Office furniture giveaway

Here is your chance to win a piece of office furniture in this little giveaway contest:

• First go check www.csnOfficeFurniture.com website and find a piece you'd like to have if you are the lucky winner. It needs to be $135 or less in value.
  
  
• Then, to participate, purchase any of the Math Mammoth or Make It Real Learning products at Kagi store between now and July 9, 2009.
  
  
• In the comments field on the order page, put either the name of the piece of furniture you'd like to win or the URL to its web page. If you leave this comment field blank, I will not know that you wish to participate, so it is crucial!
  

That's it! I will have a random draw for ONE winner within the participants, and put you in contact with csn Office Furniture company. They will pay for the shipping within United States.

Links you might need:

• www.csnOfficeFurniture.com to check what piece of furniture you'd like to win


• Math Mammoth Blue Series information and order page


• Math Mammoth Golden Series and Green Series information and order page


• Math Mammoth Light Blue Series information and order page


• Math Mammoth discounted packages / CDs information and order page


• Make It Real Learning workbooks information and order page.

Math Teachers At Play #10

Welcome to the tenth edition of Math Teachers At Play blog carnival! Here with the heat of the summer, "less is more". We concentrate on teaching issues, but also get to "play" a bit with binary numbers, geometry, integers, and an optical illusion.

TEACHING

What's a math teacher going to do with Wolfram | Alpha ?



In case you haven't heard... Wolfram|Alpha is a new, computational search engine. And if you're a math teacher, you should be aware of it.

Collection of Web Freebies discusses Wolfram|Alpha as your Personal Free Online Math Assistant.

I wrote an introduction to Wolfram|Alpha as well. I feel it can both be a benefit and a drawback to math education - a benefit because it can free us from routine calculations, and a drawback because students still need to learn to do those, but how can you easily enforce that?

W|A presents a dilemma to math teachers... because it can solve SO MUCH. It can solve just about any routine type calculation in algebra 1 or algebra 2 or calculus courses. So what can a teacher do? Jason, The Number Warrior wonders how we can be Teaching to the Limits of Wolfram Alpha. In essence, should teachers strive to find problems that cannot be solved with Wolfram|Alpha?


What's a math teacher going to do with homework?

Photo courtesy of Vicki's pics

Another, an age-old, dilemma for math teachers. What is the best way to assign, grade, and check homework? Sam Shah conducted an unofficial survey on the matter and presents the Homework Survey Results.

I glanced over the survey results, and found one response that really "struck" me as a "sweet" solution to the homework problem. It is from a 5th grade teacher, and I apologize for taking so much space for it here but I just feel it was really good (and if the person feels I shouldn't quote this, please let me know). Emphasis mine:

"I work hard at the beginning to set up a culture of responsibility for themselves. They are responsible for making sure they understand, for asking questions, for asking for more practice or another example.

When we come into class, we check the answers together. I will solve a problem or two on the board that I have learned over the years is confusing. Other than that, I expect them to ask for clarification if a problem is wrong.

They "grade" their own. If it's wrong, they are expected to take a minute right then to figure out why it was wrong. Usually it's a silly mistake. If not, they bookmark it to ask questions during our next work time.

I don't give any grades. I don't assess it. The final test/quiz is their grade. The homework is just them figuring out how to do the skills. They know they won't be graded on it. They know they won't be penalized for getting it wrong. They know that the whole point of the homework is to figure this math stuff out. If they get it wrong, they know they haven't mastered it and need to get help.

On the opposite side, if a student doesn't do their homework, I don't get too upset. We have a talk about how they hurt themselves, because now they don't have an accurate measure of if they can do it on their own. I can't help them because they didn't get the opportunity to make their mistakes before the test. However, I have a few who don't need to do homework. They still earn A's on the final test. They learned it by being in class and paying attention.

With those who obviously do need the homework practice, but aren't doing it, I problem solve that on a case-by-case basis.

It changes the whole culture of learning and mastery in the classroom. But it is VERY important to set up that culture at the beginning."

Now, I'm not claiming that middle and high school teachers could easily transfer these ideas to their classes... but perhaps they can, at least somewhat. Please discuss homework at Sam Shah's post.

A teacher's problems do not end with homework. Can you believe that TEACHING as a profession is so difficult in today's world that sites exist solely to help new teachers to SURVIVE their first year? That's exactly the word that is used. Teaching Degree.org has compiled a list of 100 Helpful Websites for New Teachers, and the list includes new teacher "survival" sites, teacher video sites, freebies, inspirational sites, and several other categories as well.

Some Math As Well

At Exploring Binary blog we find an EXCELLENT way to explain binary numbers that he found when he taught his mother binary numbers . It's true, once you struggle at explaining a concept to someone who's not a math whiz, you really get to the brass tacks of the matter.

Denise from Let's play math! has some geometry challenges for us, some of which are from ancient Egypt. I solved the puzzle under the title "Can You Explain This?", using fractions (and not avoiding them as it tells you to do). I also pondered number (2) but couldn't find an immediate (easy) way to find an answer. I don't think she ever posted answers to those.

John Cook from The Endeavour blog shows us an optical illusion that is so fooling that I couldn't believe my eyes at first. Quite amazing. He also makes an analogy from the optical illusion to a "mathematical" illusion within his own work.

Dr. Jeff is asking us to fold a humongous piece of xerox paper and see how many folds reach to the top of mount Everest or the sun, among other things. You probably won't believe the answers!

If you're into 5th-7th grade math, please check also my videos about integer subtraction.

---

This is where to send your submission for the next carnival on July 10th at Math Mama Writes. Happy summer, everyone!

Wolfram|Alpha is here

Wolfram|Alpha is a new, computational search engine. If you do a query where the answer has quantitative data, Wolfram|Alpha probably gives it.

For example, try enter your last name. Wolfram|Alpha gives you information about the popularity of that name. For example, "miller" ranks 6th within the US and there are about 1,128,000 people with that surname.

Enter a first name, and it will even give you a graph showing the name's popularity over the years. I just found out that Cindy's popularity peaked in about 1960. No wonder it is a common first name among the mothers who ask me questions about their children's math education.

Enter a town - for example Houston, and see what information comes up.

But, the reason I'm writing this post is because Wolfram|Alpha (or Walpha as some called it) especially excels in mathematical queries.

This has implications to mathematics education, especially in high school and college. This tool is completely free, easy to use, and accessible for everyone with an Internet connection (even with a smart phone). Just imagine if you are a math teacher and you assign homework for your 9th graders, "Find the equation of the line that goes through points (2,5) and (-8, -9)." W|A does it in a split second.

It also solves equations. For example, Solve ln(x)+ ln(x-2)+ ln(15). It even gives you the solution steps - just click on "show steps".

Please see a full list of examples of what Wolfram|Alpha can do in mathematics.

While W|A easily computes a lot for the elementary algebra or calculus student, it doesn't stop there. Look at the examples for elementary mathematics given on the site. It also acts as a fraction and percent calculator. Granted, normal calculators do those as well.

So, what is a teacher to do? Will a lot of the content in high school and college math courses suddenly become obsolete?

Now, Wolfram|Alpha is not what started bringing technological tools into classroom. That trend has been here for a while (think graphic calculators, computers). However, it is an extension of the trend that makes the computational tools more easily accessible and available to nearly all students.

I see Walpha both as a benefit and as a drawback.

- BENEFIT: Teaching can focus more on the concepts and less on tedious calculations, since practically all students will have a tool they can use for computations and graphing (all you need is a computer with an Internet connection or a smart phone). Students could be given more problems of the type that require thinking and problem solving, and less of the mechanical calculation problems.

- DRAWBACK: It is a fact that one cannot adequately learn mathematics without also learning many of these "mechanical tasks", such as how to find the slope of a line when given two points, or how to graph a parabola from its equation. If these skills were totally skipped, students wouldn't be prepared for the next mathematics course where such knowledge is needed. So, teachers cannot skip those topics and need to enforce student learning in such a way that cheating with Wolfram|Alpha cannot happen (putting such problems in the test).

Actually, I'm not so sure if W|A will change the actual teaching so much, because many students have already been having graphic calculators, which do similar things as W|A. I wonder if the biggest change it brings along is a decline in the sales of graphic calculators...

Read also what others have blogged about W|A :

Impact of Wolfram Alpha on Math Ed

Wolfram Alpha is up and running

Wolfram|Alpha and the shrinking future of the graphing calculator

Walpha Wiki discussion

Measuring worksheets

I finally got around to creating another worksheet generator that had been "lacking" for a while from my "collection" - measuring units worksheets. Those where you ask kids to convert 6 cups to ounces, or 5 kg 40 g to grams.

Measuring units worksheets

These are free and printable. I've made lots of ready-made links for some common type worksheets, but of course with the generator you can customize it how you want. Both metric and customary units are included; however I did not include all possible metric units, because the focus here is for grades 3, 4, and 5.

Integer subtraction

I recently finished another video of mine, this time on the topic of subtraction of integers. You can watch it here:

Subtracting Integers

In it, I explain three different models that we can use to justify the rules for subtracting integers to the students. The three models are:

1) number line jumps;
2) concept of difference;
3) counters.

Please read about these models in more detail in my updated article How to teach operations with integers.

Fraction games online

I updated my list of online fraction games and tutorials, and sorted the games according to major topics such as equivalent fractions, fraction addition & subtraction, multiplication & division, or fractions & decimals. Take a look!

Massachusetts teachers' math exam

Photo by Made In China

I was almost ready to comment on this exam, where only about 27% of aspiring aspiring elementary school teachers passed the new math section of the state's licensing exam this year...

Boston.com says about this test, "Education leaders said the high failure rate reflects what they feared, that too many elementary classroom and special education teachers do not have a strong background in math and are in many ways responsible for poor student achievement in the subject, even in middle and high schools."

...and then I noticed I had been looking at the wrong link for the practice test. The real link is this:
Massachusetts Tests for Educator Licensure, Mathematics Subtest, from MTEL Practice Tests website.

I feel that test is pretty good! In fact, I'd recommend that you do some problems from it, if you're teaching any grade from 1-12. If you're teaching middle or high school, you could use some of those problems with your students, and if you're teaching elementary, it's just to check if YOU have the adequate math skills.

The open-response item is particularly interesting, and good, I think. It shows a student response on a particular geometry problem, and asks:

"Use your knowledge of mathematics to create a response in which you analyze the elementary school student's work and provide an alternative solution to the problem. In your response, you should:

• correct any errors or misconceptions evident in the elementary school student's work and explain why the response is not mathematically sound (be sure to provide a correct solution, show your work, and explain your reasoning); and
  
  
• solve the problem using an alternative method that could enhance the elementary school student's conceptual understanding of ratios and decimal multiplication in the context of the problem."

Take a look at the math test.

---

What kind of math would I test elementary teachers on

If I made a test for future elementary school teachers, I'd ask lots of questions about elementary and middle school math INCLUDING "WHY" questions. If they know that, then they can explain the math to their students as well.

I might ask questions related to common errors and misconceptions kids have. "Sally calculated that 0.5 + 0.12 = 0.17. What concept is Sally not understanding (and it's not decimal addition)? What kind of intervention do you think would help?"

I would ask questions that test their understanding of why long division or long multiplication works.

I'd test their knowledge of middle school level math and some high school level math. I'd test for problem solving abilities.

Elementary teachers should know middle school math well (percents, proportions, equations, geometric constructions, statistical graphs, etc.) so that they know what the elementary math they teach is leading to. For example, they should know square roots and Pythagorean theorem. That way, when they teach multiplication, they can throw in a "teaser" for the best kids in the class, asking, "What number multiplied by itself is 64?" Or, "I say a number, you say what number multiplied by itself gives that number."

So, I might actually ask, "What further mathematical concepts after 3rd grade depend on a good knowledge of multiplication tables?" Or, "Students study prime factorization in 6th grade. Give two examples where the understanding of this concept is needful in further mathematics studies within grades 6-12."

See also what MathMama writes about Tests .... (TIMSS & the MA teacher licensing test)