Engaged Learning: Thinking Outside the App

By Dawn Woods, RME Elementary Mathematics Coordinator

Technology, an essential tool for learning mathematics in the 21st century, not only stimulates students’ interests, but also maximizes understanding and proficiency in mathematics. As touch devises, iPads, iPods, iPhones, Kindles and other tablets, become a standard tool in the classroom, it is noteworthy to realize that these tools can be more than a way to access apps that support curriculum content or as an e-reader. These devices can be creative tools that enable teachers and students to learn beyond the walls of the school.

As a classroom teacher, armed with a single iPad and a few iPods, I found that myself, as well as my students loved the ease of operating these tools because of their intuitiveness! We found that we needed very little instruction on how to operate the tools; all we needed was a willingness to play and explore. Since my classroom “touch device” supply was limited, I began to think of innovative ways to use the iPad and iPods. I discovered that these tools easily incorporate into a learning center, as a productivity tool where partners and trios create a multi-media product, and as a presentation tool for students and myself. Eventually, I adapted a BYOD (Bring Your Own Device) policy, which permitted students to bring in their own personal devices to use and manage.

Through my own iPod and iPad explorations, I have discovered that these tools not only deliver content in an interactive and differentiated way but also allow my kinesthetic and visual learners to manipulate the content, providing individualized and engaging instruction. The iPad also lends itself to inquiry or problem-based learning where students are engaged in authentic learning activities based on interest.

Since there are more that 100,000 iPad Apps, and countless other apps that work on a variety of platforms, deciding on where to get started is very overwhelming. A rule that I keep in mind as I evaluate apps is to “think outside the app” or how can the app help students as they consume essential knowledge, collaborate with others, and/or create a product? For example, if I wanted apps to support my instructional goals, I would look for ones that students could use on their own during center or independent activities. Some of my favorite instructional apps are Khan Academy (videos and challenges aligned with instructional goals), Algebra Touch (algebraic lessons and skill practice), Pearl Diver (conceptual number line activity), Pick A Path (activity that tests skills with powers of ten, negative numbers, fractions, and decimals), and Equivalent Fractions by NCTM (activity that builds conceptual understanding of equivalent fractions).

From Discovery Education

There are many great apps like Skype and Twitter that enable students share work. These are both free and easy ways for your classroom to meet people, talk to experts, collaborate and share ideas with peers, and create experiences with others. Another example is Dropbox. This is a free service that allows photo, document, and video sharing. You can save a document to a Dropbox folder and it is accessible on any computer or mobile device. You can also share the folder with others so that they can access documents for collaboration. Pair this app with CloudOn and you can edit documents, anywhere at anytime.

Apps can create multi-media products. ShowMe Interactive Whiteboard allows users to record voice-over whiteboard tutorials and share them online. Here, students could be the teacher, sharing how to solve a problem, then post it to the classroom website. Diptic enables users to combine photos to make new images, while VoiceThread enables the user to create and share conversations around documents, videos, and diagrams.

Summing it All Up
Touch devices such as iPads and iPods are awesome tools for the 21st century classroom. With 100,000 plus apps to choose from, users are challenged to find the best way to consume knowledge, collaborate with others, and create products that fit their individual needs. Using these tools in the classroom maximizes the potential of technology, enabling teachers to develop students’ understanding and proficiency in mathematics.

So, how are you going to “think outside the app” in your classroom?

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Key Priorities for Implementing Change

By Sharri Zachary, RME Mathematics Research Coordinator
 
From a classroom perspective, implementing change for the improvement of math requires that we, as teachers,
1.    Remain Flexible
2.    Reflect on Current Practices
3.    Build Relationships

One thing about TEACHING…Every school year is different!

As we work toward improving the outcomes in our math classrooms, one of our key priorities has to be that we plan to incorporate any changes or additions that are made at the State level into our curriculum and that curriculum should then drive our instruction. The State standards are our “non-negotiables.”  They tell us what students should be able to do upon completion of a grade level.

The flexibility comes in being able to adjust your lesson plans and calendar which is not always easy to do when you have assemblies, pep rallies, and other “special” bell schedules that (while important) take away from your instructional time.  This is why it is important to remain flexible and have a backup plan.  Even with all of these special events going on, we still are required to make sure students know the material.

Second, when trying to implement change for the improvement of math, the greatest thing you can do as a teacher is be a reflective practitioner.  When I worked with teachers, I often gave the suggestion to include a reflection piece on their lesson plans and at the end of each day or at the end of the week, jot a few notes describing how the week went.  Was the activity a complete disaster? Did I spend too much time lecturing?  Did I provide enough opportunities for students to work cooperatively?  How can I tweak this activity so that students are more engaged?  And so on and so on.

It is not uncommon to refer to what was done in previous years to plan out the current school year.  What is useful is to see what went well, what didn’t go so well, and what could be done better.  By making it a priority to reflect, you will begin to make those adjustments to your lessons that will improve the quality of your math instruction.

Lastly, a key priority for me is to always build a relationship with my students.  When I served as a math instructional coach to middle and high school math teachers, I reminded them every year of the importance of building a relationship with their students.  Your students need to know that you care about them and that they can trust you.  When we relate to our students and they begin to genuinely care about us beyond simply having respect for us, they want to make us look good.

So if that means, putting forth a little more effort in class, being just a little more attentive when you are speaking, trying a little harder on that test, they will do it.  When they reach that point of caring, they will understand that what you do is reflected through how they academically perform and when they measure up, you shine.

Summing it All Up
In identifying some key priorities for implementing change to improve math outcomes, I suggest being more flexible, practice being a reflective practitioner, and strive for better relationships.

What are some other key priorities you see are necessary for improving math outcomes?

Converting Fractions to Percentages

By Beth Richardson, RME High School Mathematics Coordinator

As a high school math teacher, I taught a wide range of students from ESL Algebra 1 and regular Geometry to Pre-AP Algebra 2. The resounding similarity I saw between all of my students was that, for some reason, students cringe when they see rational numbers. They feel like rational numbers automatically make the problem “hard”. I was amazed that by high school, students were still struggling with something as simple as converting from a fraction to a percent. Perhaps this is because, as teachers, we sometimes teach our students shortcuts that leave out the logic behind the scenes of the procedures they learn.

The IES Practice Guide, which is supported by research evidence, recommends that teachers “'help students understand why procedures for computations with fractions make sense’ and ‘develop students’ conceptual understanding of strategies for solving ratio, rate, and proportion problems before exposing them to cross-multiplication…’ (Siegler et al., 2010).”

Some common shortcuts teachers use are changing the fraction to a decimal then multiplying by 100 or changing the fraction to a decimal then moving the decimal to the right twice.

Examples:

Neither method above leads students to a percentage as the final answer, unless the student “remembers” to tag it on at the end. Units are crucial when converting in any context. In order for students to understand why they must multiply by 100% rather than 100 when converting from fraction to percent, units must be used properly.

Instead, students should be taught to set up proportional relationships, including units, between the fraction and unknown out of 100%. It is important that students understand that when the units of the numerator and denominator are the same, they cancel and the fraction is unit-less.

Example:
25 students went on a field trip and 5 wore a hat. What percentage of the students wore a hat?

20% of the students wore a hat on the field trip.

Through the process above, students see why they are multiplying by 100% and why the units in their answer must be a percentage. Also, students can use number sense to reason that x must be a percentage between 5 and 100.

Summing It All Up
Fellow teachers: it’s not safe to assume that our students understand why they are doing a particular procedure, even if it is one they “should” have mastered several grade levels ago. If we take a little more time to illustrate examples with labeled units and explanation, we will hopefully catch any previous misconceptions our students have and steer them on the right path towards math success.

Now it’s your turn. Share with us common misconceptions, similar to what we described above, that you’ve found in your classroom!

Resources:
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.

Siegler, R., Carpenter, T., Fennel, F., Geary, D., Lewis, J., Okamoto, Y., Thompson, L., & Wray, J. (2010) Developing effective fractions instruction for kindergarten through 8th grade: A practice guide. Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education. Retrieved from http://ies.ed.gov/ncee/wwc/publications/practiceguides/