Numberless Math ?!

Numberless Math Word Problems

It sounds like a contradiction in words, but in fact it's a great way to get student to think about math in new ways. The basic idea is that you give students a math scenario in which none of the quantitative aspects have been defined. Then the students have the liberty to either add numbers to define those aspects, or to work entirely conceptually to create solutions.

Things this process does:

1. Allows students to think about math conceptually. This is very important for the long term development of skills in algebra and calculus. While there is no arguing that formulas and proofs are a big part of these types of math, the need for conceptualization skills in problem manipulation is pervasive.  

2. Reduced math anxiety by removing the aspect that most people fear, the numbers. Math anxiety so often comes from the fear of not being able to get the right answer. When there is simply no one right answer, just a right approach, then students can focus more on the process.

3. Allows for natural differentiation. Students will naturally work at their own skill level. By removing the numbers, you can remove the innate academic level associated with them. Doing so will allow students to work through the problem at their actual skill level. If students want to create large complex problems to show their exceptional math skills, they can. If students are new to some math concepts, you'll be able to see that in how they approach their solutions.

In addition to the practical aspects, these types of problems can be fun. In this case it was about pirates and treasure, which in itself can be more interesting than traditional numeric math problems.

Long Division...but why?

LONG DIVISION

"In arithmetic, long division is a standard division algorithm suitable for dividing multidigit numbers that is simple enough to perform by hand. It breaks down a division problem into a series of easier steps"

In our efforts to better understand long division, we started breaking down the divisions problems into its parts. Many of us know how to do long division using the traditional methods, but not many of us could articulate why we do it that way.

Using a combination of separating  numbers into its sets (thousands, hundreds, and ones) we tested several different methods for dividing. Each time we tested a method or strategy we talked about why it works or doesn't.

The activity first started with a refresher on what division is. It's the sectioning of a number into a series of equal sized parts. This conceptual awareness can be very important for understand why we use the steps that we do. We often take for granted the underlying reasoning so we can focus on the process.

 To help make the lesson more interesting, and memorable, we decided to use our desks as our idea boards. It's a fun way to approach a new lesson but also breaks up the routine enough to get students thinking in a new way. Simple changes to the tools, methods, or environment can have a surprising impact on creative thinking. 

We tracked our ideas about how to approach division. We used illustrations. We used diagrams. We used numbers. Really whatever we could come up with to help understand how the division steps we were taking worked.

This conceptual approach allows us to not only explore the deeper meaning of mathematics, but also inherently lets us differentiate the material for each of our skill levels. Each of us got to ask questions that helped us understand the concept at our own skill level. That could mean that if one of us had questions about method or strategy, we could focus on that. But that also means that if someone had a question about how this applies to broader concept, we could talk about those as well. 

Survival Day - Revolutionary War

Reporting for duty! Revolutionary War simulation actors reporting in. The value of a simulation can be amazing for students learning about a new topic. Our simulation was geared toward being an introduction to the concepts we'll be studying for the next three weeks.

We made fortification supplies, such as lanterns. We learned about what forts looked like at the start of the American Revolutionary War. 

 

We calculated our costs for fortification building and living supplies using prices from the time period. It was a fun way to integrated real world math into our simulation. 

 After studying fashions from this era, we created vests and hats to be help us in our role-playing. 

We ate popcorn to refuel our minds.

 We pondered the defensive structure of our forts. 

We created some very tall hats. 

 Most of all we had fun learning about math, science, history, and engineering all at the same time.

Point Defiance Zoo's Washed Ashore Exhibit

What is the Washed Ashore exhibit? 

Here is some information from http://washedashore.org/

Washed Ashore is a non-profit community art project founded by artist and educator, Angela Haseltine Pozzi in 2010. The project is based in Bandon, Oregon, where Angela first recognized the amount of plastic washing up on the beaches she loved and decided to take action. Over the past six years, Washed Ashore has processed tons of plastic pollution from Pacific beaches to create monumental art that is awakening the hearts and minds of viewers to the global marine debris crisis.

One of our goals this year is plastic reduction. But the intent of this goal is to draw attention to the impact of industry, society, and commerce on the environment. We are trying to look at these impacts through an unbiased lens. We want to understand things like... what is really happening, where the impact occurs, how this impact affects or effects the various aspects of our lives.

How does this relate to school?

Science Standards! 5-LS2-1 and 5-ESS3-1

Washington now uses Next Generation science standards. The 3-5 science standard includes an understanding of ecosystems and how they are inter-elated and co-dependent. The title of the standards reads as follows: " 5-LS2-1. Develop a model to describe the movement of matter among plants, animals, decomposers, and the environment. " One of our approaches to meeting this standards to do evaluate systems with a global mindset, accounting for human impact, which in this case is plastic. The second Next Generation science standard we addressed with this trip is 5-ESS3-1. In this standard the goal is to:Obtain and combine information about ways individual communities use science ideas to protect the Earth’s resources and environment. Addressing plastic waste is a very important part of analyzing and understanding the human impact on our world.

You can find out more information about Washington's new science education standard here: http://www.nextgenscience.org/

Science & Tech - Sculptris

Teaching students skills that will be relevant when they are adults can be tough. As teachers we spend a lot of time theorizing what skills will make current students marketable, employable, and successful. That often means exploring uncommon areas of technological learning. 

One big aspect of our technology time is learning about tools used for 3D printing. One of the programs we have grown to love is Sculptris. It's a 3D sculpting program using computers. Sounds easy but the mechanics are complex.

Masked as an art program, Sculptris actually provides a lot of opportunities for developing tech schools. Students learn how to :  

-recognize file types associated with 3D printing

- saving and sharing documents into shared drives

- use of rendering programs for design and coloring

- visualization of objects with multiple dimensional

This type of modeling and rendering are used in various fields ranging from movies to merchandising. 

Here are a few samples of our work so far.