I’ve also witnessed technology used brilliantly in a classroom. In the school I tutor in, each Kindergarten class gets split in half for their literacy lesson – half to work independently on computers, and half with the teacher (then they switch). The key to this success was careful technology instruction in the beginning of the school year and making sure that all students understood how to use the program. It was also important to find software that was engaging and age-appropriate. Finally, a positive reinforcement system was put in place so that students were motivated to complete their computer activities without supervision.

Technology can (and should!) also be an integral part of math instruction. Khan Academy is an excellent resources for both students and teachers. For example, if I wanted to teach about prime factorization, I could use the Khan Academy videos to brush up on how to teach it, or I could post it on a class website so that students can refer back to it once they’re home. Students that have completed an assignment early could also use Khan Academy’s skill site to get in extra practice and receive immediate feedback. The usefulness of KA is endless!

Technology is a blessing, if we use it appropriately in our classrooms. Have you ever had any tech blunders? Successes?

]]>You would think that this information is a blessing. Sometimes, though, the wealth of information becomes overwhelming. It seems like there’s always another method, another opinion, another strategy. This is often referred to as the Paradox of Choice. Essentially, we get anxiety when there are too many options and regret whichever option we end up choosing because we think that there could also be something better out there. For example, when I searched Pinterest for “fractions”, a seemingly infinite number of responses were provided, as well as suggestions – did I want to also search for adding fractions? Teaching fractions to 1st graders? Improper fractions?

What if I picked a strategy that doesn’t work for my students? These thoughts and more often race through my mind while doing online research. As I’ve continued pursuing my elementary education degree, I’ve had to come up with some basic rules to deal with this anxiety…

1. Understand the concepts you want to teach. If I want to search for lessons to teach my students fractions, I need to have a solid foundational knowledge of what a reciprocal is and how the invert-and-multiply rule works.

2. Understand your students. If I know that my group is a particularly hands-on bunch, I’ll search for “teaching fractions using manipulatives” to lessen the overwhelming amount of information coming back to me.

3. Don’t spend more than an hour searching online. Clicking on one link leads to another link leads to another link leads to another. Suddenly you’ve spent five hours online doing research and haven’t actually started writing your lesson. Too much information is just going to overwhelm your students anyway.

4. Don’t substitute the Internet for your brain. Personally, I have to really force myself to hunker down and get creative when creating lesson plans. Often I find that browsing the Internet for resources and ideas helps get my creativity going so that I can adapt what I find online for my own lessons. Other times, I find that it only hinders my fully-capable brain of creating a lesson on my own. And it’s the 100% self-created lessons that I’m the most proud of.

That’s it! It’s not ground-breaking, but it helps me fight the paradox of choice. I’m obviously in the very, very early stages of my teaching career, so I would love any insight others have on using online resources for lesson planning. Good? Bad? Overwhelmed too? Let me know!

]]>As students become more familiar with integers, they should continue to be introduced to real-life situations. Our textbook, *Mathematic Reasoning for Elementary Teachers*, presents the following problems:

*At mail time, suppose that you are delivered a check for $20. What happens to your net worth?*

….*suppose that you are delivered a bill for $35. What happens to your net worth?*

…..*suppose you receive a check for $10 and a bill for $10. What happens to your net worth?*

These types of questions make my heart flutter with happiness. Back in my accounting days, I volunteered with a program called Junior Achievement, whose goal is to increase students’ financial literacy. Those that volunteered in the middle and high school would talk about budgeting, economics, etc., but I volunteered in elementary classrooms where we started small – like how our roles in the community work, why we pay taxes, and so on. Like learning about negative integers by comparing them to our frigid temperatures, asking questions like those posed above will help students make connections to their life and better retain what they’re learning. I believe that these types of real-world connections not only help students to understand what they’re learning, but also set them up for success in their day-to-day, and post-high school, life.

(Even if their day-to-day life includes using the phrase *polar vortex* more than any human should ever have to.)

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I was wrong.

It turns out that studying ancient numeration systems can actually be quite beneficial when it comes to teaching math, as it demonstrates why certain math systems don’t work and why we have our current system, the Indo-Arabic (aka decimal) system, in place.

The Egyptian numeration system was base-ten like our Indo-Arabic system, meaning that they had different symbols to represent different powers of 10. For example, “a staff” represented 1, “a yoke” represented 10, “a scroll” represented 100, and so on. (Side note: the last symbol, that represents 1,000,000 is often called “an amazed person”, which cracks me up.)

To write a number, the Egyptians would combine symbols additively (see the example above for 4,622). This makes it relatively straight-forward to write a number, but when it came to addition, subtraction, multiplication and division things got complicated and time-consuming. Having students learn the Egyptian numeration system should get them thinking about regrouping, place value, how important zero is and why we use the base-ten system. It’s also a great way to integrate other subjects into math – for example, students could research Egypt’s history and geography, then write a letter to a friend describing what daily life in Egypt is like.

There are several other ancient numeration systems that can be useful to learn, in particular the Roman System, Babylonian System, and Mayan System.The Roman System is important, as it’s still used in a variety of ways today. It’s additive and subtractive (similar to the Egyptian system), which, again, can become quite cumbersome for performing math problems. This can help students understand why we use the decimal system, where adding, subtracting, multiplying and dividing are significantly easier to do. The Babylonian numeration system was a base-sixty system that used a variety of symbols similar to arrows. Learning the Babylonian system is beneficial to students, as our current time and angle-measurement system is also base-sixty. The Mayan numeration system was a base-twenty system that used a combination of dots, lines, and “shells”. It’s similar to our current system in that it was a positional system and contained a symbol for zero. To help organize and use these systems further in the classroom, I created a Mind Map through Mindomo that has a variety of resources for teaching ancient numeration systems in the classroom, as well as methods for integration.

Thanks, King Tut!

]]>Dan Meyer’s theory is that the way we currently teach mathematical reasoning is wrong. We often provide all the information to the students, lay out the steps, provide coordinates/labels/etc. and have them solve accordingly. In his TED Talk, Dan explains that we should instead provide students with the problem, and allow the students to determine the steps, label when necessary, and find their own way to the solution. When asked to solve in this way, students should be more engaged and will be able to clearly “see the point” of learning math in the first place.

In the weeks since I first saw Dan’s Ted Talk, I’ve been thinking about how to apply his technique in elementary classrooms, when very basic math skills are being taught. When I think back to my very first math lessons as an elementary student, I recall being told *how* to add, but not *why* it works. Rote memorization was a huge part of our classes. In reality, basic building blocks of math, like the addition and subtraction algorithms, should be taught in a hands-on setting. Manipulatives help students understand both *how *and *why* adding and subtracting works. Like Dan Meyer suggests, we can provide students the problem (“Mrs. Johnson had ten cookies, but then gave two of them away….”) and allow students to determine the steps with sticks, blocks, etc. I believe that if students are taught math in this way, they will be much more engaged, have better retention, and perhaps the math teachers of the world can finally stop hearing “What’s the point!?”.

This semester began covering concepts that I recognized. In week 2, however, I was not so lucky. We began learning about sets and whole numbers, and my head started spinning. It continued to spin until yesterday when a friend of mine responded to my complaining about learning new math concepts (I must have forgot to remind myself about the whole “math people” thing…) with a hint that turned things around….

Her hint went like this:

The intersection of two sets, A and B, is written *A* ∩ *B*, (the upside-down U is technically called a *cup*) and is the set of elements common to both A and B. In a Venn Diagram, it would look like this:

or this:

The union of two sets, A and B, is written A ∪ B, and is the set of all elements are in A or B. It would look like this:

or this:

I was struggling to remember the difference between the two symbols and what they meant, and that’s where the hint comes in. The union symbol (technically called a *cup*) looks like a “U” (obvious) but it also looks like a smile. And you would smile if more was included, right? OK, so my hint isn’t revolutionary, but it helped me to remember one small thing, and for that I’m thankful.

Do you have any tricks?

*all photos from Wikipedia.

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