Math makes its way into our lives whether you like it or
not. For those nay sayers who think they don't need math because it’s a skill
they don't require for the type of work they're going in, I say math will
inevitably find its way into your heart. It’s like a cold you think you'll
never get and then you get it. At first you're upset but then you accept it and
life goes on. Math is a language we all must speak in one form or another
because it is omni-present, ubiquitous, staring at us no matter where we are. A
parent at home must know how much time (hours) they have before they must pick
up Billy at the bus stop because they want to surprise Billy with a cake. So
they have to determine if there is enough time, then measure out the
ingredients (ml) and bake it. What if they need to make half (fractions) the
amount because the cake is too big? Math is certainly present in the
construction field, I'm sure I don't have to explain but I will. How many
"feet" or "metres" of lumber is needed for that home and
the amount of concrete required for the foundation in cubic "yards"
or "metres" (volume) needs to be figured out in order to stay on
budget. So math doesn’t have to be that ugly 4 letter word it can be that
beautiful 4 letter word like love. So don't fight it, it may be difficult at
first but I ask you what great relationship doesn’t need a little bit of work
in the beginning?
Tuesday, June 18, 2013
Sunday, June 16, 2013
Communicating with Parents
Since I started at the Faculty of Education in September I have been kicking around an idea about teacher's communicating with their students parents. From what I have seen in the classroom, communication is still in the stone-age... teachers send notes home in a student's agenda where parents (allegedly) read them, initial, and maybe send something back. If something really severe happens, the teachers will get all 19th century and attempt to call the parent... who is either at work or screening calls and ignoring the school number. So the teacher leaves a message, and proceeds to play telephone tag with the parent after school and on lunch.
What I am proposing is a (not so) radical approach to communicating with parents... email. We all know it and love it, and I think its time that we began using email and associated technologies to better include parents in their children's educations. Below are a few examples of things I think we, as educators, could do:
1. Get an email address for the parents of every student in the class at the beginning of the year. Create a group for your class (so you type say "Class 2012" into the "To" category and the message is sent to all the parents) and start using it to disseminate information. Having a hot lunch next week?... Let them know. Planning on going on a field trip... Send a message their way. Have a test coming up in the next few days their children should be studying for... fire away! With younger grades you could even ask parents if they would be interested in having a daily list of homework sent home. It would remind parents and keep them in the loop.
2. Tell parents about positive things their kids did. Most parents only here from the school when something goes wrong. Teachers are busy and don't have a lot of time look up numbers, make a call, leave a message etc. But it only takes 30 seconds to write a quick message to Mrs. Kimmel about how nice Jimmy was to Sally today when he shared his snack.
3. Send an email instead of using a daily communication log. You can get responses from the parents almost instantly (yay email on smart phones) and you have a record of all the emails saved in the cloud in case that communication book somehow disappears.
3. Use Google Docs. Now this one is a little more advanced but I think its worth it. Ask the parents to sign up for a (free) gmail account. Now create a document for each student titled "Assessments." Now when you mark a piece of the students work, enter the title of the assignment, the student's grade and a few comments into the Doc. It keeps track of marks for you and allows the parents to stay in the loop with how their student is doing... no more surprises at report card time.
In general I think using email would be an excellent way to improve communication. Wouldn't it be nice to know that little Jimmy won't be at school before you get there because Mom has sent you a quick email saying he is feeling sick... and you have already replied letting her know to just have him read a bit if he is feeling up to it? Or be able to email worksheets to that student who has been away for 2 weeks, or even answer questions for a student who is away on vacation and trying to finish up a project.
Email isn't a radical thing. I just think the Boards and we as teachers are very much behind in harnessing the power and potential to foster better communication between parents and teachers.
New Teacher's College Program
While I know that someone has already posted about the new Teacher's College Program I wanted to give my 2 cents as someone who just graduated from the Faculty of Education on Wednesday.
I truly have mixed feelings about the two year program. As many people have mentioned already, it is a benefit if all that it does is stop there from being new teacher's college graduates for one year to hopefully soak up some people into the job market. Other than that, though, I'm sceptical that it will truly make a difference.
I truly found that the only time I learned anything useful about teaching this year was during my practicum experiences. The time spent in class was an utter waste of time. We listened to professors drone on about differentiated instruction, inclusive lesson planing, inquiry-based learning, community classroom etc. without every learning what any of those would look like when implemented. We also learned next to no content. You would think that PM Benchmarking––an evaluation done to all students from Grades 1 - 3 a couple of times a year to assess their reading level––would be mentioned at some point in Language's Arts class... but it was not. You would think students would have a chance to use manipulatives, interactive software and try the "new" math methods in class... alas it was not so. Assignments were make-work projects intended solely to find some way to try and differentiate you from your peers with some sort of grade and served no learning purpose whatsoever.
The only way I could see the new two year program being a positive change is if the second year is spent completely on practicum. While it would undoubtably be a burden to associate teachers, I think it would be an amazing experience as a student teacher to be present in the classroom from September - June. Not only would you be able to see the students progress throughout the year, but you would be present in the crucial first month of school where experienced teachers develop routines, discipline, and a rapport with their class that has already been established by the end of October when student teachers first walk in to the classroom.
So while I welcome the changes to the Faculty of Ed. in terms of lowering the number of graduates, I think that a second year of "classes" will only be what the first year was... a waste of time.
I truly have mixed feelings about the two year program. As many people have mentioned already, it is a benefit if all that it does is stop there from being new teacher's college graduates for one year to hopefully soak up some people into the job market. Other than that, though, I'm sceptical that it will truly make a difference.
I truly found that the only time I learned anything useful about teaching this year was during my practicum experiences. The time spent in class was an utter waste of time. We listened to professors drone on about differentiated instruction, inclusive lesson planing, inquiry-based learning, community classroom etc. without every learning what any of those would look like when implemented. We also learned next to no content. You would think that PM Benchmarking––an evaluation done to all students from Grades 1 - 3 a couple of times a year to assess their reading level––would be mentioned at some point in Language's Arts class... but it was not. You would think students would have a chance to use manipulatives, interactive software and try the "new" math methods in class... alas it was not so. Assignments were make-work projects intended solely to find some way to try and differentiate you from your peers with some sort of grade and served no learning purpose whatsoever.
The only way I could see the new two year program being a positive change is if the second year is spent completely on practicum. While it would undoubtably be a burden to associate teachers, I think it would be an amazing experience as a student teacher to be present in the classroom from September - June. Not only would you be able to see the students progress throughout the year, but you would be present in the crucial first month of school where experienced teachers develop routines, discipline, and a rapport with their class that has already been established by the end of October when student teachers first walk in to the classroom.
So while I welcome the changes to the Faculty of Ed. in terms of lowering the number of graduates, I think that a second year of "classes" will only be what the first year was... a waste of time.
Friday, June 14, 2013
Express Check Out - 20 days or more?
I haven't been an occasional teacher for long, but the last few weeks/months have been unreal. Unreal in the fact that kids have gone nuts. The nice weather is here, NOBODY wants to be in school allllllll day (teachers included).
I have a hard time understanding why North America is completely different from the rest of the world when it comes to education. I see test results showing Canada ranked 5th, and the US at 14. So basically, as I see it, we spend September and some of October reviewing the prior year's curriculum because we all know that most students forgot everything over the summer, and we all know that the last month, maybe month and a half students have completely checked out. That leaves us with 6 months of quality instruction. I've heard talks of the new Campbell Ave. site is going to be a year round school. My question is, what has taken so long for this to happen? I believe most schools not in N.A. use this format and their test scores show that.
The break up of the long break provides students with less time off and therefore (hopefully) able to have more material sink in and doesn't allow for students to lose interest, well as much anyway.
I am a firm believer that you need to adopt the best method of delivery, and if this is it, why aren't we doing it? it's like everyone is doing it...AND IT WORKS..so why not?!
I have a hard time understanding why North America is completely different from the rest of the world when it comes to education. I see test results showing Canada ranked 5th, and the US at 14. So basically, as I see it, we spend September and some of October reviewing the prior year's curriculum because we all know that most students forgot everything over the summer, and we all know that the last month, maybe month and a half students have completely checked out. That leaves us with 6 months of quality instruction. I've heard talks of the new Campbell Ave. site is going to be a year round school. My question is, what has taken so long for this to happen? I believe most schools not in N.A. use this format and their test scores show that.
The break up of the long break provides students with less time off and therefore (hopefully) able to have more material sink in and doesn't allow for students to lose interest, well as much anyway.
I am a firm believer that you need to adopt the best method of delivery, and if this is it, why aren't we doing it? it's like everyone is doing it...AND IT WORKS..so why not?!
Last day of school...how do we keep kids motivated?
What can we do to keep our students motivated on the last day of school? I ask myself this question all the time. I know by the end of the year everyone including administrators need a break from school. If staff is feeling this way so are the students.
So let's think what would keep us motivated on the last day of school:
So let's think what would keep us motivated on the last day of school:
- food
- ice-cream
- no work
- activities
- guest speakers
- party
- water fights (weather permitting)
- teacher - student sport game
Getting students to come to school on the last day and be motivated I think applies more to the high schools. Correct me if I'm wrong. Therefore, teachers have a hard time already motivating high school students on a regular school day. So what might it look like on the last day?
Well let me tell you:
- water fights outside on the field
- skipping classes
- horse playing in the halls
- food fight in the cafeteria
- pulling the fire alarm
- and much much more
Help me, because us teachers need to stick together. What type of motivating strategies have you used on the last few days of school?
Thursday, June 13, 2013
Views on Teachers
As we all know, this past year has been rather rough for teachers because of Bill 115 and the views of the teacher's unions, the provincial government, and the general population. As a result, one of the things we sometimes talked about in my classes at teacher's college was the way in which other countries view their teachers, as well the education systems those countries have. One country that came up over and over again was Finland. In Finland, teachers are held in very high esteem, much like doctors and other professionals. They have a very rigorous training program, and you have to have a master's degree. Finland also has some of the best test scores in the world. For those of you unfamiliar with Finland, you can see a couple of short videos here and here.
It just got me wondering why it is that, here in Canada (or maybe it's just Windsor?), many people view teachers in a very negative light. Lately, I've been finding people's reactions on finding out that I just graduated from teacher's college to be a bit disheartening. I guess I just don't understand why so many people look down on us, when a lot of us are who we are today because of teachers we've had in the past (myself included!!).
Any thoughts?
It just got me wondering why it is that, here in Canada (or maybe it's just Windsor?), many people view teachers in a very negative light. Lately, I've been finding people's reactions on finding out that I just graduated from teacher's college to be a bit disheartening. I guess I just don't understand why so many people look down on us, when a lot of us are who we are today because of teachers we've had in the past (myself included!!).
Any thoughts?
Wednesday, June 12, 2013
Test Anxiety
One of the students that I tutor was talking to me the other day about his upcoming exams, and he was mentioning that he often feels anxiety when writing a test. I think that this is extremely common, and so I was looking at ways to help him overcome this so that he can do well in his exams. I found this article in my searches and I think it has a lot of really valuable information.
The article gives ways to better prepare the students for their test. Learning in test-like conditions and creating practice tests are methods that we all know, but I was interested to see that the author recommended that students work in a bit of exercise before a test (if possible) to lower the effects of adrenaline on the body. In fact, it's almost helpful for everyone to read this because it gives ways to manage anxiety NOT within a classroom setting.
Did anyone experience classroom anxiety? And how did you deal with it?
The article gives ways to better prepare the students for their test. Learning in test-like conditions and creating practice tests are methods that we all know, but I was interested to see that the author recommended that students work in a bit of exercise before a test (if possible) to lower the effects of adrenaline on the body. In fact, it's almost helpful for everyone to read this because it gives ways to manage anxiety NOT within a classroom setting.
Did anyone experience classroom anxiety? And how did you deal with it?
Why don't students want to know why?
This is something that has bugged me since high school. Why don't students care to understand the math they are learning? Nearly all my friends in high school only cared about getting a math formula, plugging in numbers, and hoping for a right answer. They didn't want to know anything beyond that. They only wanted to do the bare minimum and pass the course and move on.
As I am someone who likes to know why things are the way they are. I want to know WHY students like this don't ask WHY in math class! It can't possible be just because they don't like math can it? I didn't like biology class but I still asked my teacher "why" whenever I was confused. Do you think this mentality os math-specific? Don't they realize that without knowing "why" they will only ever be able to get through the basics? Don't they realize if they don't truly understand, they won't be able to problem solve and apply their knowledge to more complicated questions and even real-world situations?
How can teachers combat this kind of mentality in math class?
As I am someone who likes to know why things are the way they are. I want to know WHY students like this don't ask WHY in math class! It can't possible be just because they don't like math can it? I didn't like biology class but I still asked my teacher "why" whenever I was confused. Do you think this mentality os math-specific? Don't they realize that without knowing "why" they will only ever be able to get through the basics? Don't they realize if they don't truly understand, they won't be able to problem solve and apply their knowledge to more complicated questions and even real-world situations?
How can teachers combat this kind of mentality in math class?
Ontario Teacher's College Program
There has been some talk in the last couple years about extending the teacher's college program in Ontario to two years rather than one and cutting the number of students admitted to the program. This is something I was PRAYING for years ago so that when I was a B.Ed grad I actually had a shot of finding a job! It is so unbelievably frustrating that this has gone on for so long.
I did my B.Ed at the University of Ottawa. My class size was huge, we barely fit everyone in our classrooms, and all of our material was so crammed into the semesters that I walked away from every class feeling like there was so much more to learn. And did I mention our actual teaching experience during the program? 9 weeks! Is that really enough to prepare us to start teaching in our own classrooms? By the time I was feeling comfortable and getting the swing of things in my schools it was time to pack up and finish! The program could EASILY be stretched to two years by adding more practicum experience and more pedagogical learning.
Now, as for the number of graduates each year. It simply infuriates me how little jobs there are out there and how hard teachers have to fight to find positions meanwhile the number of teachers being pumped out of the program each year remains the same.
Something is finally going to be done about this I only wish it had happened years ago.
Time for Change
I did my B.Ed at the University of Ottawa. My class size was huge, we barely fit everyone in our classrooms, and all of our material was so crammed into the semesters that I walked away from every class feeling like there was so much more to learn. And did I mention our actual teaching experience during the program? 9 weeks! Is that really enough to prepare us to start teaching in our own classrooms? By the time I was feeling comfortable and getting the swing of things in my schools it was time to pack up and finish! The program could EASILY be stretched to two years by adding more practicum experience and more pedagogical learning.
Now, as for the number of graduates each year. It simply infuriates me how little jobs there are out there and how hard teachers have to fight to find positions meanwhile the number of teachers being pumped out of the program each year remains the same.
Something is finally going to be done about this I only wish it had happened years ago.
Time for Change
Monday, June 10, 2013
Probability Games
I was having a dinner party on the weekend, and we ended up playing a dice game after dinner was finished. Everyone was having a great time, and another teacher friend of mine piped up and said, "Oh my God, Laurie - thank you so much, you just planned my next few lessons for me to finish up this unit on probability! Perfect!" We got to talking about activities that you could use for probability to make it engaging for students, while still allowing to learn what we need them to learn. Now of course, I'm not exactly sure how she will introduce this game to the students, what activities they will do to connect to the actual 'math,' etc., but while thinking about it, I also realized that there are many ways a game like this could be used!
I'm not sure if anyone has heard of it - but it doesn't exactly have an appropriate name.!! Anyhow, the kids could separate just 'playing' and enjoying, with calculating the probabilities of getting different roles.
We are probably often being 'stared-in-the-face,' with lots of great games, scenarios that we could use with our students that would make our lessons engaging/interesting while learning, and while putting the learning in a real-life context for them (some things that come to mind for probability, for example, are games like Yahtzee, card games - BlackJack, and a roulette wheel!). Anything that we take notice of that we can use, can be beneficial, especially when we are talking about DI and the need to reach students in different ways. We just need to keep our eyes and ears open to see when this great opportunities are right in front of us!
I'm not sure if anyone has heard of it - but it doesn't exactly have an appropriate name.!! Anyhow, the kids could separate just 'playing' and enjoying, with calculating the probabilities of getting different roles.
We are probably often being 'stared-in-the-face,' with lots of great games, scenarios that we could use with our students that would make our lessons engaging/interesting while learning, and while putting the learning in a real-life context for them (some things that come to mind for probability, for example, are games like Yahtzee, card games - BlackJack, and a roulette wheel!). Anything that we take notice of that we can use, can be beneficial, especially when we are talking about DI and the need to reach students in different ways. We just need to keep our eyes and ears open to see when this great opportunities are right in front of us!
Sunday, June 9, 2013
Weigh in...what's the solution?
6÷2(1+2)=?
This one almost caused knock-down drag-out fights with some of my friends, believe it or not...and they were math majors and engineers who could not agree...and each was convinced there was no way they could be wrong. Apparently there is a large debate in the mathematical world over this one...with brilliant people on both sides...what do you think?
Linda
This one almost caused knock-down drag-out fights with some of my friends, believe it or not...and they were math majors and engineers who could not agree...and each was convinced there was no way they could be wrong. Apparently there is a large debate in the mathematical world over this one...with brilliant people on both sides...what do you think?
Linda
Math Tricks - Cheating or Genius?
When I was a child, my mathematician father told me that I needed to memorize the multiplication tables, memory tricks were cheating. Years later in teacher's college we are told that memorization doesn't work because the info in short term memory does not necessarily (and most oftenly) end up in long term memory. On top of that, we learned all kinds of strategies for adding and multiplying that I had never seen before! For example...those darn 8x tables, toss 'em out, to find any number x8, simply double it, double it and double it again! What?! Why was I robbed of this gem as a child? Guess what? Want x16, double once more...x32, double again...oh, my, how easy!
For Christmas this year I requested a copy of Rapid Math Tricks and Tips - 30 Days to Number Power. Not only does it offer tips on simple mathematical calculations, but others that appear to be more complicated, but really are not (if you know the tip or trick). Putting strategies like these into the minds of our students will give them mastery over numbers like they've never experienced before...it has for me, and I'm not even done my 30 days yet!
What's your opinion...math tricks - cheating or genius?
Linda
For Christmas this year I requested a copy of Rapid Math Tricks and Tips - 30 Days to Number Power. Not only does it offer tips on simple mathematical calculations, but others that appear to be more complicated, but really are not (if you know the tip or trick). Putting strategies like these into the minds of our students will give them mastery over numbers like they've never experienced before...it has for me, and I'm not even done my 30 days yet!
What's your opinion...math tricks - cheating or genius?
Linda
Thursday, June 6, 2013
Always Look for PD Opportunities
One of the cornerstones of being a great educator is keeping up with professional development (PD). The field of education is constantly evolving, whether it be a new technology, a new method for class management, or a new approach for instruction. Being on the leading edge of these developments will help you hone your philosophy of education and develop your personal teaching style. You will be able to figure out exactly what works for you and your group of students to maximize learning potential.
The opportunities for PD, although immense, are often overlooked and lost completely. It is important to be proactive about PD and look for the various avenues that will help you grow professionally and give you confidence in the classroom. Professional organizations such as OAME and NCTM constantly present ways to develop as a teacher, becoming a member or even visiting their websites often is worth the time. PD opportunities are also widely available through your school board. If you are employed by a school board it may be beneficial to look into the workshops, courses, and conferences they host, as many include the latest information on the profession and are often free of charge. For example, in my first year supply teaching, a fellow teacher brought my attention to a Tribes course that our board was running - I took advantage of this opportunity and feel that I grew professionally and learned valuable information about the classroom community. Without my peer mentioning this course to me, I may have missed out on a chance to develop my approaches for engaging students and build classroom community. It is important to always be aware of the resources for PD that are around and available to you. This awareness can be as simple as, looking for and recognizing PD opportunities in the experiences you have in class each and everyday.
How do our students really feel about using iPads?
I tutor a student who misses a fair amount of school for an illness that he can't control. We spend a few hours a week playing catch-up in order to help him understand the work that he misses, which at times can end up being four days in a row. His school uses iPads in the math classroom (for everything, not just as an extra resource), and we were talking the other day about getting access to a textbook to help with his exam review. He told me that they use an online textbook. When I asked him about how he felt about it, he said that he didn't like it. It takes away from flipping through the pages and writing things down on paper. The time that it takes to switch from the line function to the pencil function, changing font colours, erasing mistakes, etc etc; he feels that he's not learning the same as he would if he were using a paper and pencil, because there are so many added distractions from using the iPad.
What has been everyone's experience with using an iPad? Do the students truly like it? This particular class does EVERYTHING on the iPad, like I said. They have all of their notes on there, they write directly on to the iPad, they do textbook questions off of it, onto a Google doc which they then submit, etc. My tutoring student thinks they're cool, yet does not really care for it all that much. Does anyone find that the students really want to use them for all things math? Or would they rather just use it as an extra resource to help them understand something better? I'm interested to see how the STUDENTS feel about it.
What has been everyone's experience with using an iPad? Do the students truly like it? This particular class does EVERYTHING on the iPad, like I said. They have all of their notes on there, they write directly on to the iPad, they do textbook questions off of it, onto a Google doc which they then submit, etc. My tutoring student thinks they're cool, yet does not really care for it all that much. Does anyone find that the students really want to use them for all things math? Or would they rather just use it as an extra resource to help them understand something better? I'm interested to see how the STUDENTS feel about it.
Sunday, June 2, 2013
Students in High School Who Are Missing Fundamentals in Math
There is no question that some students in high school are missing fundamental knowledge and skills that are supposed to have before passing grade 8. Working in private high schools and tutor companies in the same time very often I come across several cases were students have significant gaps in math in their knowledge. The question how student get through and pas grade 8 that way might generate many answers, because this whole process is very complex.
I think that building a solid math framework in student knowledge requires a fair amount of work both sides, teachers and students. It looks that in certain cases there’s lack of efforts from teachers to be consistent in their teaching process and in the same time lack of preparation from the students side. On the other hand it’s possible that gaps from previous math classes may not be identified in an early stage, first from students themselves, their parents and teachers as well. Many students struggle with concepts in maths and don't know why. It happens when something in a previous math topic was missed for a reason or another and didn't make sense for them.
The question is that tiny math gaps in students in an early stage are neglected often from teachers. However these gaps carry on quickly expending until in high school we meet student who can’t use operations with fractions ore can’t use inverse operations to isolate a variable. Another reason that we see students with gaps in math in high school is that both teachers and students don’t pay attention when it comes to reviewing all math concepts until grade 8. Reviewing is a process that is supposed to be done in regular basis in order not to miss anything basic which make student to struggle in high school.
I’ve noticed from my experience that most of the students struggling with gaps from previous years can’t use operations with fractions. Some of them don’t know the rules how to add, subtract, multiply and divide too fractions. Some others know that adding and subtracting fractions they have to find the least common denominator (LCD) but struggle finding it because are not familiar to find common multiples or common factors in their head. In most severe cases I’ve experienced when students still haven't memorized the multiplication table, that won’t let them to find these factors.
Another gray area in students’ knowledge to solve a question with multiple operations (add/subtract, multiply/divide). Students in this case are not able to follow the BEDMAS order. In and expression like this
3x^2+x/2×3x-7x+(5-7x)2/3 I have seen some students subtracting 3x-7x before multiplying x/2×3x
Almost all students with gaps in math have difficulty to use inverse operations to isolate a variable. Without having a clear concept in this area they have memorize to move terms from one side of an equation to another, in order to isolate a variable but they think that this could be applied in every case and wrongly use that when terms are multiplying. In an example like this
2y+7 ×3x= 5x I have seen some students writing 2y+7 = 5x×3x instead of writing
2y+21x= 5x and then 2y= 5x-21x
The same situation is with students who don't apply the method of cross-multiplying properly.
Another area that students have gaps is when they are able to perform arithmetic operations but they can’t perform these operations with terms containing a variable.
There are several attempts that could be done to minimize math gaps in students but the main one I think is having teachers design individual learning plans, and classroom mathematics programs that provide support especially for this range of students. Helping students fill gaps in basic knowledge start by rebuilding their foundation skills by going back to operations with multiple operations, with fractions, working with variables, etc. it’s up to the teachers to guide these students with special worksheet in order to have them complete independently several exercises related to the areas they are weak. Because math builds on prior knowledge teachers have use their tutor support services and to focus their teaching process to those particular content areas that create links in students’ knowledge. That way they could ensure a solid understanding of prior math concepts to students in order to move forward.
There is no question that some students in high school are missing fundamental knowledge and skills that are supposed to have before passing grade 8. Working in private high schools and tutor companies in the same time very often I come across several cases were students have significant gaps in math in their knowledge. The question how student get through and pas grade 8 that way might generate many answers, because this whole process is very complex.
I think that building a solid math framework in student knowledge requires a fair amount of work both sides, teachers and students. It looks that in certain cases there’s lack of efforts from teachers to be consistent in their teaching process and in the same time lack of preparation from the students side. On the other hand it’s possible that gaps from previous math classes may not be identified in an early stage, first from students themselves, their parents and teachers as well. Many students struggle with concepts in maths and don't know why. It happens when something in a previous math topic was missed for a reason or another and didn't make sense for them.
The question is that tiny math gaps in students in an early stage are neglected often from teachers. However these gaps carry on quickly expending until in high school we meet student who can’t use operations with fractions ore can’t use inverse operations to isolate a variable. Another reason that we see students with gaps in math in high school is that both teachers and students don’t pay attention when it comes to reviewing all math concepts until grade 8. Reviewing is a process that is supposed to be done in regular basis in order not to miss anything basic which make student to struggle in high school.
I’ve noticed from my experience that most of the students struggling with gaps from previous years can’t use operations with fractions. Some of them don’t know the rules how to add, subtract, multiply and divide too fractions. Some others know that adding and subtracting fractions they have to find the least common denominator (LCD) but struggle finding it because are not familiar to find common multiples or common factors in their head. In most severe cases I’ve experienced when students still haven't memorized the multiplication table, that won’t let them to find these factors.
Another gray area in students’ knowledge to solve a question with multiple operations (add/subtract, multiply/divide). Students in this case are not able to follow the BEDMAS order. In and expression like this
3x^2+x/2×3x-7x+(5-7x)2/3 I have seen some students subtracting 3x-7x before multiplying x/2×3x
Almost all students with gaps in math have difficulty to use inverse operations to isolate a variable. Without having a clear concept in this area they have memorize to move terms from one side of an equation to another, in order to isolate a variable but they think that this could be applied in every case and wrongly use that when terms are multiplying. In an example like this
2y+7 ×3x= 5x I have seen some students writing 2y+7 = 5x×3x instead of writing
2y+21x= 5x and then 2y= 5x-21x
The same situation is with students who don't apply the method of cross-multiplying properly.
Another area that students have gaps is when they are able to perform arithmetic operations but they can’t perform these operations with terms containing a variable.
There are several attempts that could be done to minimize math gaps in students but the main one I think is having teachers design individual learning plans, and classroom mathematics programs that provide support especially for this range of students. Helping students fill gaps in basic knowledge start by rebuilding their foundation skills by going back to operations with multiple operations, with fractions, working with variables, etc. it’s up to the teachers to guide these students with special worksheet in order to have them complete independently several exercises related to the areas they are weak. Because math builds on prior knowledge teachers have use their tutor support services and to focus their teaching process to those particular content areas that create links in students’ knowledge. That way they could ensure a solid understanding of prior math concepts to students in order to move forward.
Saturday, June 1, 2013
Calculator in elementary school
Calculator in elementary school
There are many different opinions about the use of calculators in grade school. I personally believe that calculators should be used as a tool to ENHANCE THE LEARNING PROCESS.
Unfortunately, most children who are allowed to use calculators early on become dependent upon them and don't learn their basic math facts. There is a group out of California who call themselves the Mathematically Correct Group, who firmly believe that calculators are the ruination of children learning math.
There was a recent article in the UK News (July 6, 1998) stating that school children up to the age of 8 will be banned from using calculators. The restriction is part of "a drive to improve mental arithmetic."
I believe that since there is so much abuse of using the calculators, that administrators feel the pressure not to allow calculator use at all!
Calculators can support development of number sense and operations when children are given appropriate problems, (suggestions in NCTM Addenda Series) and students can certainly discover when they are useful or not. It might be interesting to find out whether students think the calculator helped them to learn your material and in what way. I wonder what grade level you will be investigating.
To find calculator activities for primary students is a challenge, and like so many other topics, there will only be a few ideas to fit your group of students in any one resource. However, once the calculators are in the room and the teacher is willing to let children use them, lots of opportunities will come up.
We have tried using the constant feature to let children count things in the room. For example, on the TI-12 you press + 1 = and then every time you press the = key, the display increases by one. So if the children want to count the number of tables in the room, or the number of shoes, they simply press the = key once for every item and read the display. This is not necessarily a better way to count, but it's one that gets a calculator in their hands.
To do skip counting, press the number you want to count by, then +, and then =. For example, with 5 + =, each time you press = the display increases by 5. The teacher might ask the students: What is happening when you press the = key? Could the calculator count by 3's? What do you think you will see if you press the = key 3 more times? 5 more times? How can we make the calculator count by 10's? Is 78 a number we will get when we count by 10's? How do you know? etc.
Other ways to get this constant feature are to press 0 + 5 =; or 5 + + +. If one method won't work on your calculator, try another.
Young children have heard about multiplication, and with a calculator the mystery becomes doable. Last year my kids had fun making a game. They began with a 3 x 3 grid like tic-tac-toe. A product would be entered in each square of the grid. The factors were written in a row below the grid. Players would take turns choosing 2 factors and putting a chip on the correct factor on the game board. The winner placed 3 in a row. The calculator was handy in creating the game and checking during play. Multiplication "facts" were memorized pretty quickly.
Another calculator game we liked was "Target 21." Two children use one calculator and take turns pressing a 1, 2, or 3 followed by =. The winner is the first player to make the display read 21. After playing a few games, we talk about strategy and each child writes down the strategy s/he used to get 21. Before long, 2nd graders are hard to beat! Yep, it's a nim game 20th century style.
Another activity is to write a number inside a square and then ask the children to put a number at each corner of the square so that those 4 numbers add up to the number in the middle. Or, you might ask kids to use the calculator to list ways to make the number of the day's date - how many ways are there to make 17?
"Using the Math Explorer Calculator" by Bitter and Mikesell has a section on higher-order thinking skills for K-3 with some good activities. Two books with good calculator work are "Calculator Exploration and Problems" by D. Miller (1979), available from Cuisenaire, and "How to Develop Problem Solving Using a Calculator" by J. Morris (1981). Although these books are for upper elementary, I have adapted some of their ideas. The Addenda Series on Patterns for K-6, published by NCTM, also has good primary calculator activities. We use the TI-108 and sometimes the TI-12 at the primary level.
There are many different opinions about the use of calculators in grade school. I personally believe that calculators should be used as a tool to ENHANCE THE LEARNING PROCESS.
Unfortunately, most children who are allowed to use calculators early on become dependent upon them and don't learn their basic math facts. There is a group out of California who call themselves the Mathematically Correct Group, who firmly believe that calculators are the ruination of children learning math.
There was a recent article in the UK News (July 6, 1998) stating that school children up to the age of 8 will be banned from using calculators. The restriction is part of "a drive to improve mental arithmetic."
I believe that since there is so much abuse of using the calculators, that administrators feel the pressure not to allow calculator use at all!
Calculators can support development of number sense and operations when children are given appropriate problems, (suggestions in NCTM Addenda Series) and students can certainly discover when they are useful or not. It might be interesting to find out whether students think the calculator helped them to learn your material and in what way. I wonder what grade level you will be investigating.
To find calculator activities for primary students is a challenge, and like so many other topics, there will only be a few ideas to fit your group of students in any one resource. However, once the calculators are in the room and the teacher is willing to let children use them, lots of opportunities will come up.
We have tried using the constant feature to let children count things in the room. For example, on the TI-12 you press + 1 = and then every time you press the = key, the display increases by one. So if the children want to count the number of tables in the room, or the number of shoes, they simply press the = key once for every item and read the display. This is not necessarily a better way to count, but it's one that gets a calculator in their hands.
To do skip counting, press the number you want to count by, then +, and then =. For example, with 5 + =, each time you press = the display increases by 5. The teacher might ask the students: What is happening when you press the = key? Could the calculator count by 3's? What do you think you will see if you press the = key 3 more times? 5 more times? How can we make the calculator count by 10's? Is 78 a number we will get when we count by 10's? How do you know? etc.
Other ways to get this constant feature are to press 0 + 5 =; or 5 + + +. If one method won't work on your calculator, try another.
Young children have heard about multiplication, and with a calculator the mystery becomes doable. Last year my kids had fun making a game. They began with a 3 x 3 grid like tic-tac-toe. A product would be entered in each square of the grid. The factors were written in a row below the grid. Players would take turns choosing 2 factors and putting a chip on the correct factor on the game board. The winner placed 3 in a row. The calculator was handy in creating the game and checking during play. Multiplication "facts" were memorized pretty quickly.
Another calculator game we liked was "Target 21." Two children use one calculator and take turns pressing a 1, 2, or 3 followed by =. The winner is the first player to make the display read 21. After playing a few games, we talk about strategy and each child writes down the strategy s/he used to get 21. Before long, 2nd graders are hard to beat! Yep, it's a nim game 20th century style.
Another activity is to write a number inside a square and then ask the children to put a number at each corner of the square so that those 4 numbers add up to the number in the middle. Or, you might ask kids to use the calculator to list ways to make the number of the day's date - how many ways are there to make 17?
"Using the Math Explorer Calculator" by Bitter and Mikesell has a section on higher-order thinking skills for K-3 with some good activities. Two books with good calculator work are "Calculator Exploration and Problems" by D. Miller (1979), available from Cuisenaire, and "How to Develop Problem Solving Using a Calculator" by J. Morris (1981). Although these books are for upper elementary, I have adapted some of their ideas. The Addenda Series on Patterns for K-6, published by NCTM, also has good primary calculator activities. We use the TI-108 and sometimes the TI-12 at the primary level.
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