Hello and greeting again folks,
We are moving right along and time has come again for a second discussion. Before the topic, however, let's just recap on an item that may require your attention.
As Christine mentioned, the Teach Like Your Hair IS On Fire book study on moolde is now up and running, but unfortunately, not all of you are running with it. As of this moment, only 12 of the 40 MTMs have even logged into the site. Furthermore, only 1 MTM, congratulation to you SS, has even answered any of the forum questions. I realize you have until December 15 to do the book study, but it defeats the purpose to try and do the whole thing in one evening, right at the deadline.
Please folks, get busy on the book study!
I was helping my son with his 4th grade math homework and he was working on translating word problems that involved multiplication and division. Since their current topic is division, he generally wanted to assume that ALL problems should involve division and made a few consistent mistakes. When we slowed him down and forced him to think through the material, frequently asking him to paraphrase the situation or asking him "Could that make sense - could that really happen?", he fairly quickly realized his errors and got the problems corrected. His main problem seems to be he likes to get the work done fast, regardless of if it is right or wrong, and loathes checking his work.
How do you help your students to avoid these types of errors and how do you encourage them to check their work. Even at the college level students see checks as an odious task, what magic words should we use to motivate them to the need of this task? At the college level, I try to tell them that 15 seconds of work checking a problem and thus correcting an error may save them a full semester's worth of work if they were to consistently make the mistakes, fail, and have to take the course over. Like my son, I see students roll their eyes at me and think I am just mothering and smothering them with this advice. Help!
You may also feel free to discuss other predicable errors you see students make and either offer or request advice.
I really look forward to this discussion...so have at it!
Thanks, Richard for the book study reminder. I had sent an e-mail earlier this week expressing the same sentiment. Here are a couple of links with interesting information about "great teachers" that I think would be worth everyone's time to take a look at. I know they may be about a year old, but they are still pertinent.
Thanks for the links Christine. I watched the videos and they were interesting. I applaud the financial commitment that Bill Gates is putting behind his beliefs, but I have really never been a fan of high stakes big time standardized testing and have strong personal doubts that great teaching is truly quantifiable. I realize this may not be a popular opinion, but I have always believed that what makes a teacher memorable or effective, or inspirational goes so much beyond the scores students get on tests. When I was an undergraduate, some of my most memorable teachers, the one I thought I learned the most from, were sometimes the most demanding and rigorous. As a direct result of these high expectations, students learned, but did not always score "higher" than students in competing classes. In graduate school, I had one course where virtually everyone got an "A", yet I never really felt challenged, nor do I have profound memories of the material.
Before I ramble on indefinitely, I will close. I found the videos interesting, especially the part about our teaching habits being formed within the first three years. That part really made me think retrospectively about innovations I have made in my teaching and practice and at what relative time I did them. Good videos! Still having trouble with the quantifiable "great teaching" part...
First of all, many of my students seem to have the same issue. They rush to finish the problem and actually believe that because they answered it, it is automatically correct. Last year, I decided that when it came to solving word problems, they had to put their pencil in their desk. read the problem 3 or 4 times, ask themselves what the question was asking, figure out what kind of problem it was, and how they were going to solve it. Once they did all of that, they would pick up their pencil and start their computation. We, of course, went over several problems together in class.
This year, I am also implementing the same method. I feel that this has helped them not rush to finish their work.
Through CSCOPE, we are using make a table, guess and check, work backwards, and draw a diagram. I used this several years ago. It's back and it works!!!!!!!!!!!!!!
The students rushing through their work and just hurrying to get it done, has been a huge problem in my classroom since the first time I started teaching. One thing that I have decided to do to help my students not rush through their work is have the students explain why their answer is correct. Usually the studetns would have several answer choices to choose from. They have to say why their answer is correct and why the others are incorrect. They are also required to draw a picture explaining their thought process. This has seemed to help.
Nice to hear from you and everyone else! Time is at a premium; however, the group always has good ideas to share.
My high school students also want to rush through their work. Furthermore, they want me to help them with each step of their practice work. I tell them to try "it" on their own and then compare with a peer. They say they might do it wrong and will then have to redo it. I just keep on telling them that that is the proper sequence - do, redo, do, redo >> until you get it right.
This past Sunday, I had several students come in to make up hours - they had excessive absences or referrals to the office. They all had work solving equations for their Algebra class - I had them "check" each problem by substituting in the answer they had gotten - half of all their answers were incorrect. Because they were captive for 3 hours, they had to check their answers - on their own, they would not have done it. I guess we just have to keep stressing how important the act of checking their answer is.
I will join the book study today - if I have problems with the process, I will get back to you.
Talk to you soon! Christy Gonzalez
I do the same in my classroom. My students must have been told that there was a 1st to finish award that i am not aware of. They have to be constantly told to slow down and check their work. When I am over their shoulder and asking them how they got their answer they look at me and say "oops"! i messed up and give me that little grin they are known to give the teacher.:) I just have to tell them over and over again to slow down and make sure their answer makes "sense". It's a just take it day by day situation, and hope that one day they actually take our advice to slow down and check their work.
Dear Richard, the second topic for discussion is a common predicament in Math classes, especially when the topic is word problem solving. We always remind our kids to go over and review their work, double check if their answer makes sense. When I attended Melissa Kulchak's Problem solving the Singapore Way Grades 6-8, I felt like my problem was answered somehow because with this process, the students learn how to analyze the word problem, thus slowing them down and giving them enough time to think and understand the problem. Here is one discrete example I got from the book: "Janet picked 3 daisies and 2 sunflowers from her garden. How many total flowers did Janet pick from her garden?" There are a few steps to follow to chunk the word problem.#1. Read the entire problem.#2. Rewrite the question in a sentence form, leaving a space for the answer: "Janet picked a total of ----- flowers from her garden." #3. Determine who and what are involved in this problem. (We're talking of Janet and her flowers.) #4. Draw the unit bar(s) to represent the 3 daisies and 2 sunflowers.The title of the bars is Janet's flowers; 3 unit bars are labeled "D" for daisies and 2 unit bars are labeled "S" for sunflowers.#5. Read the question again: " How many total flowers did Janet pick from her garden?" How are we going to figure out the total number of flowers that Janet picked? ( Students will say add 3+2=5). #6. Are we finished? No! we need to go back and add the answer to our sentence. Let's reread our answer and make sure that it makes sense. "Janet picked a total of 5 flowers from her garden."
Melissa gave us other examples, ranging from simple addition to rate, ratio, percent, and even some problems bridging to Algebra! These step by step problems will really help the students to slow down and will give them enough time to think what process to use and if their answer makes sense. I would recommend this workshop to any Math teacher strongly!
Great discussion question! I have made posters for my class that say "Show your Thinking". Several of my students rush through their work and I have had to conference with them. I let them know that I am not just looking for an answer, I want to see their path of thinking. I also have them explain the steps they used.
We have also worked through the C-Scope lessons for problem solving. Make a Table, Work Backwards and Guess and Check.
I am finding that my students lack self-confindence with Math. They are struggling with taking risks. They don't want to be wrong. Many of my students are waiting for me to model and go over the answers. I am trying my best to teach them to think on their own.
My students are also scare to take a risk with word problems. I use the theT chart with my students. They have to write the understanding, planning, solving and checking. They must prove their answers two different ways. Examples---Lattice,Partial product, 5-Up for multiplication, 9 rule and In and out rule and etc.... I use the Spiral Review and the 5-minute check daily. If they would only slow down and read the question more carefully it would make a difference.
When we taught rounding and estimation, I showed them how to check their answer by using the actual numbers. If the actual answer could be rounded to equal the estimated answer then the student had done the work correctly. However, if the estimated answer is something like 25 and the actual answer is 38 then they should go back and work the problem again.
Another thing I do is make my students search for keywords and write the operation(s) anytime they are working on a word problem. For example - Tina has 12 apples. She gives 3 apples to each of her friends. How many of her friends get apples? They should circle or highlight 12 apples, 3 apples, and each. They should underline the question. They should write division next to the problem. After that they can begin to solve. It worked well for my students last year because they had to SLOW down, READ the problem, and THINK about what it was asking them to do. I've shown my students how check subtraction by adding. Now we are working on multiplication and division, so they are learning to check division problems by multiplying. I've also told them to reword the question if it's written in a confusing way. Sometimes word problems are written to confuse, and I want my students recognize this when they are being tested.
I stress to my students that it's better to be slow and correct than the first one finished who has to redo their work. At this point in the year (end of the second six weeks), the class knows that if I'm not satisfied with the effort they put into an assignment, then they won't be allowed to turn it in. As they complete work, I spot check it for errors (forgetting to regroup or using the wrong operation for example). If I see a major mistake, I give it back to them and point it out. I continue to give it back until the problem is corrected or they ask for help. As I monitor I ask them questions to lead them toward the answer. "Look at the digits. Are you supposed to borrow?" or "If the questions says, how many more, what operation do you use?" Most of the time they should need a hint to make that lightbulb come on.
This is a very good question that I think all teachers stress over. I recently have started making my students rephrase the question in their own words, write out the important facts, and show a diagram or picture to demonstrate what is going on in the problem. Working out the problem is the final step. This seems to have really helped my students with their problem solving. When I ask them how they know their answer is reasonable, they are able to justify what they did through their diagrams. They are now begging to show how they solved the problem and love that their diagrams or pictures are different from everyone elses. The math seems to be more personal and they really own it.
As mentioned by everyone else, this issue is especially prevalent in math classes. I even have kiddos who immediately say "I don't get it" so that they can get help...I have implemented many of the same strategies many of you have done..
1. There is no prize for being first to finish...in fact, you will stay longer for tutoring if you are not successful
2. Limit the number of problems so that the assignment is not overwhelming
3. Have students break down the problem into its parts starting with "what is question?" I have them rewrite the question into an answer statement to help them understand what they are looking for; then I have them identify all information paying particular attention to labels...these are especially important for multip-step problems. Key words can be helpful, but I also point out how "key" words can be misleading.
4. I have my kids think about the problems as mysteries that have to be solved...noting that the problem will give them some clues, and that they are to use the clues to determine the answer.
5. We also talk about the different ways we can solve the problem and I encourage them to show two ways to solve the problems (I can't get everyone to...but I do have kids share their different ways to the whole class)
These are just some of my thoughts pertaining to this post...it is certainly a pertinent concern as we face this everyday and strive to slow the thinking down for these kids and help them "think it through".
I agree with everyone. In teaching 2nd graders, most are not fluent enough readers just yet, so there is a lot of group and small group work. After the problem is completed, then students will share how they worked it out and we learn from each other. However, when a unit test is given or six weeks test is given, the same issues occur that have been mentioned: just writing down the numbers and solving the problem and not thinking if it makes sense, just finishing the test and getting through, etc... We keep working on this problem with daily math. I do like the idea of giving fewer problems and then checking. When a stapled booklet of questions is given, the kids just seem to want to get finished.
I attended an Autism conference several years ago in which one of the guest speakers was an occupational therapist researcher. She stated that years ago, children were placed on the floor at home. It was up to them to figure out how to go after a ball across the room and they started moving to get what they wanted. It was an internal process. In more recent years, many children are raised in cribs in larger daycare situations and they are confined to the bed and wait for someone to come to see about their needs, so the kids somehow are waiting on adults to do things for them or tell them how to do things--external. It was a very interesting session!!-- Something to think about.
Ahhh it is one thing to do the math and another thing to think about the math. I tell my students, my own children, to act out the math problem in their mind. Ya know method math! Most students are disengaged with the math that they have zero connection to the common sense side of problem solving. Having them slowdown, methods like Singapore Math, and manipulations help bring the math to life!
When we worked on division, my students had a very difficult time with it. I got the impression that some of my studennts thought that if they "stayed under radar" during the duration of the lesson and moved on to another lesson, they would not have to deal with division again. I reminded them that division would be a part of their life from this moment and into adulthood. In my Math classes, we use spiral review problems which use divison as a possible solution. We use T-Charts which require the students to set up their problems with necessary information, solve the problem and lastly but certainly not least, to CHECK their answer. This is the part where I lose many of my students as they refuse to check their answer. More times than not (as we all know) their answer will be a likely choice but NOT ALWAYS the correct answer. On a daily basis, I remind my students that they must check their work to ensure that they worked it right to begin with. We use different methods of checking to include repeated addition when feasible, partial product, lattice, 5-up, 9's rule and standard multiplication.
In my experience with addition, subtraction, multiplication, and division, memorizaation is the key to
being successful. Checking and rechecking must be a strategy that must be used each time.
Showing their work is a must. The students must be responsible with each math activity. Sometimes
in my first grade class, I give stickers as an incentive if the procedure is done correctly. The kids
I'm behind on these discussions but wanted to give my input if its not too late. I started a Math detective booklet that I have the students solve mystery's in. I put up a word problem and I tell the students to only write down the question, as you all know some of the students (4th) do not know and will want to copy down the entire problem, well to me that's a major "problem" not knowing the question. I then have them search for "clues" pertinent information. Polya my favorite has a few problem solving strategies and one is go back to the problem and ask yourself does it make sense. I have the students to do that also. The students like that I do not make them copy the whole problem down so they are willing and I break it down so they think they are not really "working". Oh I also put on the inspector gadget theme song to tell them to get their booklets out so they like that also.
The students that I teach also do not want to show their work or even read the whole problem. I have them focus on the question, paying attention to the nouns and verbs used in each question. Then I ask them to go through the problem again and find the information that goes with the question. Using diagrams, t-charts, and what ever else will help them solve the problem is encouraged. It is amazing and fun to watch the many different approaches students use to solve math problems. I always tell them that there is more than one way to find the solution and then let them share their work on the smartboard (which they love to use). It is an ongoing process to get them to slow down, read the problem, and check their work to be sure it is correct.
I have to agree with everyone here, slowing down is hard for our students. However it is essential. Taking the risk is by far the biggest problem I have, some of my brightest students would look at a problem, not even read it, then say, I need help it's too hard. This unfortunately is only my second year teaching math, and I have learned so much, but it was nearly the end of the year, (after STARR) when one of my higher achieving students came to me 3 times in a matter of minutes. I was working with a small group and kindly asked her to go back read the problem and tell me what it is asking after the third time, I realized we had a problem, I had done this child a great injustice, I held her hand! She was so afraid to even try the problem, she had no confidence in her own skill (that she has plenty of). She would rather not even try. I have read many of your strategies, and while I have little to offer, I will defiantly be using your ideas next year.
One thing I do in class and it is with any problem is take the answer choices away. This way even if they use the wrong strategy I can see if they used addition, subtraction, multiplication, or division. I also always make them draw a picture or show their work some way. Before they start the problem they are to just read it and make sure they understand all words. Then, they are to look at questions to find out what it is asking and then go from there. No matter what you do there are those kids that are going to rush and do the wrong thing then they see that their answer is there when you have choices so they think it is right. By taking the choices away it makes them stop and think a little more. All kids want to add or multiply and even if they do the wrong thing the answer may be there because the choices they put on the test is for those kids that they know are not going to read the question and find which one makes sense.
Something I do to make my students slow down and think about the problem is I make them rephrase the question into a statement with a blank at the end. They must write this out in a complete sentence. That helps slow them down and really understand what the problem is asking. Then, I also tell them they must show their work - either through a drawing, a t-chart, or any other model they feel comfortable with. Also, if I have one of those classes that have problems showing their work, I often give students two grades on assignments - one for accuracy and one for showing their thinking!
I feel your pain here. I tell them over amd over again to check their work. I emphasize to them that if they check their work, they won't get any problems wrong. I also grade them on whether they show me they checked their work, at least in the beginning of anything new that we do. I think this helps somewhat anyway.
We used Singapore Math alot this year. My favorite thing about it is that the first thing you do is find the main question and then rewrite it as a sentence with a blank. When you finish the problem, your answer should fit in the blank and make sense. This helped some with the problem of trying to finish too fast!!!
I liked the idea of using the Mary's choice of music playing while students are working on the problem. I use the word problem template where you divide the paper in fourths and place the word problem in the middle of the page. They chunk the word problem using the four sections.
? Answer the question in a sentence. Info needed to answer the question.
_____________________________ Word Problem Here______________________________________
Illustration of Problem Soluttion/Checking your answer
(Students draw a picture of the problem and
some do number sentence here.)
I model problems through constant questioning. How can I answer the question in a sentence? As you chunk each sentence, ask Do I have information in this sentence to answer the question? What can I do to illustrate the problem? It's a full time job of repitition, questioning, and monitoring. I hope this helps.
Not only do my students not want to check their work, they don't want to show their work. Those students that do show their work easily find their mistakes. My policy is "no work, no credit!" Even with this policy many students still choose not to show their work. In Geometry there is always a few problems that do not require work so they know they will get some points. They just want the answers or they want someone to tell them every step on every problem.
Every year I have students who want to complete their work quickly and they are not careful with their work. Sometimes, a way to solve this problem is if they know they might have to do the work on the board and explain each step. Many of my students enjoy working problems on the board and when they do this, they have to explain the problem and the steps they took to solve it. This doesn't work with all students, but it will help some of the "rushers" slow down a bit.
Re: 2nd Six weeks required discussion
I, too, have problems getting the students to see the value of checking a problem, as well as to slow down in solving it. It takes quite a big of convincing that a problem should be read, first, to figure out what the problem is. I encourage them to draw a simple picture or diagram to show what's going on. Then they need to go back and reread the problem to see how the given information relates to the problem. This becomes increasingly important in 6th grade as the year progresses into integers, in which the "biggest number" may not necessarily go first in an equation. I then ask them to back, reread the problem again to see if the answer actually is a reasonable one. I find that most students know how to estimate an answer, but do not understand that the estimate should be made first before actually solving the problem.