The children born in the 1990’s and 2000’s are growing up during a very exciting time in the history of human kind. Technology is ubiquitous in developed countries and is expanding daily. With newer models of devices arriving on the market approximately every six months to a year it has become almost impossible to keep up with the pace of development. Due to the prevalence of technology in society and the rapid development, the children of this digital era are experiencing life in a way that is very different from any previous generation. This digital generation has never known life without the internet or cell phones, and is unable to fathom a life without the conveniences of credit and debit cards, online payments, instant communication and collaboration tools, or having to wait for a letter in the mail.

In addition to growing up in a vastly different world from their parents, and most definitely their grandparents, this generation is facing a world that will require a whole new set of survival and job skills. In the past, it was expected that in order to be a successful member of the workforce a person must have the knowledge of a specific skill such as carpentry, airplane mechanic, or farmer. Then, as a result of technological advances the skill set needed to be successful changed and it was no longer required for a person to have a specific skill. Recently, it has become more important for a potential employee to be computer literate and be able to work with a group or team members in the same company. We as a society are evolving and the skill set is changing once again; the digital native is perfectly equipped to handle this change. The newest set of skills being required is the knowledge to access, assess, and utilize tons of available information, create digital products, and collaborate with people from different organizations and cultures from all around the world.

The digital generation is facing one great obstacle in the course of their lives: attending a school system that is geared toward educating students who no longer exist. The education system is antiquated.

Reading, social studies, English, mathematics, and science are still very relevant to the lives of the digital native, but it is the manner in which these subjects are being presented that is killing the drive to learn and handicapping these students. This paper will discuss the reasons that change to education, specifically mathematics education is necessary, how a teacher can accomplish this, and also provide several resources and organizations that can make the evolution of the mathematics classroom efficient and effective.

Why is an evolution in mathematics education necessary?

The digital native is completely different from previous generations of students. This generation has adopted multitasking as part of its culture. For example, an average student can be expected to listen to music while doing a project for school and have a conversation via Facebook and text messaging all at the same time. This demonstrates that digital native is completely comfortable with parallel processing which is the ability to process more than one stream of information at a time. Another aspect that should be examined is the way that children today learn. Instead of reading the instruction manual for a new phone or computer that they have just powered up, the digital native will spend time “playing” with it to discover the abilities and limitations of this device. Digital learners are very comfortable with making mistakes and learning from them instead of being concerned with knowing how to do it correctly from the start. Children are constantly exposed to digital experience and their brains are wired differently than previous generations. Current brain research confirms this is true.

In the field of neuroscience there has been a traditional belief that people have “fixed-memory, fixed processing power, and fixed intelligences- and that the brain we developed by the age of three was essentially the same brain we would have at death” (Jukes, McCain, Crockett, pg. 20), but in recent years with some advances in technology we now know this is not true. These advances have shown that the brain is actually highly malleable and changes according to the stimuli that the brain experiences over a lifetime. It is now known that the brain “restructures neural pathways,…makes new cells, creates new connections, sets up new circuitry, and as a result, constantly creates new thinking patterns.” (Jukes, McCain, Crockett, pg. 21)

Because of research being done regarding brain development, we now know that the brain is similar to a plant. In the same way that the stems or branches of a plant die and fall off if they are no longer useful to the plant, the brain keeps only the neural pathways that are used frequently and thus quantified as “useful”. “Heavily used pathways become coated or insulated by myelin, a fatty insulating sheath that speeds signal transmission…the most useful connections develop into a neural network as a result of regular exposure, or if the connections are not useful, they’re pruned away.” (Jukes, McCain, Crockett, pg. 25) This leads to the question of what constant exposure to digital multimedia experiences causes, and what are the implications for the teachers of digital learners? The answer is that digital learners are able to process visual information quickly and efficiently, while unable to do the same with text and verbal information. This is where it becomes necessary for education to examine its current approaches to teaching. Since the digital generation is more capable of learning from visual sources it only makes sense for educators to move its approach in this direction, and since digital learners are less capable of processing text and verbal information it is of course imperative that teaching be steered away from this medium.

It is common knowledge in the field of education that one of the necessary components of teaching something new is to build upon previous knowledge. This previous knowledge is known as, “schema”. Because the children in this generation are very familiar with multimedia it is important to understand how this familiarity has affected the learning preferences and styles of the students. Educators must be familiar with and adjust instruction accordingly to allow digital learners to access information through pathways with which they are already familiar. The following is a graphic that displays some learning preferences of the digital learner versus the preferences and common types of learning/teaching styles currently used by many educators:

Despite the knowledge that educators have regarding the digital generation’s brain development and function, knowledge of this generation’s learning preferences, and knowledge of how differently these children have grown up from previous generations, educators have yet to acknowledge the need to connect with digital learners through existing schema.

What does this mean for math educators?

Since digital learners are different from other generations it is necessary for mathematics educators to examine current practices to determine if they are relevant to the learning style and needs of the group of students they are currently working with. A quick examination reveals that math teachers are still using the “tried and true’ text book, worksheets, and “sage on the stage” methods to educate children in math. These methods, once so effective, are no longer effective or relevant to the students sitting in the classroom today, and as a result current educators must change the way they are teaching or lose an entire generation of students in the “digital gap” that exists between student and teacher.

The first and possibly the most influential change mathematics teachers must make is abandoning the “sage on the stage” teaching method. This method involves students sitting quietly, listening and taking notes while the teacher, “sage”, speaks about the concept and explains the algorithms that the students will be expected to perform. This method has never been very engaging, and now more than ever, it is completely out of touch with the way that digital learners have adapted to absorbing and retaining information. The digital learner preference for receiving information involves rapid access and receiving the information from multiple multimedia sources. This is nearly polar-opposite to the “sage on the stage” method, and it is therefore necessary for teachers to understand that this method is detrimental to the goal they are trying to achieve. To further explain this concept, a visual of “Dale’s cone of learning” has been included:

Dale’s Cone of learning has been verified countless times since the 1960’s when it was first created. The point being made is that passive learning, (reading, hearing and seeing) is the least effective way to teach. Students simply do not internalize much of the information and is therefore a waste of time. This was true for students in the 1960’s, and is especially relevant for the students of the 21st century. As the above graphic further illustrates, if a teacher wishes for the students to retain the information then ‘active learning’ must be utilized. This requires that students be given the opportunity to receive the information in a rapid fire way and then work with or perform the activities laid out in the bottom half of the cone.

In addition to stepping off of the stage, math educators must allow students to access information in a way that they are familiar with. This provides a platform from which the students’ schema may be accessed and make the learning more intuitive for students. Digital learners prefer to receive their information via pictures, sounds, videos and digital interactions before any text is presented to them. This means that students require access to the internet either by computers or other digital devices. By providing guidance and online resources for students to explore the content being taught, the digital learner will more readily process and retain the information. Closely related to accessing information digitally is the need for students to collaborate. This digital collaboration is not only part of engaging the digital learner, it is also a skill that is needed in the workforce that these students will enter. Math teachers can provide opportunities for students to collaborate simply by setting up discussion boards on class websites, or creating projects that require a group of students to work together to produce a digital product.

The third component of teaching the digital generation addresses two of the learning preferences of this generation: instant feedback, and relevance and fun of learning. Through the use of online games and interactives an educator has the ability to alter teaching methods to allow students to indulge in instant feedback and include fun, relevant use of information. Such interactive activities and games will be examined in more detail in the “Analysis” section of this paper. The changes that educators must make will challenge the traditional methods that have been used in mathematics education for hundreds, perhaps thousands, of years. These changes will be met with adversity, particularly from seasoned educators and administrators that may not be comfortable with digital life or accept that a new set of skills should be addressed by schools. It is however imperative that current and new educators alike be willing to learn to incorporate use of technology and step away from the traditional methods that are being used in order to reach this new type of learner. This leads to the overriding question of this paper: What type of technology currently exists that mathematics educators can use right now to start transitioning their teaching methods?

Literary Review

EdTech Magazine is an online magazine dedicated specifically to integrating technology into the 21st century classroom. Though it is not mathematics education specific, the articles that I found here are completely relevant to the topic. One of the articles that I found is titled, “Flipped Learning Interest on the Rise: New Speak Up data reveals enthusiasm for leveraging digital tools and upending traditional instructional methods.” From this article it has become clear that more educators are becoming interested in using technology to update education practices. This article is one of many that cover the “flipped” model of instruction. This model utilizes video and online resources outside of the classroom, so that in class time may be used for discussion and hands-on use of the materials learned through the digital sources. A couple of interesting statistics presented in this article are that “One out of six math and science teachers are implementing a flipped learning model using videos that they have created or sourced online“ , “41 percent of administrators say pre-service teachers should learn how to set up a flipped learning class model before getting a teaching credential”, “66 percent of principals say pre-service teachers should learn how to create and use videos and other digital media within their teacher preparation programs” and finally “75 percent of middle and high school students agree that flipped learning would be a good way for them to learn; 32 percent of them “strongly agree” with that idea”. These statistics show an interest in the use of technology to bridge the digital gap from students and administrators alike. Additionally, it brings to my attention that university teacher preparation programs are sorely lacking a digital technology component, and are therefore creating a new generation of teachers that are not prepared to educate the students they will encounter in the classroom.

The National Council of Teachers of Mathematics, NCTM, produces a magazine for secondary mathematics teachers called, “Mathematics Teacher”. In the February 2014 ‘technology’ section of this magazine the authors recount their experiences with two different models of a flipped classroom. The two authors utilize similar methods in that they both assign digital media for their students to view and interact with outside of class. This left time for both sets of students to use class for discussion and actual use of the information instead of the traditional format of warm-up, homework problems, definitions and then examples. Most of the students enjoyed the flipped model and homework completion rates rose in all classes. One student in particular did not like the flipped model and is quoted as saying, “it makes me think harder”. This is a wonderful complaint to hear from a student because it reassures the teacher that this model does foster higher order thinking. From reading this article it is apparent that there is real merit in using a flipped model classroom in order to integrate technology in the curriculum and to maximize class time for actual synthesis and application of the learned materials.

This research conducted by SEG Research with the financial support of BrainPop, “Understanding Multimedia Learning: Integrating multimedia in the K-12 classroom” is a project that includes brain research as it pertains to educating students, and finds the key components that are necessary for successfully integrating technology into the classroom. From this article it is glaringly clear that the use of multimedia instruction is the most effective way to reach a wide variety of learning styles and maximize instruction time in the classroom. The following is a graphic that summarizes the findings of the most effective use of multimedia as a teaching tool.

From these articles it can be concluded that there is acknowledgement by the education community that multimedia tools are useful for reaching students of the digital generation, and there is a great deal of interest from new and seasoned educators in the integration technology in today’s classrooms. Learning about this acknowledgement and interest is encouraging because it indicates a willingness of the education community to make the effort to bridge the digital divide, and help the digital generation to be successful in their academic endeavors.

Methodology

The purpose of this paper is to locate online resources that will be convenient for mathematics educators to use and integrate into the current curriculum. The question that will be focused upon is: “What type of technology currently exists that mathematics educators can use right now to start transitioning their teaching methods?”

The research that has been done here focuses upon finding digital tools that align with the “digital learner preferences”, the Texas Essential Knowledge and Skills, TEKS, standards set by the state of Texas and the principle of effective use of multimedia tools outlined in the research paper written by SEG research. Though it is not possible, due to the medium in which they are to be presented, to include the actual interactive abilities of these websites, an attempt will be made to provide an accurate and concise description of the tools that are available. Each description and graphic has been included in the next section because it aligns with the standards and preference outlined earlier in this paper.

Analysis: What Technology is Currently Available for use in Secondary Mathematics Classrooms?

I have included several of the websites that I found during my research. The majority of these websites offer free interactives that students can use to explore mathematics, and though I have reviewed these websites with grades nine through twelve in mind, it must be noted that most of the websites offer content that is appropriate for the elementary, middle, and post-secondary level. Therefore, it is necessary for any educator that is interested in using these tools to delve into the sites and discover what each has to offer. This list is not exhaustive, and I have included a list of resources that can be used to further explore the topic of integrating technology in the secondary mathematics classroom.

www.Mathplayground.com

Description: This website offers a huge collection of games to give students an opportunity to learn and practice math through play and interactive activities.

TEKS:

§111.34 Geometry

(4) Geometric Structure. The students use a variety of representations to describe geometric relationships and solve problems. The student is expected to select and appropriate representation (concrete, pictorial, graphical, verbal, or symbolic) in order to solve problems.

(5) Geometric Patterns. The student uses a variety of representations to describe geometric relationships and solve problems. The student is expected to:

(c) Use properties of transformations and their compositions to make connections between mathematics and the real world, such as tessellations;

Review: Mathplayground.com is a free website that provides a large selection of games and manipulatives to offer students a chance to be involved with and enjoy their interaction and practice with math. With puzzles, games, and interactive manipulatives this website has something for the math classroom from elementary to tenth grade. The manipulative that I found especially useful for a geometry classroom was the “transformation workshop”. This tool allows a student to select and change a shape in the Cartesian plane and then apply between one and four transformations to it. Once all of the transformations have been selected, the student starts the animation and watches each transformation being performed individually. This tool allows the student to control and investigate transformation in the two dimensional plane at their own pace.

The Geometer’s Sketchpad

Description: The geometer’s sketchpad is a software package that is available for purchase online. It touts the ability to be used by grades 3 through college.

TEKS:

§111.34 Geometry

(2) Geometric structure. The student analyzes geometric relationships in order to make and verify conjectures. The student is expected to:

(A) use constructions to explore attributes of geometric figures and to make conjectures about geometric relationships

Review: This software package can be used to allow students from third grade up to the college level to experience math in an interactive setting. The program allows students to draw, animate and manipulate figures such as polygons, lines, and graphs of trigonometric and polar graphs. The software is reasonably priced and offers yearly subscriptions and updates to those who purchase it. This is an invaluable tool in mathematics classroom regardless of grade level.

www.Desmos.com

Description: Desmos.com is a free website that offers this and many other graphing tools. The Desmos app is also available for Ipad.

TEKS:

§111.35 Precalculus

(5) The student uses conic sections, their properties, and parametric representations, as well as tools and technology, to model physical situations. The student is expected to:

(d) use parametric functions to simulate problems involving motion.

Review: This website/app is a fantastic tool that can be used in the mathematics classrooms ranging from grade 7- college. This app contains a graphing tool that allows the operator to explore properties of function such as domain and range of a function, how changing the equation changes the graph (and vice versa), and offers tools in statistics. It can be used for a variety of purposes that are only limited to the teacher’s imagination.

Graphic: Online Resources to Supplement the Secondary Mathematics Classroom

As previously stated, this is a sample of relevant low-cost and free websites that are currently available to the mathematics educator. This is not an exhaustive list, but it does outline several of the online resources that were located during my research.

Conclusion

The digital generation is a group of people that are growing up and learning in a very exciting time period. This generation has never known life “unplugged”, and will be entering a workforce that requires a set of skills that have never before been encountered or taught.

Brain research has shown just how unique this generation really is from previous generations, and it is our job as educators to evolve from the traditional methods of teaching that have been used for hundreds of years. To bridge the digital gap that is present between educators and students, the educators must be prepared to live digitally and integrate technology into their classrooms. While this change may be uncomfortable for many, it is necessary for education to succeed in assisting this generation with the goal of achieving academic success. Embracing technology is labor intensive the first year, but with practice and networking with like-minded colleagues it will become easier and the process will produce huge rewards. The result will be a generation of children that is well educated and possesses the skills needed to survive and thrive in this new and constantly changing digital era.

Additional Teacher Technology References:

NCTM.org
Flippedmath.com
Edtech Magazine
Freetech4teachers.com
Teach.com
Edudemic.com
Edutopia.org
4teachers.org
Google.com- any search for mathematics technology tools will yield a plethora of information, tools, and collaboration opportunities for teachers and students alike. (Get in there and live like a digital native!)

Works Cited

Clark, Marla. "CoSN 2014: Flipped Learning Interest on the Rise." EdTech Magazine. N.p., 24 Mar. 2014. Web. 7 Apr. 2014. <http://www.edtechmagazine.com/k12/article/2014/03/cosn-2014-flipped-learning-interest-rise>.

Jukes, Ian, Ted D. E. McCain, and Lee Crockett. Understanding the digital generation: teaching and learning in the new digital landscape. Kelowna, C.-B.: 21st Century Fluency Project ;, 2010. Print.

Moore, Amanda, Matthew Gillett, and Michael Steele. "Fostering Student Engagement with the Flip." Mathematics Teacher 1 Feb. 2014: 420-425. Print.

SEG Research. (2008, September 1). Understanding Multimedia Learning: Integrating multimedia in the K-12 classroom.. www.brainpop.com. Retrieved April 7, 2014, from http://www.brainpop.com/new_common_images/files/76/76426_BrainPOP_White_Paper-20090426.pdf

Wong, Wylie. "How Technology Enables Blended Learning." EdTech Magazine. N.p., 1 Apr. 2014. Web. 7 Apr. 2014. <http://www.edtechmagazine.com/k12/article/2014/04/how-technology-enables-blended-learning>.`

Samantha Henegar

Texas Educator

Technology in The Secondary Mathematics Classroom

Introduction

Why is an evolution in mathematics education necessary?

What does this mean for math educators?

Literary Review

Methodology

Analysis: What Technology is Currently Available for use in Secondary Mathematics Classrooms?

Graphic: Online Resources to Supplement the Secondary Mathematics Classroom

Conclusion

Additional Teacher Technology References:

Works Cited

Recent Posts

Comments