Cell Phones: Get out of Jail Free!

So this "cell jail" theory dominated my timeline for some reason this week. It's the idea of having students turn in their cell phones into a "cage" of sorts (often utilizing some teaching related material) to keep them out of the hands and off the minds of students during instructional time. With some of the post comments, I read that teachers would use the "incentive" that students would get participation points for it or could use it as a time to charge their phone in one location. Ironically enough, the idea of it all arrested me and wouldn't allow me to rest without offering an educational alterative.

Imagine, if you will, these students in the real world in a few years. How would they analyze data, quickly retrieve a definition, share a message or thought, and collaborate with colleagues? Let's bring it a little closer to home. In less years than that, what application would be used to submit documents and retrieve their immediate feedback? In all honesty, it's not even in a few years...it's their current reality.

As students walk down the sidewalk, headed home or sitting in the stands at a football game; they are doing more than social networking and texting. They are collaborating with their families on dinner plans through groupme, comparison shopping for the tickets to their favorite concert, and collecting data on the next showing at the movie theatre. All by their phone.

So our challenge is how do we "get them out of jail"...for free?! How do we free our students from attending the isolation cell that is our classroom and release them to make the connection between their world and the learning they must attain? How do we, as educators rise to the occassion and bring learning to the student by helping them find value in core content. One of the process standards for math says we should be helping students see the value of math in everyday life! What better way to connect their math standards (for example) to everyday life than to present it through the means of utilizing their mobile devices? The Technology Application standards summarize that by late middle and high school, students should be colloborating and evaluating products that were created digitally by other students.

What better way than to demonstrate how the "smart phone" is in fact smarter than we think than to allow them the opportunity to explore those possibilities. Let's help them use it to the capacity for which it was designed! This may require some education on our parts, but isn't that what we are as teachers- life long learners?
Rather than be afraid of their open use, encourage it! Educational Conferences offer various seminars on how to incorporate technology into the curriculum. Try attending one the next time you're at a conference.

Here are some other "FREE" ways you can help release your students' cell phones from jail:

• Todays Meet (todaysmeet.com) - Enables discussion and empowers student voice! Great for facilitating discussions possibly while students are doing a silent reading activity or even while you're giving a lecture. 
• Padlet (padlet.com) - Allows students to collaborate and express their ideas about a common topic. Great for use in any subject.
• Kahoot! (kahoot.it) - Game based learning; great way to poll your class, give quizzes and play a game with immediate feedback. 
• Train the how to use their device responsibly and explain why. Allow THEM to set the norms and consequences for stepping outside of these boundaries as you assure them that your duty is to provide opportunities for usage. Trusting them, builds their trust in you!

These are just a few to get your started. I even heard of an experiment where students were measuring the height of different balls using a measuring stick. The problem was that the ball was bouncing too fast and they couldn't accurately read the height on the stick. The teacher had the students pull out their devices and use their video recorder to capture the process. Then she had them play back using the slow motion feature to capture a more accurate reading. What a powerful method of engagement, collaboration and integration! 

Kudos for that teacher; but you ARE that teacher! You are the one who uses technology everyday just like your students; not only that but you know what learning they're accountable for. So you are in the best position to train them to use their technology responsibly. Every meeting I go to, when I'm sitting in church, and when I'm driving, I'm challenged with the task of using my technology responsibly. Why not give your students a chance to practice, in class, a discipline they must already utilize in real life! 

Free their cell phone! 

Investigating Equivalencies

How many of you have ever taught equivalent fractions to students? If that's you, try to complete this phrase:

"What you do to the top, you must do to...."

This teaching phrase is commonly used as a "rule" to help students remember how to simplify a fraction (or what we used to call "reducing"). If we allow students to investigate and explore fractions in a concrete manner, they can create their own rules as early as third grade.

Now, in 3rd grade, equivalencies are already being determined on a number line (hopefully through exploration and utilization of fraction tiles)! *See 3.3G

In 4th grade, however is where we find ourselves reading TEK 4.3C "Determine if two given fractions are equivalent using a variety of methods." And almost immediately we think 'Let's make an anchor chart that tells the students to multiply or divide the top and bottom number by the same numeral to get a larger or smaller fraction'.

A few problems occur when we teach this way:

1. We teach a rule that kids feel the "need" to memorize. As a result, they feel defeatedd when they cannot memorize or recall that rule. 

2. We impose on students (yet another) rule in math, causing them to believe math is made up of a lot of rules that are impossible to remember. 

3. We become the ones imparting knowledge rather than giving students an opportunity to discover the relationships (not rules) that math creates!

Cathy Seely, author of Smarter than we Think, writes "If experience influences a person's intelligence, then the mathematical tasks and problems we present to students, and how we present them take on critical importance." I love this picture she paints of expanding a students capacity by allowing them to struggle. This concept addresses all of the aforementioned problems. 

So let's pose this problem to 4th grade students. 

Build/construct/compose an array of objects to reflect 3 out of 12 (3/12ths). Find another way to divide this array in order to find a fraction that is equivalent to three-twelfths. 

You may find this "struggle task" vague and complex for students. But allow them to struggle. The concrete model should assist them in finding equivalencies. Some students who struggle a little longer and harder may need a little assistance.

Once students have found that 1/4 (one-fourth) is a fraction that is equivalent to 3/12ths, have them explain why (justify their solution). It may help to have them record the two fractions side by side to help them prove their answer. Some students may extend their exploration to find that two out of eight also equals 3/12. With all of these fractions sitting side by side, they should be able to compose their own rule (relationship) between the three fractions. 

If students can visually see that one green chip out of 4 chips doubled is the same as two green chips out of 8 total chips due to a multiplicative pattern, they will determine that equivalencies are built upon multiplication. They will have created the information necessary to create an anchor chart (together as a class).

(credit: lawlerjoyinthejourney.blogspot.com)

This method addresses what Cathy Seely calls the "upside down" strategy and problems #1 & 2 from above. The students take ownership of their learning therefore releasing them from the pressure of having to memorize rules. Likewise, the concrete investigation seals their understanding and gives them the power to build on their discoveries. As uncomfortable as this may make the teacher by changing their role from teacher to facilitator, it's also powerful because students no longer see us as pouring knowledge into them, but rather bringing out what they know. This, in turn, significantly increases student efficacy.

Happy investigating!!

Fractions of Area?? In 3rd grade?

I'm sure some of these new math TEKS have taken many of you by storm! If you're not ready to throw in the towel, then you're a real trooper! As Math Educators, we are really on the "front line" out here because we are having to re-structure our thinking, all while teaching our students. It's almost the "blind leading the blind"...ALMOST! Hopefully, many of you are staying a few feet ahead of the students.

As an Instructional Specialist, I'm not suffering any less. I'm challenged to stay a few feet ahead of the teachers! So let's explore a TEK that shows up in the Geometry and Measurement Unit!

3.6E "Decompose two congruent two-dimensional figures into parts with equal areas and express the area of each part as a unit fraction of the whole and recognize that equal shares of identical wholes need not have the same shape."

In English please??? Right?

Layman's terms??: "Upon creating 2 flat shapes (using area models) that have the same product or area, separate/divide the shapes in different ways but so that both are separated equally. Do this so students understand that no matter how you separate a shape, its partner (same size, not same shape) shape will have the same amount of parts."

Let's explore this concept.

If I had 4 quarters and gave you two of them, I would have given you $0.50, right?
Well, if you had 10 dimes and you gave me five of those dimes, you would have given me 50 cents.
We both had the same value of money ($1.00); though we displayed our values in different ways (4 quarters, versus 10 dimes) we still both ended up with the same value ($0.50).

So how do we get our students to understand this concept?

Teacher: (Place students in pairs) Have students work with colored tiles (concrete) or colors and grids (representational) to display an array that creates 12. Encourage each partner in a pair to create an array different than their partner.

Students may make 1x12, 2x6, 3x4 and/or the commutative property of these arrays.

Teacher: Have students discuss whether they think dividing their perspective shapes in half will create the same amount of tiles. Simple YES or NO prediction. **Estimation opportunities are critical for students. It's a great way to get them to question their own thinking and justify their reasoning.

Students: Challenge students to divide their shapes in half (perhaps using a popsicle stick) and ask them to find out how many tiles are represented in this "half".

Teacher: Lead a discussion as to "why" each figure, though divided differently, might yield the same result in number of tiles? Have each student (in the pair) write a statement about their findings. Offer ELL students & struggling learners language support via sentence stems.

So when we look at the original version of the TEK, it may sound foreign to us and from that stand point a bit intimidating that we are essentially teaching our students how to find a fraction of a whole! And indeed we are! But here's the relief: we aren't teaching them an abstract concept without first laying the concrete foundation! One day the algorithm of multiplying a fraction by a whole number will make sense because they received a foundation in 3rd grade. Students are capable of understand myriads of things when given the opportunity to manipulate items. Are you giving your students that chance?

Here's a released STAAR question: 



Now, without this sample lesson I just shared, which answer do you think they would have chosen? I'm thinking A, due to spatial reasoning.
Students may be inclined (without the proper instruction and investigation) to assume that since the shaded portion in Figure M looks thicker than that in Figure N, that A is the answer.

But the true answer is C. With proper instruction (an investigative format coupled with a concrete standpoint), students can develop the cognitive reasoning that when both shapes have the same area and both have one-fourth selected (or separated) then the portion shaded in both figures represents an equal area. Third graders can "learn"; it is imperative that we, as teachers, remain lifelong learners so we can pull out the abilities of our students. Then and only then, will we witness the rewarding success of (not just our own practices, but) our students achieving what seems impossible!