- Be very concise. Make simple points. Address main ideas as opposed to trying to cover every point made by Johnson.
- Follow the rubric on blog posts. Now that you have read Every Minute and possibly observed a classroom you should start making connections between this reading and other ARC activities. Don't forget to address how this reading will inform YOUR teaching (not teaching in general).
- Original post is due Sunday, May 18 at 11PM
- Respond to questions posed to you and respond to at least one classmate by Sunday, May 25 11PM.
Friday, April 27, 2012
Jonnson's Motivation
Choose a couple main points from this book and explain how they inform your concept of effective teaching.
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From Randy:
ReplyDelete"A student-centered class allows the teacher to step back and let the students build their own relationship with and passion for the subject."...and on a less profound level, people like to do stuff as opposed to just listening. You will hear this repeatedly (in a pleasant tone) "shut up and let them do stuff!" :)
From Jen:
ReplyDeleteIn the beginning of Motivation Counts, Johnson further refines many of his ideas from Every Minute Counts, including updating the U-shaped classroom so students are seated in pairs, naming his Teaching By Walking Around (TBWA) method, and defining “being ready” at the bell as following a desktop code in addition to starter or bell work. As I mentioned, much of this merely refines ideas he put forth in Every Minute Counts. I think pairing is a good compromise for the current push towards everything being group work. While I appreciate the value of group work, I hesitate to always have kids sitting in groups. I think sitting in pairs is much more manageable for introverts, who like to have their own space and time, and for the extroverts who can’t help but talk to whomever they’re near.
Chapter 2 focuses on the key aspect of his TBWA, the art of questioning. I found 2 parts particularly useful: 1) Going through the sample questions at the end to determine why they aren’t strong questions and 2) the “when, who & why” of pausing chart. The former was a good chance to evaluate how well I assimilated his ideas. I don’t think all of them are terrible questions and sometimes I like putting out a question like “What is my next step in solving this equation?” before directing them to write down the answer or discuss in pairs. I think as long as I realize I have to give an explicit direction following it, they’re not bad to pepper in sometimes. The “When, who & why” chart for pausing really helped me visualize the various situations. It can be hard, as Johnson put it, not to show how smart we are with a quick answer. But teaching kids to answer each other’s questions is a much better use of time for everyone involved. (Coming from the theater, I can’t count HOW many times I’ve emphasized the power of the pause, or silence, on stage. It’s nice to see it transfers!)
His ideas on homework and exams seem quite practical. As Tim mentioned, it’s vital that you leave enough space for work on exams if you really want to see it. Yet many teachers forget or underestimate how much room students will need. I also appreciate the explicit modeling and teaching of how to take effective notes and how to prepare for an exam. We expect students to study for math tests, but we don’t tell them how they can do this. Having them list the objectives for what they’ve learned and be able to do problems that satisfy each of these objectives is a great way to prepare them for studying for other classes too.
Finally, I appreciated the idea of introducing the variable more thoroughly. Much of algebra becomes about manipulating the variable and if students don’t have a concrete idea of this abstract notion, it is all rote computation that doesn’t connect to any prior ideas. Putting variables in a problem-solving context—and one they care about, like who has more homework, freshmen or seniors—makes them more accessible.
I will also definitely keep his problems on hand—particularly the appendices and chapter 6!
From Randy:
ReplyDelete"In the beginning of Motivation Counts, Johnson further refines many of his ideas from Every Minute Counts, including updating the U-shaped classroom so students are seated in pairs, naming his Teaching By Walking Around (TBWA) method, and defining 'being ready' at the bell as following a desktop code in addition to starter or bell work."
Good, explicit connection to other activity from ARC.
The point about a variable and underlying CONCEPTS is a profoundly important issue that will be ever present in our program this summer.
Thanks for starting us off Jen!
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DeleteHaving started with the second book in the series, I now see that Johnson repeated, and in some cases revised, several concepts from “Every Minute Counts” to his writing of “Motivation Counts”.
ReplyDeleteIn Every Minute Counts, I found the concept of employing activities in which all students are obliged to participate (no fence-sitters) useful. These can be paper and pencil activities, as Johnson suggests, or the mini white boards, as a couple fellow ARCers had mentioned last week.
I found it quite interesting how the traditional classroom routine can persist for so long. With minor deviations, I saw this routine played out during my middle school observation day (with an experienced teacher). Several of Johnson’s early routines, which he eventually changed for the better, were deeply ingrained in this classroom. We will need to incorporate our own routine into our daily plans, for which Johnson conveniently gives us a template.
To go along with the traditional routine, the middle school classroom arrangement also followed the traditional setup (5 rows of 7 seats facing the front of the classroom). The major difference that I noticed between the two classroom setups (one traditional rows and the other arranged in tables of four students each) was when students attempted to discuss problems or try to help each other. The table classroom was fairly subdued, with students at the same table talking among themselves, whereas the rows allowed students to ‘pick’ who they would ask for help, resulting in several students talking across two or three rows of students…end result was very loud and chaotic. Classroom arrangement is another conscious decision to be made/experimented with.
The chapter on the art of questioning highlighted the obvious, except that this would not have occurred to me if the author had not mentioned it…ha! Obviously, if you want something to go well, you make a plan for it and execute to the best of your abilities. This concept is no different with questioning. That is, when introducing a new learning objective, include prepared questions (and relatable applications, when possible) that require thoughtful responses. Much easier to include it in the plans than to try to figure it out on the fly.
I found the homework chapter most illuminating. The concept that homework is the place for students to make mistakes, and then to learn from them, really struck a chord. This (ungraded HW) is a great way to make learning cost-free, which brings with it additional benefits (confidence building, asking for help, etc.). I think, when you couple the ungraded HW with the HW quizzes (which additionally promote/enforce student organization skills), you are teaching your students not only the math content, but also how to be good students, which just might be the most important lesson we can teach them, especially in the younger grades. Oh, the heresy!
Johnson’s advice on not including HW grades is counterintuitive but makes sense…don’t hold errors against the students while they are learning. Give them credit for completion, even if done incorrectly. This reinforces the primary goal of getting students to understand the material, especially when they are encouraged to understand the HW solutions in the event of a HW quiz (mutually supportive behaviors). BLUF: HW is cost-free learning and the goal is understanding!
I did have one question for the group. Notebook Checks: To me this seems like too much hand-holding, especially if we are in the high school. Is there an appropriate level/frequency/method of notebook checks that will still promote development of good student habits and organizational skills? Thx.
Hi Tim,
DeleteI learned a new acronym from you: BLUF--which I quite like!
As for the notebook checks, fresh from my high school observation day, I can definitely see that some classes and some students would need this level of guidance. The difference between the regular geometry class I saw (of sophomores) and the AP calculus class (of seniors) was pretty much night and day.
Perhaps a good compromise would be doing fairly regular notebook checks at the beginning of the year and decreasing them as the year wears on--once the students have established good habits. I'm imagining maybe at the beginning of the year it's twice a week, then once a week, then once every two weeks, 'til it's once a month. It seems like it'd be an easy thing to check while the kids are taking exams.
I was also thinking if most of the kids are getting it and doing well on quizzes and tests, I'd just check on those who aren't doing so well on assessments, to see if they're struggling with notes, have inaccurate or disorganized ones, etc.
Hi Tim!
DeleteI absolutely agree with the idea that Johnson continues to portray the obvious...and yet I would have never thought of it. I really appreciate that about these books. The changes that can be made to any classroom are not monstrosities, but rather just common sense!
I worked as a tutor and instructional assistant at E.O. Smith High school, and I found that only Freshman and Sophomore Classes really provided the hand-holding type of notebook checks that Johnson outlines. It was incredibly helpful for the students, and even prior to reading Johnson's book, I had every intention to bring this to the classroom.
Many teachers in upperclassmen courses did still hold notebook checks, but did not provide the same type of specific outline or requirements. It was really just a way to ensure students were taking notes effectively and keeping the materials and completed work.
I wish teachers had done this when I was in high school, I think I would have felt better prepared for college and even employment. It does seem like a bit of hand holding, but I think that high school is a time where they really are just beginning to learn time management and organizational skills. I think it's a great way to build a solid foundation and prepare students for the future.
That being said,I think you are right -- their comes a time in their high school career that our leash on them needs to become a little looser. Perhaps each year, the notebook checks should become a little less guided and specific in organizational structure, so that by senior year, the check is less about organization and more about their written content.
Hi Tim,
DeleteI hate to admit it, but I after rereading the paragraph several times, I still can't quite decipher the meaning of BLUF… a little help please!
As far as the notebook checks and hand holding, I see it as a priority for most high school classes as wholes. There are always some students who just mix all their subjects together in a jumble of papers in their backpacks or in the pockets of their binders (even when the pages are punched!) I was one of those kids until my senior year calculus class. That was where I adopted a similar system to Johnson's spiral-bound notebook with an accompanying pocket folder that I then used throughout the rest of my college math courses.
Well kept notebooks are essential in math because they are so necessary for being able to retain the knowledge. There are so many little rules, tricks, and formulas that are difficult to retain if not consistently used. But the notebooks I kept from my college courses have made refreshing the knowledge contained in them so much easier when I was studying for the Praxis II and refreshing to tutor students in Trigonometry and Calculus!
So, true, some students probably don't need that kind of hand-holding, but some will benefit from it immensely, and there's no way to give the support to those that need it without singling them out, unless you make it a policy for the whole class. It is also an easy way for kids who struggle in math to earn top marks on something in class!
I googled BLUF-- "Bottom Line Up Front." :-)
DeleteInteresting dialogue on the notebook checks and structure. At my middle school observation there was a staff meeting and this came up in discussion. The teachers in general chose to strongly suggest various ways to organize notebooks and/or binders but let the kids decide their own personal way as long as it was organized. (Especially given that the kids were distributed hand-outs every day instead of a text, lots of paper to juggle!) Interestingly, some of the motivation behind the discussion was due to parents' complaints that the expected supplies to buy over the summer were getting expensive and kids' backpacks were full and weighty.
DeleteThanks, Jen.
ReplyDeleteThat is a great idea! I had a similar experience with observing a standard geometry class and an honors class. It seems obvious now, but this is not a 'one size fits all' problem or solution.
I have come to the conclusion that I have been living a very sheltered life!
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ReplyDeleteMotivating a teen can be a difficult task, especially to do something academic in which student interest or confidence (or both!) is in short supply. Johnson’s take on motivating in secondary education is one that addresses the problem with more than just his personal philosophy or instruction manual.
ReplyDeleteWhat I appreciated most about this book was the multitude of examples – actual activities, and suggestions on how and when to run them. Compared to his previous book, I found “Motivation” to be far more realistic in today’s classroom because it focused more on activities and less on hypothetical strategies and ideals. Activities can always be modified to the student capabilities within the classroom.
His section about the “art of questioning” was particularly helpful. I do find it difficult to never ask generic, broad questions during a class, so I appreciate the suggestion to follow up a broad question with a back-up plan. Upon receiving no response, Johnson regains interest by first prompting an individual response, followed by partner work, then group presentation. This method is a great way to bail out of a situation where you’ve asked too broad of a question and lost interest in many students. It gives me optimism for those frustrating moments. I now know they can be turned into a truly positive learning experience.
After reading the section on “good questioning techniques,” I am feeling more inspired to develop quality exit slips for my daily classes. I believe it will be important to provide a space for the student to ask questions in this manner, as many students are too intimidated to ask during class. I can then address these questions in my next lesson, and/or present them as “bellwork” questions the following class.
Since finishing “Minutes,” I have been doing more interactive activities, and it has been astounding to see how effective the students are at teaching each other. Johnson is very shrewd to tie this back into the actual lecture by providing space for students to respond to other student responses. I have worked on leaving space for students to respond to their peers and this has yielded great conversations. This really does work well!
I cringed a little while reading Johnson’s approach to word problems– not at what his ideas, but on their current application. The new Common Core standards and Smarter Balance Testing are highly concentrated with questions either presented as word problems or requiring a written response. I fully appreciate the importance of extrapolating an equation from a word problem. Even more so, I feel it is important for students to be able to articulate an explanation for their own responses; students seem to be losing the capability to form well-founded responses. However I feel that any Common Core activities focus more on general and interdisciplinary analysis than on the mathematical process. Common Core activities are often presented with topics that are historical (not in future tense as Johnson recommends) and are not of great interest to the students. I like a lot of Johnson’s ideas on how to teach problem solving skills in a comprehensible and unintimidating way. I am very interested to discuss Common Core more over the summer. I am hoping to learn more about the best application of the activities, and the potential flexibility in modification or supplementation of the material to better follow Johnson’s suggestions.
After applying some of the methods from his previous book and seeing the success that it brings in student learning, I am eager to try many of the activities Johnson provided in this book. I particularly like the test review bingo, as well as the exercise requiring students write their own stories about algebraic expressions. I was also very intrigued by the card tricks. I ran through the first “trick” myself at home. Despite my understanding of the algebra behind it, I still was left feeling relatively awestruck. Applied math is just awesome! I look forward to bringing this and many other hands-on activities from “Motivation” to the classroom
Hi Emily,
DeleteThank you for commenting on Johnson's approach to word problems - I cringed too! Especially the one on p. 53: who reads (3x-6) books or (x+17) books per year?! That "context" does not relate or apply to the situation he tried to put it in. At least he pointed out the unrealistic conditions of the p. 72 problem on p. 74. I hope he made it so farfetched with the intention of illustrating that step.
I did like the one he applied to their car washing fundraiser. As I mentioned in my post, I plan for the first homework assignment I assign to be an extensive survey of the students' interests so I can try to make to word problems as interesting and relevant to their interests (especially their futures and potential career choices) as possible!
One thing that I have observed in the classes I assist in has been the "state mandated close reading protocol". Have you seen this in your classes? If so, how have you approached it? From what I've seen, everyone bangs their heads against the desks when it comes up and I'm not sure how I would handle it myself.
Hi Emily, a quick comment on the common core interdisciplinary approach. I should start by saying that I am not currently teaching full time, so I can only approach this from the perspective of a parent. I know that school systems are struggling with this issue and that at times the results seem nonsensical and lead to the new story about the foolish common core questions. I suspect this is just the normal issues we have anytime things change. I do think that being able to relate math to other disciplines can be motivating. I just took a course in "Teaching Math with an Historical Perspective" and was inspired with some of the examples. A few possibilities:
Delete- The Pythagorean's attempt to suppress knowledge of irrational numbers as evil"
- "Alan Turing's, who solved the enigma code in WWII and was one of the most brilliant mathematicians of the 20th century, struggle with discrimination and societies disapproval of his lifestyle"
- "Newton and Leibniz's fight over who developed calculus'
I think these are all good ways to bring other disciplines into math teaching in a way that enhances the mathematics.
From Randy:
Delete"What I appreciated most about this book was the multitude of examples – actual activities"
All, keep in mind that the program will be filled with ideas - TONS of them. Reflection is what you use to figure out how to use them. There is no decision tree we can offer because there are so many factors at play for a given situation. You will ask us several times to share what to do for a given situation. We can share our thinking for a possibility but ultimately a teacher must figure out things on his or her own with the input.
I also like your idea of finding out the students' interests in the beginning of the year to aim word problems which are relative to them. Also Common Core is such a hot topic now, it was mentioned a lot in my observations (which were made subsequent to my post on Motivation Counts). The schools I visited seem to be on track implementing the units and topics after a busy year of change. There are teams set up to coordinate handouts and new material. Textbooks were not visible anywhere because their chapter sequence was not in line with CC's. All the teachers were using thick ring binders to coordinate the CC units. I think their issues were mostly with teacher evaluations and how fast the Common Core envelope had been pushed, when Elementary Ed wasn't quite 'there yet.' I am really looking forward to hearing more about CC this summer!
DeleteOne of the topics discussed in my "Teaching Mathematics Meaningfully" chapter (8) talks about determining student interests at the beginning of the year so that you can make more enjoyable word problems. Even doing something like including them in the word problem gets them more interested in them. I think that a student interest survey is a great first day activity for class or homework, especially for those who need a day to get back in school mode!
DeleteI love the idea of tying history into the math course. It's easy, because many historical events have data to accompany them. I wonder if there is a way to first find what student interests are, then find relevant historical events (even small, local, or seemingly trivial)....and yet still follow Common Core's seemingly rigid activity structure. I'd really like to explore this more!
DeleteRandy, you are very right. As Lemov put it, we're gathering our tools, and then we have to decide which tool to use and when once we are in the classroom. After reading Johnson's "Minutes," which seemed more focused on strategy for the hypothetical, it was really great to take the next step with this book and start getting those tangible tools!
DeleteIf anyone is interested a couple of good websites on math History are
Deletehttp://www-history.mcs.st-and.ac.uk/ (MacTutor) and
http://www.math.harvard.edu/~knill/teaching/mathe320_2014/index.html
(not well organized, but lots of stuff)
Johnson’s "Motivation Counts" offered many techniques aimed at motivating students to be engaged in Math class, such as artful questioning, homework and tests, problem solving, and making variables more meaningful. Some of the ideas were extensions from the prior 2 “Minute” books, such as TBWA and the U-shaped classroom.
ReplyDeleteWhen reading Motivation Counts, I found several topics to which I was drawn as a future teacher. I liked the concept of questioning student responses with “Why?” but in the less stressful form of “How did you arrive at that?” When I try to relay a concept to my co-workers, or my son, or anyone I am training, it is imperative that I know the thought process they are using to achieve their answer, so I can assess if they understand. Asking, “How did you see that?” is a great, informal way to let the student explain in his/her own words. Plus, the other students can benefit from hearing the thought process. The art of questioning, as Johnson explained, is crucial in motivating students to participate. I am scheduled to observe my first class for ARC on Monday, May 19th. I will be curious to see how the teacher questions her students, as opposed to straight lecture. I recently observed a video segment of an Algebra 1 class learning patterns and sequences using a pool and patio tile story. The teacher, instead of talking for 40 minutes, spent much of the class asking students questions, having them offer ideas, and going up to the board, in order to teach the new topic. I was impressed at how interested the kids looked because they were actively involved in finding solutions to this pool problem.
Part of the reason the kids looked engaged was because they were working in teams. I love the idea of pairing desks. Working in pairs or teams takes pressure off one, especially shy students. Working together not only brings out a wider variety of skills to solve problems, but it prepares kids for working together in the workforce someday, where teamwork is critical. Going up to the board in a trio or pair is something I will want to incorporate in my classroom. As a former shy student, I find the “buddy system” a good approach to not being afraid of being incorrect.
Another of Johnson’s techniques I would most like to implement is using a story or problem setting to illustrate a computation. For instance, to illustrate division of 90 by 14, Johnson instead asks how many pizzas can you buy with $90 if each pizza costs $14? I would like my lesson plans to always include examples relative to the learner. Additionally, I would like to incorporate some form of the sample lesson plan that Johnson offered. It is wise to include an area of your daily lesson plan listing which NCTM Standards are being addressed in the lesson. (I think now that would be replaced with which Common Core State Standards are being addressed in the lesson.)
Lastly, I must comment that the “magic” card tricks ideas are clever, yet I’m not sure I could pull those off. I think I would tend to modify that concept slightly with number tricks instead, such as “pick a number, multiply by 2, subtract the original, etc.” And while I really liked the idea of Bingo for test preparation ( definitely want to add that to my tool box), I chuckled at the thought of giving peanuts for prizes since most schools are “peanut-free zones” these days due to nut allergies.
All in all, the book offered some great examples, in detail, to motivate students. I will begin a file system to organize these ideas for the classroom.
Kelli - I so agree about working in teams or pairs. Not only does it take pressure to succeed off of those students who might lack in confidence, it provides many students to take leadership in teaching their peers. I have already seen some pretty remarkable moments with students teaching other students, coaching them through the learning process as a friend (rather than me doing so as an adult "authority" figure. It's so effective!
DeleteIn Johnson’s “Motivation Counts” the author does a great job of expanding on the earlier two books. To me this was more of a detailed account of the methods he uses and why they are successful.
ReplyDeleteJohnson talked about being a “band director”. He was there to coordinate and guide the learning and ultimately the students were each going to be responsible for bringing meaningful incite to the lesson. This is how I envision my ideal classroom. Students will be engaged with me guiding the lesson with the goal of the lesson clearly stated at the beginning of the class.
We have read three books now by Johnson and a topic that he keeps going back to is the way the teacher asks questions. Simply asking one student and assuming that the whole class is in agreement with the answer is not a great way to deliver a lesson. Johnson gives great examples of question starters and even gives some examples of questions to avoid. Working in a school and having already been exposed to delivering small group instruction, I immediately recognized my favorite and most effective question, “Stop-don’t raise your hand-just think about this…” It forces the group of students to work out the process and think about why they are performing a certain step, rather than just putting down the first idea that pops in their head. In my high school observation, the teacher used this questioning pattern when discussing slope. He asked the students to take a minute and think about how the slope of a line would look if the equation was linear and modeled the price of a car over time. The students in the class were very successful with this question and the built in pause of stopping and thinking created an outpouring of volunteers to give examples.
I found the last five minutes of class section very interesting. Johnson spoke highly of engaging and doing meaningful work in the first five minutes of class. The last five minutes are just as important. It is a valuable time where teachers can use to check for understanding of a lesson and make sure the students have the appropriate level of competency for the homework. It is also a time for me, as the instructor, to see if my objective of the lesson has been accomplished. If it is not, then at the very least then next day’s lesson will be altered. The group discussion and written reflection of the day’s lesson is one that I will try to incorporate in my own classroom.
From Randy:
DeleteBeing a "band director" means the kids are doing the work. REMEMBER THIS!
Johnson’s “Motivation Counts” begins by expanding upon some of the techniques discussed in “Every Minute Counts”. He adds a student pair component to his previous U-shaped room, something that I have had great success with (at least the pairing part, none of my rooms as a sub have ever been arranged in a U-shape!). He reiterates the paper and pencil responses coupled with a TBWA approach. He also reviews the importance of starting the class immediately and keeping them engaged until the end. The techniques that I most enjoyed and plan to use are the cooperative learning, the questioning techniques, and the homework and test suggestions that he discusses.
ReplyDeleteAs I discussed in my last blog, I am a huge fan of the cooperative learning style. I like the paired seating arrangement, although I have only ever seen it in a more traditional “rows and columns” approach rather than the U-shape that Johnson uses. When you give the students a problem to do, or worksheet, or quiz, allowing them to work in pairs is a confidence booster. Sometimes they find out that they’re not the only one with questions, and so they don’t feel so embarrassed to ask their questions. Other times you have complimenting abilities, and the students can work together to solve a problem with both of their inputs. They also like having the chance to talk and listen to a peer rather than just the teacher! I also like Johnson’s suggestion of using pairs to demonstrate problems at the board. One student isn’t singled out, he has a partner to help him out if he needs. This type of work also prepares students for the fact that they’re probably going to have to work with others at some point, and that it might not always be their best friend, but they can still solve problems with others.
Some of the questioning techniques that are discussed in this book also appear in “Every Minute Counts”. One of these is addressing questions to the class and then building in a pause so they know that everyone has a chance to think. He also discusses using paper and pencil responses for practice throughout the lesson. I like that approach since it breaks up the lecturing portion and gives them some confidence. I find it interesting and a good point that sometimes it is inappropriate to give students praise, as it can shut down any further discussion. Finally, he brought up the balance between “never pass(ing) up an opportunity to ask a question rather than make a statement” (p.20) and “not wast(ing) my students’ time by asking questions that would be better made in statement form” (p.40). I think it’s a good practice to use questions to get the students involved, but sometimes it’s better to just state it when it’s an obvious fact to them (he uses the example of adding 3x+2x=5x in a calculus class).
The homework and test suggestions are helpful as well. I like that he makes it clear that homework is a part of the learning experience; it’s not a penalty for the students, and they aren’t rewarded with “no homework” for being good or for it being a Friday. He also mentions giving in class practice before assigning the homework, something that would seem to be obvious but something that isn’t always done. My brother has had to ask me several times over the past year on how to do some homework problems because it was assigned without the students seeing any examples on what to do with those problems. I also found it interesting that he gives homework the night before the test. It seems like a good way of making the students study, since some won’t bother with self-study habits. Also regarding tests, I like that he suggests smaller, weekly assessments, and that he includes something from the previous week that the class needed better practice on.
This book was a great addition to the previous two. I like the variety of suggestions to motivate students. Another suggestion that I liked was to build up a collection of problems over time so that you always have more if the students need further practice. I will be eager to try some of these to see what fits my style.
from Randy:
Delete"He also discusses using paper and pencil responses for practice throughout the lesson."
Having them write responses builds in wait time (the pause you mention). It also helps to get all kids involved in the questioning. If you wait for kids to respond you will leave several kids out each and every time you ask a question!
In the Middle School class I observed today, the teacher said to the class something like, "When I am writing, you are writing" and the kids reciting it with him as they ran for scrap paper. My one and one discussion with the instructor between classes was almost a complete summary of the Johnson series. He told me, "Straight lecture and then a homework assignment as they head out the door just doesn't work anymore. You have to have the kids engaged, actively working, the whole class."
DeleteRandy, that kind of technique is something that I have overlooked in my short time teaching. I had previously gone with going through it with a volunteer verbally, but I like this way a lot better!
DeleteKelli, I had my middle school observation yesterday, and all of the teachers I talked to had similar thoughts about lectures. They infused a lot more group work and activities into their teaching (we did a few fun probability ones).
I had a lot I wanted to comment on while reading Johnson’s "Motivation Counts." Since I want to hit as many of my points as possible, but not the character limit, I have addressed them in a bulleted fashion:
ReplyDelete• I observed a remedial/intervention co-taught class where a no-hands system (as opposed to pp. 10-11) was used very effectively. The teachers explained afterward they usually insist on hands, but this class was an exception. They had worked hard to create a safe environment to make mistakes. Many of Johnson’s artful questioning techniques made it work, such as: pausing, remaining neutral until many students volunteered answers, encouraging student discussions of answers, and giving lots of time to work out answers individually at their desks while walking around to check.
• I liked the mention of SAT or ACT questions as openers (p. 12). I have always planned to incorporate standardized test questions because different things motivate different students, and there are always some who care about those scores!
• I also observed the use of an “Exit Ticket” to capitalize on the last 5 minutes of the period. This would be a great application for the “last-minute challenges” (p. 15) Johnson lists. The question is printed on a slip of paper students must hand to the teacher at the door to exit.
• I saw the ‘heads up’ and ‘pencils down’ (p. 23) implemented really well in one of classes I observed. It wasn’t explicitly mentioned, but it’s an ideal time to circulate, rather than stand in front to watch for when everyone’s finished.
• I agree that asking a group if they understand is worthless (p. 30), but I do think it’s worthwhile when working 1-on-1 to gauge when to switch from my showing them to them showing me. Also, my book was previously marked, and I liked the reader’s margin notes on p. 31 to have secret signals for students to use in class if they don’t understand.
• I already typically follow up responses by soliciting the students’ thought process, but I often find they need a little praise (despite what Johnson recommends on p. 33), even if it’s just for volunteering their answer, to give them the confidence to go on to explain their approach. Also, I believe a 50/50 or easy question here or there can sometimes be useful to help boost students’ confidence, particularly if the answer is “yes” since saying “yes” psychologically decreases shutting down.
• An extension of Johnson’s “mistakes as a route to success” (p. 35) I would like to incorporate into my classes would be asking students to supply problems with lots of errors, or a single hard-to-find error, for us to correct as a class. I imagine it as a math version of the Daily Oral Language exercises we did in English class when I was a kid. This would enable students to disguise their mistakes as intentional creations and learn from their classmates’ explanations.
• An idea I would like to try to implement to encourage students to explain problems with questioning and directions (p. 46), would be to invite students to impersonate or even mock how I explain problems, to add an element of humor, entertainment, and levity to the class.
• I love the idea of short weekly tests, especially including the most missed problem from the week before! (p. 48) I also love the suggestion of games for reviews, like the Bingo (p. 51).
• A word of caution: Johnson suggests ‘having students use diagrams and manipulatives whenever possible’ (p. 71) when working with word problems, but I have some students for whom it makes the algebraic work appear pointless - “Why do I need to learn algebra when I solve the word problems with logic?!”
• Similar to how Johnson rewrites his word problems (p. 72 & 75), I have always wanted to begin the year with an extensive survey to collect info about my students’ interests to use to personalize the word problems for each class.
• I loved the math tricks (p. 77) and would extend it to ask students to come up with their own!
• I also love the filing system suggestion (p. 84) – I really need to start that asap!
I really like the idea of a math DOL exercise. Kids love pointing out teachers' errors--that would be a more constructive way to use that instinct. And it forces kids to carefully go through each step to find the error.
DeleteAs for beginning the year with a personal survey--my HS calculus teacher did that and she found it very useful. Not only can you use the info to personalize word problems, but you can also find out how students feel about math, which areas they're worried about, where/when they stopped (or started!) liking math, etc. Knowing some of those stumbling blocks ahead of time, teachers might be able to plan for them better. This supposes, of course, that students take it seriously and are open and honest...but since most people like talking/writing about themselves, I don't think it will be too much of a problem!
I'm glad to hear you liked my Math DOL idea! It's hard to say to what degree all the focus on critical analysis in so many other classes affects them, or if it's just a part of their nature at that age, but teens love to find mistakes and faults in everyone and everything! It's like a little treasure hunt, and even if a kid might be overwhelmed by the idea of tackling a whole problem, picking out little mistakes - like two negatives should make a positive - would give them a safe opportunity to volunteer and participate (in addition to being able to shamelessly provide the problem in the first place.) This would further support "normalizing" participation, as Lemov promotes in many of the techniques (particularly in "No Opt Out", "Cold Call", and "Positive Framing"), since it makes participation safer and more accessible to all levels of students. I can also imagine how well differentiation could be applied to it by having mistakes to correct ranging from little computational errors to more complex or abstract conceptual errors. Throw in Lemov's "Cold Calling," and you can discretely allocate the various degrees of difficultly to the appropriately skilled students.
DeleteAlso, I'm glad you brought up including asking students about math in the survey. While I already intended it to go beyond just their interests and potential futures, I hadn't thought about asking for them to identify any particularly weak areas in math and I think that is an excellent idea! I was also planning on including questions I could use to attempt to identify their preferred learning styles (the verbiage from any descriptive short answer can be a very strong indicator), as well as directly asking them about their preferred classroom experience (i.e. to rate how much they like to be called on, if they like being called on but just don't like raising their hand, etc.)
Another way I would I would like to apply the info I glean from the surveys would be to expose them to potential careers they may not have ever thought of or been exposed to that I think would possibly suit their interests and temperaments. For example, if someone likes group work and outdoor activities, I might include a word problem that would illustrate how an Adventure Guide could use a linear equation to do the meal planning for their expeditions, or how that could applied to ration the remaining food in an emergency. I have already encountered many kids who plan to work at the same fast food restaurant their parents work at simply because they haven't had the exposure or imagination to dream beyond that.
I really enjoyed this week’s reading. The chapters on helping students understand the abstract really struck home with me. As a former mid-level finance/actuary executive my two biggest complaints about new employees was (a) a lack of quality control and (b) an inability to communicate the results of their work in real world terms. I think Johnson’s focus on understanding the abstract may help with both of these issues.
ReplyDeleteI think that good quality control comes from being able to relate a math problem to the real world and to understand the range of reasonable answers. I think that converting exercises into word problems (or “math situations”) gives student a context in which understand the possible range of answers. I might add to Johnson’s list of questions one that says “before starting the problem do you have any ideas the range of possible answers”. Also, having students really understand that variables ultimately translate into numbers promotes the very important technique of substituting in sample answers to an equation to see if works. I just completed my middle school day and I saw a couple of teachers doing this. If the class answered a question wrong, they would sometime questions like “if the answer is in pounds what do you think are reasonable numbers for the answer”. Also I can see how these techniques would work in terms of motivation. Given Johnson’s discussion of how students are afraid of being wrong, it seems that giving them techniques to check their answers would help to counteract that problem.
On the issue of communication I really liked the idea of having student write their answer in words at the end of problem solving. In modern business what manager/executives really want is not just an answer to a specific issue but how that answer relates to other issues and what does it mean in a business context. I can see where having student consistently practice that skill can help with communication. Based on my reading, plus my statistical sample of one (my 13 year old daughter), one of the biggest de-motivators is not understanding how they will use this math outside of school. Translating math into English seems like an effective technique to help demonstrate the actual use of these problems.
To end on a slightly different topic, I really liked the examples and sample questions that Johnson gave, many made me pause to make sure I knew the answer. Since I decided to make the career change to teacher, I have trying to keep a notebook with interesting problems I run across. I am adding these from Johnson’s book to it.
Hi Pennell,
DeleteI had a similar experience in my high school observation to your comment, "If the class answered a question wrong, they would sometime questions like “if the answer is in pounds what do you think are reasonable numbers for the answer”. Mine was not a case of the question being answered wrong, but the students asked if their answer would be marked wrong if, when rounding to nearest tenth decimal place, they were off a tenth +/-. The teacher responded with relevant questions: "If you ran a race on the track team and lost by one tenth of a second, wouldn't that matter? If the wheel bearing on your car is off by one tenth of a millimeter, and the car crashed, wouldn't that matter? So yes, I will take points off for decimals being off a tenth." I thought her real-life examples were right on and made a point, plus the kids answered her questions without hesitation because in the real life context, the answer was simple to them!
Pennell,
DeleteYour example of asking students to explain word problems in complete sentences is a technique I saw used successfully on my day of middle school observation. I loved the phrasing that the teacher used to queue the students into a more analytical response. The student responded with “12” as the answer; the teacher paused and said “Word problems have word answers, can you tell me more…”. The numerical answer was correct, but the focus was not on just simply getting the right answer. The student were forced (indirectly) to answer the question “when will I use this?”. Creating connections between the topic and the subjects and activities that the students are interested in is a strategy that I plan on including in my ideal classroom.