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realtalk-tj · 5 years ago

Note

Could you please explain in more detail what each of the math post-APs are and how easy/hard they are and how much work? Thanks!!

Response from Al:

This can be added on to, but I can describe how Multivariable Calculus is. First off, I want to say not anyone’s opinion should affect how difficult or easy a class would be for YOU. Ultimately, do the classes you’re interested in. Personally, I thought Calculus was cool as subject, so that’s why I pursued Multi. Multi. builds off of BC Calculus, Geometry, and even some of the linear algebra you learned from middle school (not to be confused with the Linear Algebra you can take at TJ), so as long as you have a good foundation in those subjects, I’m sure you’ll do well in Multi. Depending on your teacher, assessments may or may not be more challenging, and that’s why I strongly emphasize take the class only if you’re genuinely into it. Don’t take it because of peer pressure / because you want to stand out in colleges. I’ll let anyone add below.

Response from Flitwick:

Disclaimer: I feel like I’m not the most unbiased perspective on the difficulty of these math classes, and I have my own mathematical strong/weak points that will bleed into these descriptions. Take all of this with a grain of salt, and go to the curriculum fair for the classes you’re interested in! I’ve tried to make this not just what’s in the catalog/what you’ll hear at the curriculum fair, so hopefully, you can get a more complete view of what you’re in for.

Here’s my complete review of the post-AP math classes, and my experience while in the class/what I’ve heard from others who have taken the class. I’m not attaching a numerical scale for you to definitively rank these according to difficulty because that would be a drastic oversimplification of what the class is.

Multi: Your experience will vary based on the teacher, but you’ll experience the most natural continuation of calculus no matter who you get. In general, the material is mostly standardized (and you can find it online), but Osborne will do a bit more of a rigorous treatment and will present concepts in an order that “tells a more complete story,” so to speak.

The class feels a decent amount like BC at first, but the difficulty ramps up over time and you might have an even rougher time if you haven’t had a physics course yet when it comes to understanding some of the later parts of the course (vector fields and flux and all).

I’d say some of the things you learn can be seen as more procedural, i.e. you’ll get lots of problems in the style of “find/compute blah,” and it’s really easy to just memorize steps for specific kinds of problems. However, I would highly recommend that you don’t fall into this sort of mindset and understand what you’re doing, why you’re doing it, and how that’ll yield what you want to compute, etc.

Homework isn’t really checked, but you just gotta do it – practice makes better in this class.

Linear: This class is called “Matrix Algebra” in the catalog, but I find that title sort of misleading. Again, your experience will depend on who you get (see above for notes on that), but generally, expect a class that is much more focused on understanding intuitive concepts that you might have learned in Math 4/prior to this course, but that can be applied in a much broader context. You’ll start with a fairly simple question (i.e. what does it mean for a system of linear equations to have a solution?) and extend this question to ask/answer questions about linear transformations, vectors and the spaces in which they reside, and matrices.

A lot of the concepts/abstractions are probably easier to grasp for people who didn’t do as well in multi, and this I think is a perfectly natural thing! Linear concepts also lend themselves pretty well to visualization which is great for us visual learners too :)) The difficulty can come in understanding what terms mean/imply and what they don’t mean/imply, which turns into a lot of true/false at some points, and in the naturally large amount of arithmetic that just comes with dealing with matrices and stuff.

Same/similar notes on the homework situation as in Multi.

Concrete: Dr. White teaches this course, and it’s a great time! The course description in the catalog isn’t totally accurate - most of the focus of the first two main units are generally about counting things, and some of the stuff mentioned in the catalog (Catalan numbers, Stirling numbers) are presented as numbers that count stuff in different situations. The first unit focuses on a more constructive approach to counting, and it can be really hard to get used to that way of thinking - it’s sorta like math-competition problems, to a degree. The second unit does the same thing but from a more computational/analytic perspective. Towards the end, Mr. White will sort of cover whatever the class is interested in - we did a bit of group theory for counting at the end when I took it.

The workload is fairly light - a couple problem sets here and there to do, and a few tests, but nothing super regular. Classes are sometimes proofs, sometimes working on a problem in groups to get a feel for the style of thinking necessary for the class. if you’re responsible for taking notes for the class, you get a little bonus, but of course, it’s more work to learn/write in LaTeX. Assessments are more application, I guess - problems designed to show you’ve understood how to think in a combinatorial way.

Unfortunately, this course is not offered this year but hopefully it will be next year!

Prob Theory: Dr. White teaches this course this year, and the course’s focus is sort of in the name. The course covers probability and random variables, different kinds of distributions, sampling, expected value, decision theory, and some of the underlying math that forms the basis for statistics.

This course has much more structure, and they follow the textbook closely, supplemented by packets of problems. Like Concrete, lecture in class is more derivation/proof-based, and practice is done with the packets. Assessments are the same way as above. Personally, I feel this class is a bit more difficult/less intuitive compared to Concrete, but I haven’t taken it at the time of writing.

Edit (Spr. 2020) - It’s maybe a little more computational in terms of how it’s more difficult? There’s a lot of practice with a smaller set of concepts, but with a lot of applications.

AMT: Dr. Osborne teaches this course, and I think this course complements all the stuff you do math/physics-wise really well, even if you don’t take any of the above except multi. The class starts where BC ended (sequences + series), but it quickly transitions to using series to evaluate integrals. The second unit does a bit of the probability as well (and probability theory), but it’s quickly used as a gateway into thermodynamics, a physics topic not covered in any other class. The class ends with a very fast speed-run of the linear course (with one or two extra topics thrown in here and there).

The difficulty of this course comes from pace. The problem sets can get pretty long (with one every 1-2 weeks), but if you work at it and ask questions in class/through email whenever you get confused, you’ll be able to keep up with the material. The expressions you’ll have to work with might be intimidating sometimes, but Osborne presents a particular way of thinking that helps you get over that fear - which is nice! All assessments are take-home (with rules), and are written in the same style as problem sets and problems you do in class. The course can be a lot to handle, but if you stick with it, you’ll end up learning a lot that you might not have learned otherwise, all wrapped up in one semester.

Diffie: Dr. Osborne has historically taught this course, but this year’s been weird - Dr. J is teaching a section in the spring, while Dr. Osborne is teaching one in the fall. No idea if this trend will continue! Diffie is sort of what it says it is - it’s a class that focuses on solving differential equations with methods you can do by hand. Most of the class is “learning xx method to solve this kind of equation that comes up a lot,” and the things you have to solve get progressively more difficult/complex over the course of the semester, although the methods may vary in difficulty.

I think this is a pretty cool class, but like multi, the course can be sort of procedural. In particular, it can be challenging because it often invokes linear concepts to explain why a particular method works it does, but those lines of argument are often the most elegant. This class can also get pretty heavy on the computational side, which can be an issue.

Homework is mostly based in the textbook, and peter out in frequency as the semester progresses (although their length doesn’t really change/increases a little?). Overall, this is a “straightforward” course in the sense that there’s not as much nuance as some of these other classes, as the focus is generally on solving these problems/why they can be solved that way/when you can expect to find solutions, but that’s not to say it’s not hard.

Complex: I get really excited when talking about this class, but this is a very difficult one. Dr. Osborne has historically taught this course in the fall. This class is focused on how functions in the complex numbers work, and extending the notions of real-line calculus to them. In particular, as a result of this exploration, you’ll end up with a lot of surprising results that can be applied in a variety of ways, including the evaluation of integrals and sums in unconventional ways.

In some ways, this class can feel like multi/BC, but with a much higher focus on proofs and why things work the way they do because some of the biggest results you’ll get in the complex numbers will have no relation whatsoever to stuff in BC. Everything is built ground-up, and it can be really easy to be confused by the nuanced details. If you don’t remember anything about complex numbers, fear not! The class has an extra-long first unit for that very purpose, which is disproportionately long compared to the other units (especially the second, which takes twoish weeks, tops). Homework is mostly textbook-based, but there are a couple of worksheets in there (including the infamous Real Integral Sheet :o)

This course is up there for one of the most rewarding classes I’ve taken at TJ, but it’s a wild ride and you really have to know what things mean and where the nuances are cold.

#math #post-ap #complex #diffie #linear #multi #prob theory #concrete #amt

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mathematicool · 8 years ago

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Hey, hope you are doing well ^^ this September I'll start uni and I'll also be studying maths!! I'm so excited haha ^^ How is it for you? How different do you think is math in uni compared to math in high school (I'm from a french system so our curriculum might be different though) Thanks in advance!

Hey,

I’ve typed a reply to this message three times now because I’m so clumsy and keep accidentally closing this tab!! 😂

Firstly, congratulations on your achievements!! 🎉🤓 I hope you enjoy studying maths at uni!! (Feel free to message me about it whenever you want!!)

For me, pure maths is really different to high school maths. It’s a lot more wordy and more about definitions, statements and proofs than actual calculation. So far in my pure maths career, I’ve studied Abstract Algebra, Linear Algebra and Analysis. I think most universities (at least in first year in the UK) split pure maths into Algebra and Analysis.

Abstract Algebra involves Set Theory, Number Theory and Group Theory. Linear Algebra is about linear spaces (it involves vectors and matrices). Analysis is about the properties of sequences, series and function.

I’ll show you some questions to demonstrate what I mean when I say pure maths is wordy:

These are two Abstract Algebra questions on Group Theory.

This is a Linear Algebra question.

These are two Analysis questions. The first is about the convergence of sequences and the second is about the continuity of functions.

As you can see, all these questions build on definitions and statements. None of them require calculators. In fact, I think only the Linear Algebra question involves any arithmetic at all and that’s only basic arithmetic in part (f) of the question.

Seeing these kind of questions was scary to me at first. I barely understood the language they were presented in; the wording of questions wasn’t what I was used to and there were so many new symbols to learn. It was almost like learning a new language!!

For example, instead of writing:

for all real numbers x there is a real number y that is greater than x

you can just write:

This literally translates to:

for all x in the set of real numbers, there exists a y in the set of real numbers such that y is greater than x.

It’s quite convenient actually but might take time to get used to if you haven’t seen it before.

Because of this new “language”, I definitely struggled with pure maths in the beginning of my first semester. For me, Analysis got better and easier to understand (in fact, Analysis is my bae at the moment 💛) but Abstract Algebra was the opposite. To this day, I hardly understand it. I think I just overcomplicate things in Abstract Algebra. Sometimes another student will explain something to me and it’ll seem so simple, but my brain just can’t see simple explanations. I don’t think Abstract Algebra is for me. (But other people love Abstract Algebra and that’s completely fine!) I’m finding Linear Algebra to be much better and I’m really enjoying it at the moment.

On the other hand, applied modules e.g. calculus, statistics, probability, are very similar to high school. They build on what you learnt in school (but don’t worry; the lecturers will (or at least they should) do recaps of what you learnt at school so it’s okay if your high school maths knowledge is a little foggy). I actually find applied modules a little tedious sometimes for this reason. Applied maths at school was never really my favourite, so to have to study it still kinda sucks, but sometimes it’s a nice relief from pure maths. I used to enjoy differentiation and integration in high school, but now not so much!! I would much rather be doing Analysis proofs than complicated calculus these days! If your first year doesn’t count, use it as a way to experiment to see what you enjoy and what you don’t. Your opinion and perspective on maths will probably change!

Also, another thing I want to say: don’t worry if you don’t immediately understand things. I feel like a lot of maths students grew up having a relatively easy time with mathematics and so university maths can be quite a shock to the system sometimes (it was for me!). Take your time with it. I felt like I was the only one struggling and for most of semester 1 I felt so dumb. I didn’t have much confidence going into my exams. Everyone around me seemed to understand what was going on, whereas my brain hurt just trying to do abstract algebra homework questions. But actually, I think most people felt like this, and people just didn’t and still don’t talk about it which sucks. Don’t be embarrassed if you’re struggling - maths at university isn’t easy at all and I don’t know anyone who hasn’t struggled at least a little bit. Talk about it with others - talking about it helps you learn and fill in gaps in your knowledge, and it helps you realise that most people are in the same boat as you!! ⛵️ (Talk to me about it if you so wish!!)

I hope that helps and all the best with your studies!! 😃

#ask #juliebunny-study

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succeedly · 8 years ago

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5 Ways to Help Numbers Come Alive

Dr. Rebecca Klemm on episode 175 of the 10-Minute Teacher Podcast

From the Cool Cat Teacher Blog by Vicki Davis

Follow @coolcatteacher on Twitter

Dr. Rebecca Klemm @numbersalive shares how to help numbers come alive for all ages. From toddler to teenager to Ph.D., Rebecca informs us about the building blocks that build math success.

Today’s Sponsor: GradeCam lets you create assessments with formats including multiple choice, true/false, number grids, rubrics, and even handwritten numeric answers that can be read and scored by Aita – Gradecam’s Artificial Intelligence Teaching Assistant.Score assessments, generate reports, and transfer grades automatically. Work smarter instead of harder. Sign up for your 60-day free trial at http://ift.tt/2gzEf8G

Listen Now

Listen to the show on iTunes or Stitcher

Stream by clicking here.

Below is an enhanced transcript, modified for your reading pleasure. All comments in the shaded green box are my own. For guests and hyperlinks to resources, scroll down.

***

Enhanced Transcript

5 Ways to Help Numbers Come Alive

Shownotes: http://ift.tt/2hWxr5D

Vicki: So today we are talking with Dr. Rebecca Klemm, the “Numbers Lady” about five ways to help numbers come alive in our math classroom. So Rebecca, what’s our first way to help numbers come alive?

Tip #1: Notice numbers and shapes everywhere with students

Rebecca: First of all, math is everywhere and I like to use the numbers to tell the story of where they are in either shape, quantity, order, or name. So, you just look around the classroom.

And one of the things I love to use, cause you probably have windows or if you don’t something else…just look around and find where the numbers are and let the kids pick them out and maybe make a book of it.

So some of them will find shapes. If they’re looking for five, they’re gonna find a pentagon somewhere. If you’re looking at windows you get to decide what is a window, and that’s a really good place sometimes to do multiplication. Because you see them in pairs and you have the horizontal and vertical.

But use that for a great introduction a lot of time in could be whatever size windows you have and you decide what a window is. Or you look at the colors of the shoes, you look at whatever is around the classroom and relate geometry, order, name, and quantity in all the different ways that we encounter numbers.

Pick up the clock, look at the calendar for seven days of the week, or if they figure it out. And let them make a little list and book of the things they find. They can draw them or you take pictures. And it’s a great homework. I like that kind of homework where you go home and you do the same activity with the people you live with. So you look around your environment, take pictures or draw examples of what you see and bring them back. You see that they’re everywhere in all those varieties.

Math Tip #1: Look for Math in the Classroom Russian Classroom windows – Wikimedia Commons

Vicki: That is so important because of we want kids to relate math to the real world. Rebecca, what’s our second?

Tip #2: Combine Geometry and Arithmetic

Rebecca: The second is combine geometry with arithmetic. So often, we teach shapes with colors, I’ve seen everywhere on all kinds of posters and books.

And then there’s counting.

No, the counting and geometry should go together, and that’s one of the things that I put together in my Number Linx puzzle. That, in fact, teaches them together.

Using simple language: points instead of “vertices”

So you count the points or sometimes people like to call them vertices. But I’m a Ph.D. mathematician and I like to keep the language simple for learners. But let them count with the shapes that actually relate geometrically to the counting of the size or points.

I use a heart for two because it comes into a point at the top and at the bottom.

Math Tip #2: Combine Math and Geometry

Heart – Wikimedia Commons

I use a teardrop for one point and an oval for zero. So I like to relate geometry with counting rather than separately as it typically is done.

Vicki: And you know so many times kids will take algebra and then they go into geometry and they just feel like it’s two separate things. And really they are connected.

Rebecca: Very much so. And in fact, they were developed together.

Geometry is not proofs

And Geometry by the way, because I taught everything from elementary through Ph.D.

Geometry is not proofs. The Greeks did it as proofs because they didn’t have Algebra yet. Their language was beauty, their language was Geometry, there was no zero at the time. So the history concept is really an important part of what I do in teaching teachers about what math is. It’s rarely part of the curriculum for getting people ready to teach that subject.

Vicki: What’s our third?.

Tip #3: Use Units when you’re counting

Rebecca: Third is, use units when you are counting. Two plus three equals five, well let’s make it two dolls plus three dolls, let’s make it three socks plus four socks, make it something that’s relatable, leave the abstraction for later. And in fact, it brings the idea in also of sorting by color and size and shape.

So if it’s one of your shoes that may be different from one of my shoes.

So you can say, “Oh, this is a tennis shoe versus a different kind of shoe. But make them have units and it becomes real.

Vicki: That is excellent advice. Now, what grade level does abstraction come in?

When students can start understanding abstract numbers

Rebecca: Well, I think you can bring it in as you’re starting to get into second grade, third grade. Once they see the pattern of them. Once students begin to realize, and it depends on how sophisticated the students are. Some of them can at a later date, but if you actually start with units and they’ve had a strong pre-school and it’s all about units that’s fine. They may even need to start with the units for sure when they are in first grade.

But as they evolve after that and they’ve got the concept that you’re only adding when they’re same things. So what is it you’re trying to add, and it goes back to the windows.

What is a window? Before you add the windows, count how many windows there are, you need to decide what a window is. Is it one of the panes or is it the complete entire piece?

Vicki: And keeping it the same and understanding those units can even set us up for Algebra. Because we’re going to have those variables. I love how you’re building these building blocks, I think with the end in mind, aren’t you?

Rebecca: Yes, very much so. Because I am looking at what you’re going to be doing for math lifelong.

And getting you ready for creating new math things because the math we teach is not necessarily the math we’re going to need in the future.

It’s an evolving subject, it’s not static.

And I think that’s one of the things people don’t realize about math. It has evolved over the centuries and it is still evolving.

And one of the fun things I have there is that out of my creating a puzzle for young children goes into adults and now is a new conjecture in Geometry. It’s a new idea, that came out of trying to think about putting Geometry and Arithmetic together. I just wanted to put them together, I didn’t realize as I started making that in fact, it evolved into a new conjecture.

So that is a very interesting lesson for children to do. And to see that there are new ideas in math all the time.

Vicki: So what is our fourth idea?

Tip #4: Put subjects in the learner’s world

Rebecca: Put the subjects in the learners‘ world. If they like to make clothes, I’ve had a middle school Algebra teacher say, ”My children just don’t like the subject“. I said, ”You need to make it related to their world“.

So you say all the girls want to do is sew clothes and decorate their lockers. I said Fabulous! Think about all the math that is in there and the measurement. Everybody measures and everybody does arithmetic and some geometry in their entire life. And he said, but I don’t know anything about that. I said, Don’t worry.

They’ll teach you about what’s interesting to them, then you work with them on where the math is relevant to their interests. It flips it, don’t teach the stuff and then you’ll apply it. I did this when I taught university. What are you interested in as your subject. And let’s figure out what arithmetic, math, calculus, it didn’t matter what part of math it was, that’s relevant for your area of interest.

Vicki: Make it relatable. Okay, what’s our fifth?

Tip #5: Don’t tell learners they can’t do something

Rebecca: And the fifth is don’t tell learners they can’t do something. I have an article that went out this March that is the story of a little boy whose teacher told them you can’t subtract three from two. It’s called from Toy Trucks to Trade because it turns into a teaching lesson. I asked him what do you think it would mean?

And he talked about how he has three trucks and his other friend had two. They get together, they have five trucks, notice the units are their trucks. But he wanted to borrow his three trucks and leave him two – he owes me a truck. And I said, “that’s precisely where it came from.” So it’s a teachable moment, ask them why they have a question, and not tell them it can’t be done. I know we all as teachers have good days and bad days but let them ask and tell you what they think it means. And then you can mentor them from that.

How to be an amazing math teacher

Vicki: So Rebecca as we finish up, could you give us a thirty-secondpep talkk for math teachers about how to be amazing math teachers?

Rebecca: Well, I think the first thing is really – work with the children, learners of all ages. Cause I’ve done university and PhD students also, it’s the same.

I put it stories for young children where the numbers are trying to match up their meaning. They’re wandering the world like children are, like we all are for our whole life, we’re trying to figure out what we’re here for and what we’re up to.

So I have the numbers doing that and making it fun and engaging.

They have to see that it is relevant to their world. And if they see that, they’re off and running very fast. Textbooks and worksheets are too often just abstract.

You do need repetition but if you put units on them and if you count the wheels they you can say are they all the same kind of wheels?

So you get into sorting and counting by putting them together in groups. Then the arithmetic makes sense to the things they are interested in and off they go.

Vicki: Well, we got some great advice from Dr. Rebecca Klemm, the Numbers Lady, about how to make numbers come alive in our classroom. And you know what, it relates to every subject we teach. Because it’s all about helping things relate to a student’s world, so that it means something. And that my friends is remarkable!

Bio as submitted

Dr. Rebecca Klemm, also known as The Numbers Lady, is an accomplished mathematician, statistician, world traveler, and teacher. Since receiving her Ph.D. in Statistics, she has specialized in explaining mathematical concepts via everyday language.

After running her own research firm for many years, she founded NumbersAlive! (http://ift.tt/2hVRotf) to share her love of numbers with kids. Dr. Klemm has received numerous awards for her NumbersAlive!® apps, books, puzzles, and games which make math meaningful for all ages.

Blog: http://ift.tt/2hVRotf

Twitter: https://twitter.com/numbersalive

Disclosure of Material Connection: This is a “sponsored podcast episode.” The company who sponsored it compensated me via cash payment, gift, or something else of value to include a reference to their product. Regardless, I only recommend products or services I believe will be good for my readers and are from companies I can recommend. I am disclosing this in accordance with the Federal Trade Commission’s 16 CFR, Part 255: “Guides Concerning the Use of Endorsements and Testimonials in Advertising.) This company has no impact on the editorial content of the show.

The post 5 Ways to Help Numbers Come Alive appeared first on Cool Cat Teacher Blog by Vicki Davis @coolcatteacher helping educators be excellent every day. Meow!

5 Ways to Help Numbers Come Alive published first on http://ift.tt/2jn9f0m

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athena29stone · 8 years ago

Text

5 Ways to Help Numbers Come Alive

Dr. Rebecca Klemm on episode 175 of the 10-Minute Teacher Podcast

From the Cool Cat Teacher Blog by Vicki Davis

Follow @coolcatteacher on Twitter

Dr. Rebecca Klemm @numbersalive shares how to help numbers come alive for all ages. From toddler to teenager to Ph.D., Rebecca informs us about the building blocks that build math success.

Listen Now

Listen to the show on iTunes or Stitcher

Stream by clicking here.

Below is an enhanced transcript, modified for your reading pleasure. All comments in the shaded green box are my own. For guests and hyperlinks to resources, scroll down.

***

Enhanced Transcript

5 Ways to Help Numbers Come Alive

Shownotes: www.coolcatteacher.com/e175

Tip #1: Notice numbers and shapes everywhere with students

Rebecca: First of all, math is everywhere and I like to use the numbers to tell the story of where they are in either shape, quantity, order, or name. So, you just look around the classroom.

Math Tip #1: Look for Math in the Classroom Russian Classroom windows – Wikimedia Commons

Vicki: That is so important because of we want kids to relate math to the real world. Rebecca, what’s our second?

Tip #2: Combine Geometry and Arithmetic

Rebecca: The second is combine geometry with arithmetic. So often, we teach shapes with colors, I’ve seen everywhere on all kinds of posters and books.

And then there’s counting.

No, the counting and geometry should go together, and that’s one of the things that I put together in my Number Linx puzzle. That, in fact, teaches them together.

Using simple language: points instead of “vertices”

I use a heart for two because it comes into a point at the top and at the bottom.

Math Tip #2: Combine Math and Geometry

Heart – Wikimedia Commons

I use a teardrop for one point and an oval for zero. So I like to relate geometry with counting rather than separately as it typically is done.

Vicki: And you know so many times kids will take algebra and then they go into geometry and they just feel like it’s two separate things. And really they are connected.

Rebecca: Very much so. And in fact, they were developed together.

Geometry is not proofs

And Geometry by the way, because I taught everything from elementary through Ph.D.

Vicki: What’s our third?.

Tip #3: Use Units when you’re counting

So if it’s one of your shoes that may be different from one of my shoes.

So you can say, “Oh, this is a tennis shoe versus a different kind of shoe. But make them have units and it becomes real.

Vicki: That is excellent advice. Now, what grade level does abstraction come in?

When students can start understanding abstract numbers

But as they evolve after that and they’ve got the concept that you’re only adding when they’re same things. So what is it you’re trying to add, and it goes back to the windows.

What is a window? Before you add the windows, count how many windows there are, you need to decide what a window is. Is it one of the panes or is it the complete entire piece?

Rebecca: Yes, very much so. Because I am looking at what you’re going to be doing for math lifelong.

And getting you ready for creating new math things because the math we teach is not necessarily the math we’re going to need in the future.

It’s an evolving subject, it’s not static.

And I think that’s one of the things people don’t realize about math. It has evolved over the centuries and it is still evolving.

So that is a very interesting lesson for children to do. And to see that there are new ideas in math all the time.

Vicki: So what is our fourth idea?

Tip #4: Put subjects in the learner’s world

Vicki: Make it relatable. Okay, what’s our fifth?

Tip #5: Don’t tell learners they can’t do something

How to be an amazing math teacher

Vicki: So Rebecca as we finish up, could you give us a thirty-secondpep talkk for math teachers about how to be amazing math teachers?

Rebecca: Well, I think the first thing is really – work with the children, learners of all ages. Cause I’ve done university and PhD students also, it’s the same.

So I have the numbers doing that and making it fun and engaging.

They have to see that it is relevant to their world. And if they see that, they’re off and running very fast. Textbooks and worksheets are too often just abstract.

You do need repetition but if you put units on them and if you count the wheels they you can say are they all the same kind of wheels?

So you get into sorting and counting by putting them together in groups. Then the arithmetic makes sense to the things they are interested in and off they go.

Bio as submitted

After running her own research firm for many years, she founded NumbersAlive! (http://www.numbersalive.org) to share her love of numbers with kids. Dr. Klemm has received numerous awards for her NumbersAlive!® apps, books, puzzles, and games which make math meaningful for all ages.

Blog: http://www.numbersalive.org/

Twitter: https://twitter.com/numbersalive

The post 5 Ways to Help Numbers Come Alive appeared first on Cool Cat Teacher Blog by Vicki Davis @coolcatteacher helping educators be excellent every day. Meow!

from Cool Cat Teacher BlogCool Cat Teacher Blog http://www.coolcatteacher.com/e175/

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succeedly · 8 years ago

Text

5 Ways to Help Numbers Come Alive

Dr. Rebecca Klemm on episode 175 of the 10-Minute Teacher Podcast

From the Cool Cat Teacher Blog by Vicki Davis

Follow @coolcatteacher on Twitter

Dr. Rebecca Klemm @numbersalive shares how to help numbers come alive for all ages. From toddler to teenager to Ph.D., Rebecca informs us about the building blocks that build math success.

Listen Now

Listen to the show on iTunes or Stitcher

Stream by clicking here.

Below is an enhanced transcript, modified for your reading pleasure. All comments in the shaded green box are my own. For guests and hyperlinks to resources, scroll down.

***

Enhanced Transcript

5 Ways to Help Numbers Come Alive

Shownotes: http://ift.tt/2hWxr5D

Tip #1: Notice numbers and shapes everywhere with students

Rebecca: First of all, math is everywhere and I like to use the numbers to tell the story of where they are in either shape, quantity, order, or name. So, you just look around the classroom.

Math Tip #1: Look for Math in the Classroom Russian Classroom windows – Wikimedia Commons

Vicki: That is so important because of we want kids to relate math to the real world. Rebecca, what’s our second?

Tip #2: Combine Geometry and Arithmetic

Rebecca: The second is combine geometry with arithmetic. So often, we teach shapes with colors, I’ve seen everywhere on all kinds of posters and books.

And then there’s counting.

No, the counting and geometry should go together, and that’s one of the things that I put together in my Number Linx puzzle. That, in fact, teaches them together.

Using simple language: points instead of “vertices”

I use a heart for two because it comes into a point at the top and at the bottom.

Math Tip #2: Combine Math and Geometry

Heart – Wikimedia Commons

I use a teardrop for one point and an oval for zero. So I like to relate geometry with counting rather than separately as it typically is done.

Vicki: And you know so many times kids will take algebra and then they go into geometry and they just feel like it’s two separate things. And really they are connected.

Rebecca: Very much so. And in fact, they were developed together.

Geometry is not proofs

And Geometry by the way, because I taught everything from elementary through Ph.D.

Vicki: What’s our third?.

Tip #3: Use Units when you’re counting

So if it’s one of your shoes that may be different from one of my shoes.

So you can say, “Oh, this is a tennis shoe versus a different kind of shoe. But make them have units and it becomes real.

Vicki: That is excellent advice. Now, what grade level does abstraction come in?

When students can start understanding abstract numbers

But as they evolve after that and they’ve got the concept that you’re only adding when they’re same things. So what is it you’re trying to add, and it goes back to the windows.

What is a window? Before you add the windows, count how many windows there are, you need to decide what a window is. Is it one of the panes or is it the complete entire piece?

Rebecca: Yes, very much so. Because I am looking at what you’re going to be doing for math lifelong.

And getting you ready for creating new math things because the math we teach is not necessarily the math we’re going to need in the future.

It’s an evolving subject, it’s not static.

And I think that’s one of the things people don’t realize about math. It has evolved over the centuries and it is still evolving.

So that is a very interesting lesson for children to do. And to see that there are new ideas in math all the time.

Vicki: So what is our fourth idea?

Tip #4: Put subjects in the learner’s world

Vicki: Make it relatable. Okay, what’s our fifth?

Tip #5: Don’t tell learners they can’t do something

How to be an amazing math teacher

Vicki: So Rebecca as we finish up, could you give us a thirty-secondpep talkk for math teachers about how to be amazing math teachers?

Rebecca: Well, I think the first thing is really – work with the children, learners of all ages. Cause I’ve done university and PhD students also, it’s the same.

So I have the numbers doing that and making it fun and engaging.

They have to see that it is relevant to their world. And if they see that, they’re off and running very fast. Textbooks and worksheets are too often just abstract.

You do need repetition but if you put units on them and if you count the wheels they you can say are they all the same kind of wheels?

So you get into sorting and counting by putting them together in groups. Then the arithmetic makes sense to the things they are interested in and off they go.

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