The Place of Technology in Education

The Place of Technology in Education

by guest

My experience has thought me that there are numerous reasons why technology is a key aspect of the learning process in the 21st Century – known as the Information age. I believe we can list the topics related to technology importance in education as it follows:

1. For students: Students and children love to be interactive and technology provides that. Learning with technology has now become part of students lifestyles.

The pictures are the author’s own – Attribution CC-BY

2. For teachers: technology is known to be a requirement for the learning environment and to provide flexible learning environments. We not only use it with students but to train ourselves and help the teacher community.

The pictures are the author’s own – Attribution CC-BY

3. Children are digital natives! They know technology better than most adults. Dealing with technology in the classroom not only helps them learn better but also contribute to their multitasking skills.

4. Students can learn at their own pace: With the integration of technology into education, children have the ability and possibility to slow down, return to the lessons, watch it again, and come back to concepts they learned (in case of asynchronous learning). If synchronous sometimes they can reach out to teachers after the lesson or google information that they might still not understand as well.

The pictures are the author’s own – Attribution CC-BY

5. The limitation that existed before the internet is gone. Accessing information outside of books offer students many ways of learning a concept. Teachers can find creative ways to develop and teach their students the learning environment in lessons.

The pictures are the author’s own – Attribution CC-BY

7. Technology improves relationships between teachers and students: When teachers effectively integrate technology into their subject areas, teachers become consultants, mentors, and coaches. Students can also collaborate with their classmates through technological applications. technology builds bridges.

The pictures are the author’s own – Attribution CC-BY
The pictures are the author’s own – Attribution CC-BY

8. Technology evaluation: evaluating students’ performance can be done instantly with technology. Tools such as Google and Microsoft forms, Mentimeter, Padlet, and many other resources are easy and practical ways to do online surveys and tests. They also help to build more interactive sessions.

The pictures are the author’s own – Attribution CC-BY

See some examples of work created for interactive sections with my students (material in Turkish):

From my perspective, the reality of our present is that adults want to live yesterday, youth today, and children in the future. The concept of “digital native” is used for primary school students with Z generation because they are grown in a digital environment.

However, we also need to consider different philosophies cultures and habits of each generation, society, economic privileges, governmental support, among others. Individuals who are not born in such a “technology world” but use technological tools and equipment are called “digital immigrants”.

According to Arabaci and Polat (2013) “Nowadays, students are digital natives, and the teachers are digital immigrants. Class is one of the common places of the digital immigrants and digital natives. Therefore, it has become necessary to reconsider classroom management in this new century. As the leader of the class teachers have to be aware of the changing characteristics of students in the classroom, otherwise this will bring many conflicts“.

For effective classroom management, today’s teacher needs to be “digitally wise”, acquire digital technology literacy, have the skills to meet the students and education process needs, the expectations of students, and constantly develop themselves.

In classroom management, our digital native students are very talented and willing to use and implement collaborative web 2 tools.

With the collaborative studies and mini-evaluations we apply with our students in the lessons, they have the opportunity to both practice and reinforce what they have learned. As a conscious technology user, digital natives also guide digital immigrants in the classroom about the use and development of applications.

Check out the presentation created by me and used during my lectures (material in Turkish):

The pictures are the author’s own – Attribution CC-BY

If you would like to continue reading about the role of technology in education, check out the following resources:

Author: Nurhan Boyacıoğlu

Nurhan Boyacıoğlu has been a primary school teacher for 27 years. He explores the importance of using technology in his classrooms for both his students’ development and his professional development and gets training on how to use it with STEM applications.

Featured Photo by Kelly Sikkema on Unsplash – See License

Tags: digital education, Digital Literacy, primary education, techonology

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3 Modes Of Thinking: Lateral, Divergent & Convergent Thought

3 Modes Of Thinking: Lateral, Divergent & Convergent Thought

by TeachThought Staff

TeachThought is about, more than anything else, human improvement.

A core tenet of humanity is our ability to think critically and with imagination and creativity. Therefore, it makes sense that our ability–and the decision to–do this consistently in some ways defines us as a species. Critical thinking, in part, involves simply avoiding cognitive biases.

See also What It Means To Think Critically

Further, it’s not a huge leap to say that the ability and tendency to think critically and carefully and creatively supersedes content knowledge in importance, but that’s a discussion for another day. In general, it is our position that critical thinking is of huge importance for students, and as such is a big part of our content and mission at TeachThought.

benefits of asking questions

In pursuit, the sketch note above from Sylvia Duckworth is a nice addition to that index of content. Sylvia has consistently done a great job converting ideas into simple visuals–on our 12 Rules Of Great Teaching, for example.

You can follow Sylvia on twitter here.

We’ve taken the visual and fleshed it out with some commentary from Wikipedia (a resource we love, by the way).

3 Modes Of Thinking: Lateral, Divergent & Convergent Thought

1. Convergent Thinking

Summary: Using logic

Also called: Critical Thinking, Vertical Thinking, Analytical Thinking, Linear Thinking

Wikipedia Excerpt & Overview

‘Convergent thinking is a term coined by Joy Paul Guilford’ (who also coined the term for the ‘opposite’ way of thinking, ‘Divergent Thinking’).


‘It generally means the ability to give the “correct” answer to standard questions that do not require significant creativity, for instance in most tasks in school and on standardized multiple-choice tests for intelligence.

Convergent thinking is often used in conjunction with divergent thinking. Convergent thinking is the type of thinking that focuses on coming up with the single, well-established answer to a problem.[1] Convergent thinking is used as a tool in creative problem-solving. When an individual is using critical thinking to solve a problem they consciously use standards or probabilities to make judgments.[2] This contrasts with divergent thinking where judgment is deferred while looking for and accepting many possible solutions.’

2. Divergent Thinking

Summary: Using imagination

Also called: Creative Thinking or Horizontal Thinking

Wikipedia Excerpt & Overview

‘Divergent thinking is a thought process or method used to generate creative ideas by exploring many possible solutions. It is often used in conjunction with its cognitive colleague, convergent thinking, which follows a particular set of logical steps to arrive at one solution, which in some cases is a ‘correct’ solution. By contrast, divergent thinking typically occurs in a spontaneous, free-flowing, ‘

By contrast, divergent thinking typically occurs in a spontaneous, free-flowing, ‘non-linear’ manner, such that many ideas are generated in an emergent cognitive fashion. Many possible solutions are explored in a short amount of time, and unexpected connections are drawn. After the process of divergent thinking has been completed, ideas and information are organized and structured using convergent thinking.’

3. Lateral Thinking

Summary: Using both Convergent and Divergent Thinking

Also called: ‘Thinking Outside the Box’

Wikipedia Excerpt & Overview

‘Lateral thinking is solving problems through an indirect and creative approach, using reasoning that is not immediately obvious and involving ideas that may not be obtainable by using only traditional step-by-step logic.[1]

To understand lateral thinking, it is necessary to compare lateral thinking and critical thinking. Critical thinking is primarily concerned with judging the truth value of statements and seeking errors. Lateral thinking is more concerned with the “movement value” of statements and ideas. A person uses lateral thinking to move from one known idea to creating new ideas.’

3 Modes Of Thinking: Lateral, Divergent & Convergent Thought

Can You Get a Negative out of a Square Root?

Can You Get a Negative out of a Square Root?


Unmatched math delimiters. Adding final one for you.

The simple answer is: yes you can get negative numbers out of square roots. In fact, should you wish to find the square root of any positive real numbers, you will get two results: the positive and negative versions of the same number.

Writing a Square Root Equation for Positive and Negative Results

Consider the following:

16 = 4 * 4 = (-4) * (-4)

In the equation above, you can either multiply 4 by itself or multiply (-4) by itself to get the result of 16. Thus, the square root of 16 would be:

The √ symbol is called the radical symbol, while the number or expression inside the symbol—in this case, 16—is called a radicand.

Why would we need a ± symbol in front of 4? Well, as we have discussed before, the square roots of 16 can be either 4 or (-4)​.

Most people would simply write this equation simply as . While it is technically true and there’s nothing wrong with it, it doesn’t tell the whole story.

Instead, you can also write the equation in such a way that it explicitly indicates that you want both the positive and negative square root’s results:

This way, other people can easily tell that the one who writes the equation wishes to have positive and negative numbers as the result.

Perfect and Imperfect squares

As you may know, 16 is a perfect square. Perfect squares are radicands in the form of an integer, or a whole number, that has a square root of another integer. In the example above, 16 is a perfect square because it has the number 4 as its square root.

Positive real numbers are not always perfect squares. There are also other numbers such as 3, 5, or 13 that are referred to as imperfect squares. If a radicand is not a perfect square, then the square root of the radicand won’t result is an integer. Take a look at the equation below.

5 is not a perfect square. Therefore, its square root won’t be an integer. Additionally, the square root is not even a rational number. Rational numbers are numbers that can be expressed as fractions composed of two integers, e.g. 7/2​, 50/4​, and 100/3​.

The square root of 5 is an irrational number since it can’t be expressed as fractions. The numbers right of the decimal 2.236067 … would continue on endlessly without any repeating pattern. Still, both irrational and rational numbers are part of real numbers, meaning they have tangible values and exist on the number line.

Square Roots of Zero and Negative Numbers

We mentioned earlier that any positive real numbers have two square roots, the positive one and the negative one. What about negative numbers and zero?

For zero, it only has one square root, which is itself, 0.

On the other hand, negative numbers don’t have any real square roots. Any real number—whether it’s positive or negative—that is multiplied by itself is always equal to a positive number, except for 0. Instead, the square root of all negative numbers is an imaginary number.


By definition, the square root of (-1)​ is i​, which is an imaginary unit. As a side note, imaginary numbers do not have a tangible value. They are not part of real numbers in the sense that they can’t be quantified on the number line. However, they are still used in math and the study of sciences including quantum mechanics, electricity, and more.

To get a better understanding, let’s take a look at an example. For instance, let’s say we want to identify the square root of (-9)​, what would it be?

The #1 Most Requested Desmos Feature Right Now, and What We Could Do Instead

Linked card sort activity.

When schools started closing months ago, we heard two loud requests from teachers in our community. They wanted:

  1. Written feedback for students.
  2. Co-teacher access to student data.

Those sounded like unambiguously good ideas, whether schools were closed or not. Good pedagogy. Good technology. Good math. We made both.

Here is the new loudest request:

  1. Self-checking activities. Especially card sorts.

hey @Desmos – is there a simple way for students to see their accuracy for a matching graph/eqn card sort? thank you!

Is there a way to make a @Desmos card sort self checking? #MTBoS #iteachmath #remotelearning

@Desmos to help with virtual learning, is there a way to make it that students cannot advance to the next slide until their cardsort is completed correctly?

Let’s say you have students working on a card sort like this, matching graphs of web traffic pre- and post-coronavirus to the correct websites.

Linked card sort activity.

What kind of feedback would be most helpful for students here?

Feedback is supposed to change thinking. That’s its job. Ideally it develops student thinking, but some feedback diminishes it. For example, Kluger and DeNisi (1996) found that one-third of feedback interventions decreased performance.

Butler (1986) found that grades were less effective feedback than comments at developing both student thinking and intrinsic motivation. When the feedback came in the form of grades and comments, the results were the same as if the teacher had returned grades alone. Grades tend to catch and keep student attention.

So we could give students a button that tells them they’re right or wrong.

Resourceful teachers in our community have put together screens like this. Students press a button and see if their card sort is right or wrong.

Feedback that the student has less than half correct.

My concerns:

  1. If students find out that they’re right, will they simply stop thinking about the card sort, even if they could benefit from more thinking?
  2. If students find out that they’re wrong, do they have enough information related to the task to help them do more than guess and check their way to their next answer?

For example, in this video, you can see a student move between a card sort and the self-check screen three times in 11 seconds. Is the student having three separate mathematical realizations during that interval . . . or just guessing and checking?

On another card sort, students click the “Check Work” button up to 10 times.

Instead we could tell students which card is the hardest for the class.

Our teacher dashboard will show teachers which card is hardest for students. I used the web traffic card sort last week when I taught Wendy Baty’s eighth grade class online. After a few minutes of early work, I told the students that “Netflix” had been the hardest card for them to correctly group and then invited them to think about their sort again.

I suspect that students gave the Netflix card some extra thought (e.g., “How should I think about the maximum y-value in these cards? Is Netflix more popular than YouTube or the other way around?”) even if they had matched the card correctly. I suspect this revelation helped every student develop their thinking more than if we simply told them their sort was right or wrong.

We could also make it easier for students to see and comment on each other’s card sorts.

In this video, you can see Julie Reulbach and Christopher Danielson talking about their different sorts. I paired them up specifically because I knew their card sorts were different.

Christopher’s sort is wrong, and I suspect he benefited more from their conversation than he would from hearing a computer tell him he’s wrong.

Julie’s sort is right, and I suspect she benefited more from explaining and defending her sort than she would from hearing a computer tell her she’s right.

I suspect that conversations like theirs will also benefit students well beyond this particular card sort, helping them understand that “correctness” is something that’s determined and justified by people, not just answer keys, and that mathematical authority is endowed in students, not just in adults and computers.

Teachers could create reaction videos.

In this video, Johanna Langill doesn’t respond to every student’s idea individually. Instead, she looks for themes in student thinking, celebrates them, then connects and responds to those themes.

I suspect that students will learn more from Johanna’s holistic analysis of student work than they would an individualized grade of “right” or “wrong.”

Our values are in conflict.

We want to build tools and curriculum for classes that actually exist, not for the classes of our imaginations or dreams. That’s why we field test our work relentlessly. It’s why we constantly shrink the amount of bandwidth our activities and tools require. It’s why we lead our field in accessibility.

We also want students to know that there are lots of interesting ways to be right in math class, and that wrong answers are useful for learning. That’s why we ask students to estimate, argue, notice, and wonder. It’s why we have built so many tools for facilitating conversations in math class. It’s also why we don’t generally give students immediate feedback that their answers are “right” or “wrong.” That kind of feedback often ends productive conversations before they begin.

But the classes that exist right now are hostile to the kinds of interactions we’d all like students to have with their teachers, with their classmates, and with math. Students are separated from one another by distance and time. Resources like attention, time, and technology are stretched. Mathematical conversations that were common in September are now impossible in May.

How to Be Successful With Online Faculty Meetings

Online Faculty Meeting

As many school districts go into the new school year with at least some of their operations online, school leaders are wondering how to plan effective online faculty meetings. Faculty meetings provide teachers and staff with information, support, motivation, and inspiration. And they are essential to keep your school’s shared vision on track. But conducting them online is a new territory. How do you ensure that your time together is productive and effective? These suggestions for setting norms for online faculty meetings are a good place to start.

1. Request cameras on.

Face-to-face contact with colleagues and teammates is essential. So many of us are feeling isolated and overwhelmed. Being able to see each other reminds us that we’re part of a team with a common goal. Oh, and nobody cares if your roots are showing or your office is messy! Here are a few simple tricks that will help you look your best on video chats. 

That being said, some teachers have legitimate privacy concerns and may not want to expose their coworkers or supervisor to the inner workings of their homes. Be respectful of those concerns and allow staff to use virtual backgrounds for meetings if desired. 

2. Wear what makes you comfortable.

Some school districts have been getting in social media hot water by trying to regulate what students and teachers wear during online learning. Remember, this is a time to be flexible. While sweatshirts and leggings might not work for in-person school attire, are they really taking away from your online meeting? Let common sense be your guide when it comes to online dress code, and put trust in your teachers that they know what’s appropriate and what’s not.

3. Keep background distractions to a minimum.

By now, we’ve all witnessed things like dogs jumping onto laps, kids running in and out of the room, doors slamming, and doorbells ringing. During staff meetings, suggest that everyone try their best to find a quiet place, let others know they are unavailable, and close their doors.  

4. Use your mute button.

Listening to one speaker at a time in a group conversation is a bit tricky with video conferencing because there is that tiny bit of lag time. It’s hard not to talk over one another, particularly when the conversation is spirited. It takes a little practice, but ask participants to keep their microphone on mute unless they are speaking and encourage everyone to take a beat before they jump in.

5. Watch the time.

There’s nothing worse than showing up on time, ready to go, and having to sit around waiting for colleagues to join a meeting. It’s kind of a no-brainer, but honoring time limits shows respect and consideration for one another.

6. Allow yourself to be present. 

Connecting as a staff is more important than ever. And doing so effectively requires full attention to the business on hand. Although it’s tempting, resist the urge to multi-task. Honor this time as an opportunity to touch base and share ideas. Everyone contributes, every voice is heard.

7. Do your best to stay on track. 

When it comes to faculty meetings, everyone is happier when a clear agenda is set and followed. No doubt, everyone’s experience this fall is going to be unique and there may be a need for more guidance than usual. Break into smaller groups or schedule one-on-one sessions for individuals with specific questions or problems that are not relevant to the whole group. 

8. Keep it positive.

Times are hard, and we’re all stressed. It’s easy for staff meetings to devolve into complaint sessions. But it’s essential for the entire faculty to approach meetings with an open mind, listening ears, and a commitment to working together respectfully for the benefit of all.

9. Celebrate each other.

Our teachers are doing such an amazing job with all of the changes that have been thrown their way. Make your time together inspirational. Try opening your meeting with something fun, such as one of these 15 Virtual Icebreakers to Cheer Up Your Online Meetings. Set aside time together to build one another up with shout-outs, encouraging words, brilliant hacks, and success stories. 

10. Don’t forget the bottom line. 

As always, the ultimate purpose of faculty meetings should be focused on outcomes for kids. Agendas and conversations should ultimately be centered around doing what is best for our students, especially in this crazy, uncertain time. The more you can keep the main thing the main thing, the more productive and effective your meetings will be. 

Even though we had a taste of online learning and communication in the spring, we’re all still learning. We’re dealing with loss and change and upheaval. By adopting these few simple norms, you can help ensure staff meetings will be a time to come together to cheer each other on, share ideas, and solve problems.

How are your online faculty meetings going? Come and share in our Principal Life group on Facebook.

Plus, guidelines for in-person staff meetings.

How To Grade Assignments In Google Classroom

How To Grade In Google Classroom

How To Grade In Google Classroom

How To Grade Assignments In Google Classroom

by TeachThought Staff

How do you grade in Google Classroom?

Well, that depends on what you mean by ‘grade’ but let’s have a look at some of the larger components of grading in Google Classroom: Setting up a grading system, giving feedback on assignments, using and grading with rubrics, grading and returning assignments, and viewing and updating your gradebook on Google Classroom.

The following information is sourced directly from Google’s own Classroom support documents, which you can access directly here. So, in the spirit of How To Save Time Teaching With Technology, here are instructions how to grade in Google Classroom.

How To Set Up A Grading System In Google Classroom

For your grading system, you can choose Total points or Weighted by category grading. In both, grades are calculated for you, and you can let students see their overall grade. If you don’t want to use a grading system, you can choose ‘No overall grade.’ With this selected, grades won’t be calculated and students can’t see an overall grade. 

You can also organize classwork with grade categories, such as EssaysHomework, and Tests. For example, if your class has four essay assignments, you can organize them in an Essays category.

Note: Grades are calculated for the duration of the class. If you want to begin grading again for a new term or semester, you have to create a new class.

After you select a grading system, you can add grade categories. Grade categories are required with Weighted by category grading, but can also be used with Total points grading or No overall grade. 

Note, you can only select a grading system in the web version of Classroom.

  1. Go to
  2. Click your classand thenSettings Settings
  3. Next to Overall grade calculation, select one:

No overall grade—Grades aren’t calculated for students. Students can’t see an overall grade.

Total points—Divides total points earned by total points possible. You can let students see an overall grade.

Weighted by category—Adds the scores across categories. You can let students see an overall grade.

4. (Optional) To make the overall grade visible to students on their profile page, click ‘Show’
Note: This option isn’t available when grade calculation is set to No overall grade.

5. In the top-right corner, click Save

How To Give Feedback On Google Classroom Assignments

  1. In Classroom, open the student work (details above).
  2. Select the passage that you want to comment on and click Add a comment Add comment.

How To Grade With A Rubric In Google Classroom

You can use a rubric to grade and give feedback. You can grade rubrics from the Student work page or the grading tool. After you start grading, you can’t edit or delete the assignment’s rubric.

For details on how students can check their rubrics, go to Check your work with rubrics.

How To Grade And Return An Assignment In Google Classroom

In Classroom, you can give a numeric grade, leave comment-only feedback, or do both. You can also return assignments without grades.

You can grade and return work from:

  • The Student work page
  • The Classroom grading tool
  • The Grades page

For Grades page instructions, go to View or update your gradebook.

You can download grades for one assignment or for all assignments in a class.

Coming soon: Organize your gradebook into grading periods, such as quarters or semesters, and see overall grades for each. 

How To View And Update Your Gradebook On Google Classroom

Note: If your school participates in the grades sync beta program, you can push grades directly from Classroom to your student information system (SIS). For details, go to the beta interest sign-up form.

On the Grades page, you can view and update your gradebook. You can view student submissions, enter grades, and return work. Students get their grades when you return their work. Only teachers see the Grades page.

For instructions to set up overall grades and grade categories, go to Set up grading.

You can open your gradebook from two places.

  1. Go to
  2. Choose an option:
    • On a class card, click Open gradebook .
      Open gradebook
    • In a class, at the top, click Grades.
      Grades page

How To Enter Grades And Return Work In Google Classroom

You can return work with or without a grade. Grades you enter save as drafts until you click Return. When you return work, email or mobile notifications are sent to students who get them, and students can view their grades.

  1. Go to
  2. Click a classand thenGrades.
  3. (Optional) Enter a grade for a student’s assignment.
  4. To return a student’s assignment, click More ""and thenReturn and confirm.
    Click return

For more instructions on grading, go to Grade and return an assignment. 

In Classroom, you can give a numeric grade, leave comment-only feedback, or do both. You can also return assignments without grades. Note, you can grade and return work from:

  • The Student work page.
  • The Classroom grading tool.
  • The Grades page.

For Grades page instructions, go to View or update your gradebook. You can download grades for one assignment or for all assignments in a class.

To see many of these processes in action, take a look at the following video by Eric Curts. In the short, four-minute video, Eric demonstrates how to grade assignments in Google Classroom, including how to a brief mention of the very useful ‘Comment Bank’ that allows you to save commonly-used phrases and feedback for quick application while grading in Google Classroom.