Oh, the Places You’ll Go

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In today’s society, the presence of technology is a fact of life. Like it or not, the 21st century ushered in a computer age and digital empire that is expanding daily. For teachers and students alike, this carries huge significance while presenting inherent challenges. Longstanding teachers experience the difficulty of adjusting their traditional teaching methods while familiarizing themselves with technology that initially seems foreign. New and prospective teachers, though acclimated to the integration of technology in their daily lives, struggle to pioneer methods of teaching that incorporate technology in the classroom because they themselves were taught with traditional methods. But as with anything, difficulty need not lead to deterrence.

When used effectively, technology in the classroom broadens the scope of questions that teachers can investigate with their students by enabling constructions, representations, and calculations that were before impossible. Teachers who remain leery about the presence of technology in the classroom have often not seen it used effectively first-hand. It is true that if students only use their TI-84 calculator to mindlessly punch numbers then the calculator use is not serving to push student thinking forward. However, if that same calculator is used to analyze graphs in Calculus or generate data plots in Statistics, then it affords students the chance to make connections regarding these concepts.

Furthermore, introducing technology in the classroom is not all or nothing- teachers may choose to slowly integrate technology depending on availability of resources and student ability. Simply having a document camera and a projector facilitates discussion by making it easier for students to share their work, and having access to a computer lab opens the door for using innumerable free web-based applications through which students can investigate an array of concepts. While trying to find technology and lesson plans to use in the classroom seems overwhelming to many teachers, there exists an ever-growing community of free online professional development and support groups designed to help teachers move towards the future of learning.

With the advent of classroom technology and digital resources, this is arguably one of the most exciting times to be a teacher. Yes, the transition from traditional methods to new learning styles is difficult, but seeing how far we have come in a few short years should excite educators. As long as teachers are willing to step out and try technology as it comes, there is no limit to where we might take our students, or, having prepared them for the future, where our students might take us.

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Something to Tweet About

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The Mathtwitterblogoshere is more than just a mouthful. MTBoS for short, the Mathtwitterblogosphere identifies the online community of math teachers who connect and share ideas via the Internet, namely through Twitter chats and teacher blogs. Essentially, MTBoS functions as a platform for free, continual professional development in which teachers can both participate and contribute, regardless of the degree of their experience teaching.  Their website serves to introduce teachers to MTBoS and acts as a launchpad for teachers seeking to get involved in the realm of MTBoS.

The MTBoS scavenger hunt is a great way to see what this virtual community of educators is all about. The scavenger hunt helps teachers find a particularly helpful resource on the MTBoS website entitled “Cool Things We’ve Done Together.” This page consolidates into one location all of the beneficial resources that have been produced through collaboration on MTBoS. One such resource is the Virtual Filing Cabinet created by teacher Sam Shah, which categorizes lesson plans and ideas by grade level and subject. Another important resource is the free E-book Nix the Tricks, which uncovers and explains why many of the common “tricks” taught by teachers actually hinder student learning, and it offers methods for replacing those tricks. Nix the Tricks offers invaluable insight into how math “tricks” promote what Skemp (1978) deems instrumental understanding, while the suggested replacement methods help students gain relational understanding (knowing the why behind the how). Teachers can utilize resources like these in lesson planning, whether they start with ideas found in the Virtual Filing Cabinet or improve lessons by eliminating any “tricks” that may have been hiding.

MTBoS also aids teachers in finding avenues by which to incorporate real world problems into the classroom through resources such as the Would You Rather and Estimation 180 links. The Would You Rather page contains numerous questions (complete with photos) that ask students to choose between two options, requiring them to engage in mathematical thinking in order to justify their choices. The Estimation 180 page houses over 200 days worth of pictures and videos designed to help students build number sense over time. The activities found in these pages do not require large quantities of time, which make them well suited for warm up problems.

The MTBoS Google search engine does that which not-so-tech-savvy teachers never thought possible by limiting the scope of Google searches to blogs and pages directly connected to MTBoS. Since most of the material affiliated with MTBoS is tried and true, the MTBoS search engine saves teachers from hours spent sifting through pages of irrelevant and ineffective material that pops up as the result of a general Google search. Not only useful for tailored searches related to a given topic (like “factoring” for example), the MTBoS search engine also helps teachers quickly find blogs by other teachers who have shared experiences. For example, typing “frustrated” into the MTBoS search engine results in ten pages of blog references in which a teacher has mentioned having a frustrated student or being frustrated themselves. It is no secret that teaching is hard work, but having a support system (even if it is online) helps.

The resources mentioned above represent only the tip of the MTBoS iceberg. While a Twitter account is necessary to engage in every dimension of MTBoS, it is by no means needed to gain huge benefits from this progressive resource. Even if you do not consider yourself a technologically inclined individual, chances are that you want to live up to your teaching potential, and the Mathtwitterblogosphere will not disappoint.

References

Skemp, R. (1978). Relational understanding and instrumental understanding.

Arithmetic Teacher, 152-161.

 

Balancing Acts- Not Just for the Ringling Brothers

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For decades, the Ringling Bros. Circus has amazed crowds with its balancing acts, but these performers are not the only ones who have mastered the art of high-pressure balancing. Math teachers, too, are among those who must learn how to balance, albeit in a different form. Instead of mastering the high wire, math teachers must balance the many ways in which to present information to students, including time for group work, individual investigation, and interactive lessons that lead students to personal discovery. Among the variations in teaching methods, teachers must find how to incorporate technology into the mix. With the advent of technology, many teachers view technology use in the classroom in black and white terms: either a class uses technology or it does not. However, this view is equivalent to keeping Dorothy in Kansas while the Technicolor world of Oz is at her fingertips. That is, teachers can utilize technology in the classroom without making every activity digital or every homework assignment online.

To master the art of balancing in a math classroom, teachers must recognize the potential and limits of technology. The greatest advantage of studying math does not lie in procedural fluency or even mastery  of a given concept. Rather, the greatest benefit of studying math is learning how to reason and problem solve. Technology can be an incredible tool to promote this end. Even presenting students with a problem that requires technology but having them determine which technology would be most effective works to build reasoning skills. However, when technology is not carefully implemented in math lessons, it can serve as a crutch that hinders students from developing solutions with their mind. In today’s culture, students are inundated with technology almost 24/7. But whether they are playing games, posting an Insta, or sending a Snapchat, students almost exclusively interact with technology in a mindless manner. It follows that when students are first introduced to technology in the math classroom, they view it as a shortcut to problem solving. “As long as I can use this app, I won’t have to think as hard.” In this way, teachers must learn to involve technology in the classroom in such a way as to change students’ mindsets about the technological tools at their fingertips. When a student gets a job at an engineering firm, all of the technology in the world will be of no use if she has not developed a mind that can reason how, when, and why, it should be used.

Whether you are a veteran teacher, new teacher, or future teacher, the prospect of finding the balance of technology in the classroom can be intimidating. But remember, even even high-wire performers have taken falls when learning to balance, and past failure does not negate the potential for future success. Though it takes effort, teachers who learn to balance technology use in the math classroom will service their students by teaching them to think with the technology in their world.

 

 

You’re the Grand Prize Winner! What Are You Going to Do Next?

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For those of you who just answered, “I’m going to Disney World,” let’s add a little more information to the story. Imagine that you are a teacher currently using a classroom with the bare essentials: desks and chairs. However, through a rigorous application process, you have been awarded the grand prize for a technology grant. You have a budget of $10,000 to purchase all of the technology you could want for your classroom. The only question is, which technology will you choose? In other words, which technology will most benefit students while remaining cost effective?

Below you will find a proposed budget for the prize money. Each item includes a short note describing why it merits a place in the classroom. If you’re suspicious that a given price point is unrealistic, check out the hyperlink for each item to verify the price and source (tax does not apply, because these are education purchases).

  •  Interactive SMART Board, short throw projector, and wall mount ($2,098)
    • Enables teachers to display screen annotations, use calculator emulators and other math apps, maximize the potential of document camera use
  • IPEVO Ziggi HDPlus Document Camera ($99)
    • Facilitates discussion as an easy way to share student and teacher work
  • Classroom set of Refurbished TI-84 Calculators (three 10-packs, $799 each)
    • Provides all students access to a graphing calculator, widening the range of investigative activities available to teachers
  • 16 ct. Samsung Galaxy Tab A Tablets ($299 each)
    • Allows students to work in pairs on web-based or app-driven activities, such as graphing with Desmos or constructing figures with GeoGebra
  • Acer Chromebook 14 ($300)
    • Serves as a teacher computer that can connect to the active board and run emulator software
  • TI-84 SmartView CE Emulator Software ($135)
    • Offers visual scaffolding of graphing calculator use
  • 40 ct. Plickers , Matte-Laminated ($20)
    • Offers a different form of assessment technology, can be used to facilitate classroom discussion
  • 36 ct. dry erase boards with markers and erasers (three 12-packs, $32.39 each)
    • Provides reusable space for students to perform scratch work, hold up answers, etc.

This brings our grand total to $9930.17, leaving approximately $70 to purchase any other desired apps, software, or other classroom essentials (even a technology-rich classroom can use paper and pencils). Below you can find images of all of the technology purchased with the prize money.

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Does it all sound too good to be true? Well, maybe it is. So instead, let’s say you have “only” been awarded the second place prize of $5,000. That’s still a lot of money! However, you obviously won’t be able to purchase all of the technology you could with the grand prize.  Now, it’s time to make some cuts. Below you will find a revised budget proposal, followed by a brief explanation of why certain items made the cut while others did not.

This brings our total to $4,973, leaving $27 available for discretionary use (apps, supplies, etc.). The Acer Convertible Laptop PC serves to replace the more expensive Chromebook purchased with the first grant. The classroom set of dry erase boards did not make the cut, because while they offer an engaging way for students to work and share problems, they do not add unique learning value to the classroom. Although the tablets do provide new ways in which students can engage in learning mathematics through internet and downloadable apps, they are not the practical technology choice for a significant portion of lessons. Thus, the high cost of tablets is less justified than the other budgeted technology because the other technology can aid student learning every day.

Even with $5,000, we were able to keep most of the technology we initially bought with the grand prize. Does it still seem too good to be true? Then let’s consider another (perhaps more realistic) example. Let’s say that you have been awarded a $2,500 grant (still exciting!). Paring down our budget even more, consider the following proposal:

This brings our total to $2,497, almost exactly what we have available. From our $5,000 budget, the teacher’s personal computer can be forgone, since a teacher would be able to use his or her own computer to serve the same purpose. Plickers, while fun for students to use, do not add intrinsic learning value to the classroom, and the TI-84 Emulator software, while convenient, is not necessary for students to benefit from using graphing calculators. Purchasing three graphing calculators would give teachers a few extra in case some of their students could not afford one, and this handful of calculators could be incorporated into rotating group activities.

In each tier of the budget proposal, two items made the cut: the interactive whiteboard and document camera. At every level, these two items are worth their expense because they have the capacity to be utilized every day in the classroom. Document cameras offer an invaluable way for students to share and discuss their work with the class. Interactive whiteboards epitomize the ideal conveyance technology by allowing teachers to efficiently make and save annotations on everything from student work to graphics and photographs. Beyond their conveyance capabilities, interactive whiteboards can further serve as an interface for math action technologies, such as the dynamic geometry software GeoGebra or the graphing application Desmos. Check out the following links for more math-driven interactive whiteboard resources:

TeacherLED

SMART Exchange

Eduscapes

Although these budgets were proposed in light of hypothetical grants, technology grants are out there for the winning! Let real possibilities like the examples above excite and inspire you to find and apply for such grants. Who knows? Maybe you will be the next grand prize winner!

Could Your Regular Whiteboard Do That?

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Anyone old enough to remember the transition from chalkboards to whiteboards in their classroom would likely rank this upgrade closely in importance with the widespread move from overhead projectors (and all those transparencies) to sophisticated document cameras. Between these two additions to the classroom, conveying information to students never seemed easier. And then came the interactive whiteboard. A new technology that perfectly married whiteboard functionality with computer and document camera use. While some teachers leapt at the potential of interactive whiteboards, others viewed them more skeptically. After all, are they more than just glorified chalkboards?

Bill Ferriter is one such teacher unconvinced that interactive whiteboards are worth the thousands of dollars spent installing them in classrooms. In his article, Ferriter offers a diatribe against interactive whiteboards, arguing that they do little to promote student discovery and collaborative work, which essentially renders them an expensive way to teach the way teachers have always taught. However, Ferriter’s argument rests on an assumption that the teacher using a given whiteboard has no knowledge of how to use it and no desire to spend the time or energy finding ways to make interactive whiteboards a meaningful addition to the classroom. Granted, Mr. Ferriter wrote this article in 2010, and perhaps he has come to recognize the value of this technology since then. Either way, let’s take a look at all of the benefits afforded teachers by interactive whiteboards.

For math teachers specifically, interactive whiteboards, in conjunction with document cameras, broaden the scope of questions that can be addressed. Because interactive whiteboards enable teachers and students to write “on top of” whatever image is on the screen, teachers can take pictures to create their own problems. For example, a teacher might take a picture of a house, then using his interactive board overlay the picture with gridlines so students can find the slope of the roof. Alternatively, teachers might use their document camera to enable students to share their work with the class. Interactive boards are advantageous here because they allow teachers to annotate on student’s work on the board without actually writing on the student’s paper. Interactive boards also enable teachers to meaningfully incorporate tasks that involve graphing calculators with software programs that emulate interactive graphing calculators on the screen.

These examples only eclipse the many ways in which interactive boards can engage students in learning. Dick and Hollebrands (2011) maintain that the value of technology lies in the new questions it affords teachers. By this criteria, interactive whiteboards have earned their place in the classroom because they enable teachers to ask innovative questions that promote student discovery and collaboration.

Reference

Dick, T. P., & Hollebrands, K. F. (2011). Focus in high school mathematics: Technology to

support reasoning and sense making. Reston, VA: National Council of Teachers of

Mathematics.

Worth the Effort: Overcoming Technological Obstacles in Teaching

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As with any aspect of teaching, involving technology in the classroom comes with inherent obstacles. Limited resource availability and inadequate teacher training are two of the most obvious difficulties surrounding technology-based learning, but even teaching environments in which these concerns are addressed may still lead to ineffective learning if teachers have unproductive views about classroom technology use. As outlined by the National Council of Teachers of Mathematics (NCTM) (2014), such unproductive beliefs include the beliefs that technological tools are a frill or distraction, the learning of mathematics is static and threatened by the presence of technology, and using technology is as simple as launching an app and letting the students work on their own. Each of these beliefs are harmful to student learning because they either fail to recognize the potential of technology to increase student understanding or rely on technology as an easy fall-back method.

Replacing unproductive beliefs about technology with beneficial ones is the first step for teachers learning to use technology effectively. Long-standing teachers may be quick to argue that conventional teaching methods of class note-taking and homework assignments are tried and true, but this fails to recognize that “[t]echnology is an inescapable fact of life in the world in which we live and should be embraced as a powerful tool for doing mathematics” (NCTM, 2014, p. 82). Observing teachers who embrace this view of technology helps to prove just how beneficial technology can be. For example, a geometry teacher utilizing Geometer’s Sketch Pad to help his students discover theorems regarding circles is a meaningful alternative to having his students copy the theorems in the conventional manner before completing a worksheet. Through technology-aided discovery, the students in this example gain relational understanding of these theorems, that is, they see why the theorems are true. The latter, more conventional, alternative comparatively illustrates instrumental understanding, which Skemp (1978) explains as “rules without reasons.” Thus, teachers who re-imagine technology use in the classroom with investigative activities prepare their students as relational learners able to embrace technology in the 21st century.

Realizing technology’s place in the classroom must also come with adequate preparation for its use. Part of this preparation comes with professional development and practice incorporating technology in lessons. Scaffolding is an important dimension of preparing students for technology use and involves introducing technologically-based activities to students in a piecemeal fashion, which, as Niess (2005) explains, “keeps the activity’s focus on the mathematics.” In this way, effectively using technology requires more than directing students to an app or website and letting them go. The success of technology-based teaching depends on the degree of planning and preparation dedicated to it.

Today’s students use technology in every aspect of their lives, and they will continue to do so into adulthood. Why would teachers avoid utilizing technology in the classroom if by so doing they not only teach students math but also prepare them for the world in which they will live and work? Rather than be intimidated by all that goes into using technology in the classroom, get excited by all of the opportunities for understanding that it affords!

References

The National Council of Teachers of Mathematics. (2014). Principles to action: Ensuring

mathematical success for all [E-book]. Reston, VA: Author.

Niess, Margaret L. (2005). Scaffolding math learning with spreadsheets. Learning and 

Leading with Technology, 32(5), 48.

Skemp, R. (1978). Relational understanding and instrumental understanding. Arithmetic

Teacher, 152-161.

Popular Poll: You “Probably” Don’t Remember Much about Stats

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When asked to recall the time when they were taught statistics in middle and high school, most people will not have much recollection of the subject. Since most curricula incorporate statistics into other math courses rather than dedicate an entire course to stats, few students form foundational understanding of statistics. In many middle and high school math classes, statistics comprises a small fraction of the teaching standards required for the course, and because the focus of the course is not statistics, teachers often spend time only glossing the key concepts or handing out a few worksheets for homework. Precious class time is certainly not spent generating and/or empirically gathering data nor on connecting statistics to everyday life. Furthermore, statistics can easily be reduced to a string of formulas, and hurried teachers are likely to encourage their students to simply memorize when to use which formula and what values are necessary to solve it.

This description of the way statistics is often taught in math classrooms epitomizes what Skemp (1978) refers to as instrumental understanding. When students have an instrumental understanding of statistics, they do not comprehend how given formulas are derived or why certain formulas should be used in a given situation. However, there is a way in which statistics can be taught relationally, so that students grasp why and how statistics models and applies to everyday life.

Graphing calculators are a common-place technology in math classrooms. In many school systems, students either have their own graphing calculator or individual schools have classroom sets. Because of their accessibility, graphing calculators are a helpful tool in illustrating concepts in statistics. Consider the following class activity in which students play a role in generating, creating graphical representations, and analyzing data.

In this activity, students will first take their pulse over a time interval of 10 seconds, recording the number of heartbeats they counted in that time. Next, they will run in place for 20 seconds, immediately after taking their pulse over a 10 second interval again and recording the second number. The teacher will then collect the before and after heartbeats of the entire class, thereby generating a set of data.

Next, students will use their graphing calculators, such as the TI-84 Plus, to interpret the data. With their calculator, students can enter the before/after values into a table and from there plot various graphical representations, including histograms and box and whisker plots. Each of these charts enable students to see different aspects of the data:

  • The histogram shows the distribution of the data.
  • The box and whisker plot reveals minimum and maximum values, as well as the first quartile, median, and third quartile values.

Additionally, students can use their calculators to find calculations such as the mean, sample standard deviation, and population standard deviation. Comparing these calculations to the graphs will help students make connections about the meaning of the respective values.

The above explanation only eclipses the vast applications that graphing calculators have in the realm of statistics, but it does show how technology can be used to relationally teach students about statistics. As stressed by Skemp (1978), the heart of teaching relationally is equipping students to think for themselves. So if students cannot remember the formula for the standard deviation of a data set in twenty years, perhaps their relational understanding of statistics will have developed critical thinking skills that will serve them just as well.

Resources

Skemp, R. (1978). Relational understanding and instrumental understanding.

Arithmetic Teacher, 152-161.

Effective Classroom Technology: Should Spreadsheets Make the List?

spreadsheet

As examined in the previous post, spreadsheet software, like Excel or Numbers, has the capacity to go beyond organizing statistical data in the classroom. By making tables and graphs, spreadsheet software can be used to explore properties of sequences and series or solve algebraic equations. The question, then, is whether spreadsheets provide the most effective means by which students can gain conceptual understanding of these topics. One important consideration when answering this question is evaluating if students have existing familiarity with spreadsheet software, as this will determine the types of tasks and level of scaffolding necessary to keep students focused on the math rather than syntax and technique. However, even if students have basic skills working with spreadsheets, other available technology often proves to be more effective.

For example, consider a problem in which a student is asked to solve the following equation:

3x^2-4x-7 = x+4

We will examine two methods by which technology can be used to solve this problem.

First, we will use spreadsheet software to solve for x. In order to do this, we will set up three columns: one for the values of x, one for the left side of the equation, and one for the right side. After generating a sequence of values for x, we can then apply a corresponding formula in each of the remaining two columns, in this way quickly generating many values for the left and right sides of the equation for given x-values. Next, we can analyze the data to determine where the left and right sides of the equation are equal.

One way to do this is by creating line graphs with the coordinates from the left and right sides of the equation, as shown below. By finding approximately where the two graphs intersect, we can narrow down the interval on which the graphs are equal (as we see here, between (-2,-1) and (2,3)). Alternatively, we can examine the table of values and find the x-values at which the value of the left side of the equation becomes less than the value of the right side, and vice versa.

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Finally, we can use the same process as before to generate x-values between (-2,-1) and (2,3) in order to find more precise x-values for which the left and right sides are equal. In this problem, the solutions (when rounded to the nearest hundredth) are

x= -1.25 and x= 2.92

Using Desmos is the second method we will examine in order to solve this problem. Using Desmos,  a student can graph the left and right sides of the equation and then tap the points of intersection to find the x-values of those points, as shown below.

img_1544

Unlike the first method, which takes at least 15 minutes and a solid knowledge of spreadsheet basics, using Desmos to find the same solution takes only a couple of minutes, not to mention that Desmos has a much more intuitive interface. Furthermore, by having to manually generate smaller and smaller increments of x in order to find the approximate solution in the spreadsheet, students are distracted from visualizing the basic concept of solving equations: the expressions are equal when they have the same y-values for given x-values. Desmos clearly demonstrates this with easy to graph and easy to find points of intersection.

As seen in this example, spreadsheets are often not the most effective technology choice for illustrating a given concept. When a teacher decides the significance of a given technology, Dick and Hollebrands (2011) propose the following question is most important: “[W]hat questions could [the teacher] ask that [he or she] could not ask before?” With regard to spreadsheets, the answer to this question is very few new questions. Overall, the limited functionality and technical requirements of spreadsheets make them less than ideal for use in the math classroom.

Resources

Dick, T. P., & Hollebrands, K. F. (2011). Focus in high school mathematics: Technology to

support reasoning and sense making. Reston, VA: National Council of Teachers of

Mathematics.

 

Spreading Out with Spreadsheets

spreadsheet

In our technologically progressive society, new software, apps, and gadgets are constantly being introduced, ever widening the range of choices from which a teacher might select a technology for his or her classroom. With this prevalence of the latest and greatest technology, it is important for teachers to keep in mind that the most effective technology for demonstrating a given concept might be a familiar one. Spreadsheet software, like Excel or Numbers, is an excellent example of this. Although spreadsheet software has been around for years now, it still has useful capabilities that merit a place in a math classroom.

When one first thinks about spreadsheets, he or she probably thinks about a means by which to organize data entries, track a budget, or tally given quantities. If used in the classroom at all, spreadsheets are often limited to tasks similar to these, and they rarely find a place in math classes outside of statistics. But what if students could utilize spreadsheets to understand broader math concepts such as sequences and series or algebra?

By employing more of the features in software like Excel and Numbers, spreadsheets can find a place in a math classroom. For example, students might use Numbers to see the difference between a sequence of odd numbers and a series of odd numbers by first generating a column of counting numbers, 1 through a positive integer n. In the next column, the student could create a sequence of odd numbers by starting with 1 in the first cell of the column, and in the remaining cells in the column enter a formula such that the value of the cell equals the value of the previous cell plus 2. In the next column, partial sums of the series of odd numbers can be found by starting with 1 in the first cell, and in the remaining cells enter a formula such that the value of the cell equals the value of the previous cell plus that of the adjacent cell (which is the next odd number in the series). For clarity, see below:

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As seen above, students can make conjectures about the explicit formula for the sequence of odd numbers, which we know to be Sn=2n-1, and test their conjectures in the spreadsheet.

Also, students can see the difference between the sequence and series of odd numbers by comparing the line graphs of each, as shown below. This might help students to recognize that the partial sum of the series of odds for a given integer n equals n^2.

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A spreadsheet could also be used to graphically see the solution to an algebra problem. Take x^2-x+3 = x+2 for example. Students can create three columns, one for x, and one  each for the left and right sides of the equation. Using formulas, a student can quickly generate a range of values for each side of the equation for given x values. A student can then create a line graph comparing the left and right sides of the equation. The solution to the equation will be where the two lines intersect, in this case, where x=1. This activity can help students graphically understand what it means for two functions to be equivalent for a given x value.

A noteworthy observation is that when using spreadsheets, there is typically multiple ways in which to achieve a given task. As a teacher, it is important to ensure that students employ correct mathematical reasoning when generating formulas and analyzing data. Further, by comparing results, students might be able to probe further into thinking about how their own solution works, and why their neighbor’s method might too. In this way, spreadsheets have the potential to satisfy Dick and Hollebrand’s (2011) stipulation that effective technology serves “to push our students’ mathematical thinking forward or to probe how students are thinking mathematically” (p. xi). However, in order to push or probe student thinking, the skills needed to manipulate the spreadsheet cannot overshadow the mathematical concepts presented (Niess, 2005). Thus, it is important for teachers to gradually build assignment complexity in order to keep students focused on the math.

Investigations like the ones described above only scratch the surface of the concepts that can be demonstrated with spreadsheets. So before you reach for the newest math app, explore the possibilities of the spreadsheet software you probably already have!

References

Dick, T. P., & Hollebrands, K. F. (2011). Focus in high school mathematics: Technology to

support reasoning and sense making. Reston, VA: National Council of Teachers of

Mathematics.

Niess, Margaret L. (2005). Scaffolding math learning with spreadsheets. Learning and

Leading with Technology, 32(5), 24-25.

Evolving Technology Makes for Dynamic Teaching

the-5-most-important-questions-to-ask-before-purchasing-technology-for-the-classroom_550x366

In the modern world, few things change as rapidly as technology. One generation ago, people still used type writers, and “to be on your phone” meant that you were talking to another individual through a landline connection. The evolution of technology has left few realms untouched, and technology in the classroom is no exception. For example, the college students who use iPads and laptops today can probably remember using floppy disks and overhead projectors in grade school. This fact has critical implications for the future teachers of today.

As technology progresses, effective teachers cannot teach using only the methods with which they were taught. If all teachers did this, many of us would still be using chalkboards and slide rules. Instead, teachers must change with technology. Dynamic teaching with progressive technology enables students to make connections among concepts which would be difficult to make prior to the technology.

However, it is important for teachers to realize that using technology for the sake of doing so does not help students. As put by Dick and Hollebrands (2011, p. xi), technology should be chosen “either to push our students’ mathematical thinking forward or to probe how students are thinking mathematically.” Thus, it is worthwhile for teachers to remain up-to-date with the latest classroom technology, constantly evaluating whether or not new technologies merit a place in the classroom. As reviewed in previous posts, effective technologies range from dynamic geometry software, like GeoGebra, to graphing tools, such as Desmos. The addition of new technology does not invalidate the use of existing methods- at times a whiteboard provides the simplest medium through which to make an explanation. The key, then, for dynamic teaching is finding the most effective way in which to present a concept and willingly adapting to new technologies which achieve this end.

Reference

Dick, T. P., & Hollebrands, K. F. (2011). Focus in high school mathematics: Technology to

support reasoning and sense making. Reston, VA: National Council of Teachers of

Mathematics.