But there will always be different levels that we would have to prepare for.

Kady Dingman - Planning lessons that excite and engage all students in the classroom at all levels can be challenging for a teacher. One way that my CT tries to engage gifted students in her classroom is that she sometimes has an extension activity for the students who fly through the lesson that she puts questions from the extension on the tests as extra credit problems, so that those students have some incentive try the extension activities. I think this is a great incentive for these students to try the extension. Another way I might use differentiation in the classroom is to give the students some choice in the assignments they complete, so that it’s not necessarily more work, just more challenging tasks that the students would’ve chosen to complete themselves.

Matt Compher - I specifically read about differentiation for English Language Learners. One thing that can be done in the classroom to support differentiation is to allow students to work with one another on a given task. Pairing ELL’s and non-ELL’s would benefit the ELL’s by giving them a second source of instruction, and the non-ELL’s would be given an opportunity to practice speaking and explaining mathematical concepts.

Less of a specific differentiated lesson, but another way to differentiate to ELL’s is to speak more slowly/clearly than one would otherwise. From there, assignments, tasks, or activities can be designed specifically to practice speaking and explaining new concepts in approprate mathematical language. This would benefit all students, but would also help the ELL’s by exposing them to more mathematically charged English. An idea that I got from the text would be to cover and explain important concepts before defining new terms/words.

We have English Language Learners in our classroom this semester, so any other ideas would be greatly appreciated, party people!

Emily Holth - I really like the idea of differentiation in the classroom. I have learned a lot from my CT since he is teaching by the GLCE’s. [Michigan's middle school content expectations] So, if some students are having trouble with a particular GLCE, then during group work, those students can have instruction focused on that GLCE. Also, for those students who are not having any trouble with the content, my CT provides them with challenging activities. Sometimes it will be an extra credit worksheet that asks them to apply what they have learned and extend it to answer a question. Other activities that are available to these students include the question of the week. Each week my CT posts a question that is optional for all students, and those who get the correct answer receive extra credit. These questions are also challenging and require further thought than what was necessary for the lesson. I think by separating students by what they understand and what they are struggling with, we can really focus with them on that particular area. Some students may not need the reteaching for a particular topic, so they should be able to work on something else that will give them more of a challenge, rather than simply focusing on the students who are at a lower level. I think this is a great way to accommodate for all students.

Tess Wells - I really like the idea of regrouping students according to their struggles, at least for part of a class period. At my placement, a formative assessment (sort of a mini quiz) is given at the end of every investigation. I think it would be a good idea to look them over and group them into different categories of certain struggles if they seem apparent and then come up with an activity to help that certain struggle that students can work on the next day in class in those groups. I know time is always a huge issue so maybe that could take the place of a warm up or something some days at the beginning of class.

I also was reminded from reading the article, Dynamic Concrete Instruction, that even when teaching all of our students the same thing at the same time we can differeniate our lesson by remembering to include different learning styles. I think that idea is so basic, yet not so easy, and an idea that I have learned for so long it has been put on the back burner or maybe kind of second nature by now and does not get that much attention. However it is still a very important part of differentiation in the classroom.

Gerald Smolka - There are so many challenges that we as young teachers must face. While I have already been contemplating how to keep extra attention focused on the student’s who are struggling, I hadn’t given much thought on those students who are excelling with the material. Fortunately, I have been seeing differentiation modelled for the ‘gifted’ students in my FST class. Mrs. Robbert always makes sure to have some kind of supplemental activity reading for students who finish an assignment or project before the rest of the class. The big question with the extra activity is how to grade it. But I don’t feel its necessary to always grade materials that are given to students. I believe that students want to be challenged and enjoy activities. As a matter of fact, removing the grade from an activity might serve to motivate them to explore it without the possibility of failure. My ED 310 prof, Mr. Stockton, is using this approach with a couple books that he would like us to read. They are on the required textbook list, but he isn’t testing us on any of the material and isn’t giving us a schedule to have things read. He has left it up to us as to whether we will read it or not. Well, now since I don’t have to read it I want to read it at a pace that is comfortable to me.

Katelyn Marckini - I read the article about differentiating Instruction for the English Language Learners. This could be particularly useful in the school that I am working in now We have a few students who I can tell speak Spanish at home. Therefore, they have broken English in the classroom at times. I think that I could help these students by giving directions slowly, repeating directions, allowing ELL students to work with non-ELL students (have all students pair up), etc. Usually when I am working one-on-one with students I will have them read the question that they are asking about out loud. This way they get a chance to verbalize math and I can make sure that they are capable of doing so. I may try to start having students pair up to work on things in the classroom and see how it goes.

Ashley Eastman - we see a lot of differentiation in our classroom because we have many students at different levels. we have one class full of students with learning disabilities so we change our lessons for them even though they are in the same course as the other three blocks our teacher teaches. then in our normal class we have a couple of gifted students who go above and beyond what we expect. these students will usually look at the problems in a different way then most kids to challenge themselves, especially one of our students. they usually start their homework in class so they aren’t ever just sitting there they are always doing something.

Bibliography:

• “The Gifted Student”. Kathryn Chval and Jane Davis, Mathematics Teaching in the Middle School, December 2008/January 2009, pp 267-274.
• “Differentiating Instruction in Mathematics for the English Language Learner”. Deandrea Murrey, Mathematics Teaching in the Middle School, October 2008, pp 146-153.
• “Dynamic Concrete Instruction in an Inclusive Classroom”. Bradley Witzel and David Allsopp, Mathematics Teaching in the Middle School, November 2007, pp 244-248.
• “Building Responsibility for Learning in Students with Special Needs”, Karen Karp and Philip Howell, Teaching Children Mathematics, October 2004, pp 118-126.