Technology Integration in the Classroom

 The more we advance technologically, the more important it becomes to adapt our pedagogical approaches to instruction using technology. If we do not, then as students become members of the industrial world, they will be left behind and left at a disadvantage to those who have been exposed. This will produce a society of inequity and will serve to further divide those who are privileged and those who are not.

A Lack of Good Technological Teaching

There are many factors which lead to teachers not integrating technology in their approaches to education. One such factor comes from a lack of quality professional development. This is partly due to the speed of technological advancement. As people are learning a new set of technology, another has come to replace it. Ultimately, this leads to fatigue of teachers trying to constantly adapt to current trends.

One aspect of technology integration that math teachers struggle with is the use of calculators in the classroom. In some sense it is very liberating to not have calculate endlessly monotonous computations. However, in another sense it takes away from the rigor of adding fractions and dividing whole numbers. With the new TI-Nspires, students do not even need to solve equations anymore. So, teachers are struggling to find the right balance of allowing technology to aid students and students becoming overly dependent.

Another aspect of lack of quality professional development is its nature of being voluntary. One way the state of Texas addresses this is by requiring that every five teachers receive 150 hours of Continuing Professional Education. 

Tips For Having Emphasizing Technology in the Classroom

Like Texas, it is important to showcase the new technology through mandatory trainings. While it is impossible to keep up with all of the new trends, administration should sift through quality educational resources and those that are not fruitful. An issue that comes up in educational technology is implementing resources that hinder learning. The teacher is the one who is responsible for seeing what the students need and how to best facilitate the learning in the classroom.

Administrators can aid teachers by giving data driven metrics showing the benefit of utilizing the technology in the classroom. With this data and proper training, teachers may become inspired to utilize technology in a way that motivates students to learn and prepares them for the working world.

References:

Agency, T. E. (2020, September 16). Continuing Professional Education Information. Tea.texas.gov. https://tea.texas.gov/texas-educators/preparation-and-continuing-education/continuing-professional-education-cpe

‌Lawless, K. A., & Pellegrino, J. W. (2007). Professional Development in Integrating Technology Into Teaching and Learning: Knowns, Unknowns, and Ways to Pursue Better Questions and Answers. Review of Educational Research, 77(4), 575–614. https://doi.org/10.3102/0034654307309921

Author

John Snell is an M.S. in Mathematics with a concentration in the study of Arithmetic Functions. He has spent the last seven years teaching, educating students from 8th grade to Calculus. His passion is for student growth and an appreciation for mathematics as a whole.

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Wolfram MathWorld: The Web's Most Extensive Mathematics Resource

Online math teaching tools are becoming more and more important not only to educators but students alike. There are many tools that one can access to learn math such as YouTube videos or Kahn Academy. Also, there are outlets which aid in understanding such as GeoGebra or Desmos. However, today we will focus on a resource which claims to be "the most extensive mathematics resource;" Wolfram MathWorld.

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What is Wolfram MathWorld?

Wolfram MathWorld is an encyclopedic repository of all of mathematics, ranging from simple Algebraic equations to complex concepts of Analysis. Also, if one wants to learn about some biographical information of famous mathematicians, this is the resource that can aid approaching that topic. 

How Does Wolfram MathWorld Challenge Users?

Because of the nature of the resource, Wolfram MathWorld does not facilitate challenges but presents concepts in a terse, objective way. Once the user explores a topic, they are responsible for seeking more information themselves externally.

How Can the Teacher Use This Resource?

This resource is excellent for teachers to gain topics to engage students. However, it does require in depth knowledge to use effectively. A teacher may get lost using this resource because there are no user-friendly search engines.

How Does Wolfram MathWorld Engage Social Aspects of Learning?

Because this is an encyclopedia, there is no place for collaborative learning. There is no means of communication.

What is Great About Wolfram MathWorld?

This platform is an excellent stepping off point for getting research topics to inspire students. Because this platform is exhaustive, a teacher can have potentially infinite avenues of discovery. Yet, it does require a teacher with apt knowledge in the subject.

How Could Wolfram MathWorld Imporove?

Being called Wolfram Math"World" insinuates a connection with others. Adding a social aspect to this platform could bring others to math topics in a way that genuinely fosters learning. As of right now, the best social math experience is found in the math subreddit. Having a website complexly dedicated to math socialization can bring more mathematicians together.

Author

John Snell is an M.S. in Mathematics with a concentration in the study of Arithmetic Functions. He has spent the last seven years teaching, educating students from 8th grade to Calculus. His passion is for student growth and an appreciation for mathematics as a whole.

Learning Math in a Modern World: Analyzing the Secondary Sequence

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 Math has been a fixture of education ever since people could educate themselves. However, recently, many question how to make the mathematics we teach more relevant to the students of the upcoming generations. The math we once thought as important (maximizing area of farm beds, finding the best phone plan, etc...), no longer seem relevant to younger students. This in no fault of the teachers, it is just the exponential speed of technology has drastically changed how society functions on a day-to-day basis, as well as the expectation of how people function in the real world. Currently, we see an emphasis placed on data and data collection. Yet, most curriculum is not geared towards this burgeoning field of mathematics. We are still stuck, in a sense, in a pre 21st century mode of mathematics, and students are suffering for it.

Changing the Landscape

Consider the sequence of math at the secondary level. Students start with Algebra I, then in most cases take Geometry then Algebra II. After this, many students either end their mathematical journey or go into more computationally based courses like Pre-Calculus or Calculus. It is not to say that Algebra I, Geometry or Algebra II are bad classes, yet the material taught does not prepare them for the expectations seen in reality. In a data driven world, students should be exposed to courses that engage that sensibility of thinking. So, we should analyze these classes, specifically, and see how we can retool them to better address the needs of the next generation of students.

Algebra I

Algebra I is essentially a student's first introduction to functions. Yet, in most cases, students do not understand what functions are and how they apply to everyday life. Yes, a student can tell you that a relation is not a function because it fails the vertical line test but will not be able to construct a function based on relationship trends in Smart Phone sales as Smart Phone prices increase or decrease and then give a graphical model based on the data to interpret the trend. For many years, we have "been solving for x" but have never really asked "y." There has been a push in recent years to see regression analysis implemented in the curriculum but as long as it is not a real emphasis in state testing, it will be blip in the course that students will soon forget.

Geometry

Geometry has been a respected subject since the time of the philosophical Greeks, starting with Euclid's Elements. Many world leaders have cited the importance of learning geometry, specifically proofs, as a means of keeping one's intellect sharp. It has even been suggested that Abraham Lincoln would keep a copy of the Elements by his bed side so that he could keep his argumentative skills sharp. Now, with this being said, I do not feel Geometry is the best way to communicate the language of proofs to a modern audience. Since Abraham Lincoln, the language of mathematics has changed. Thanks to Cantor, we have set theory and with that a new way to do proofs using Algebra. While Geometry is important to learn, especially in Calculus, it is very jarring to introduce proofs in this course. Proofs are important, but it would make more sense to start introducing the idea in Algebra I or even Pre-Algebra. It may be good to reconsider where Geometry fits in a modern landscape, as there are many other math fields a student could be learning which will aid them in life more. 

A Different Sequence

Sometimes as educators we lose sight of what the goal of education is; to prepare the next generation for the world they will live in and work in. In reality, the math we teach is not very applicable to a contemporary audience. This all starts with Algebra I. I propose we re-work (not abolish) the current sequence to better meet the needs of a technological generation. We could still have Algebra I as a starter for higher math, however, we start introducing concepts of logic in this course. Then, with a firm understanding of functions we move to practical problems using real data sets. After Algebra I, instead of Geometry we should teach students Statistics. People are bombarded with endless polls and data charts with no understanding of how they are generated or what they mean. In a modern world, Statistics seems to be becoming more relevant to a functioning person every day. In addition to this, we also do not lose a whole year of what we just learned in Algebra I but are instead applying that knowledge to real world scenarios. As for Geometry, there are many students finding success in middle school with this subject.

Conclusion

While it may not be obvious what path we should take going forward, we cannot deny the fact that students, in general, do not feel motivated to do math. An aspect of this is likely due to math being outdated in a modern sense. The past is something not to look down on, but we cannot be afraid to move forward in a different direction.

Author

John Snell is an M.S. in Mathematics with a concentration in the study of Arithmetic Functions. He has spent the last seven years in teaching, educating students from 8th grade to Calculus. His passion is for student growth and an appreciation for mathematics as a whole.