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Free Decolonizing Math Webinar

Incorporating Indigenous perspectives into all subjects is an important aspect of decolonizing and Indigenizing your classroom. Many educators wonder what this looks like in math classes because math is often viewed as a neutral and objective subject governed by strict rules and universally accepted principles. However, math, like any other discipline, is shaped by the cultural context in which it is taught.

Are you wondering how you can integrate Indigenous perspectives into your math classroom? Education Consultants Hannah Arseneau-Danielis and Naomi Bender share insights from their own experiences decolonizing their math teaching and provide practical strategies and best practices for creating culturally inclusive math classrooms.

Watch the webinar recording here!

Webinar Wrap-Up: Resources and Lessons

Last week, we were excited to host a webinar for our partnering communities. Learning Bird’s Education Account Leads Joelle Chemali and Rebecca Smith presented the session “Using Learning Bird to Guide Your Pedagogy.” They looked at the different ways educators can incorporate Learning Bird content into their everyday practice. They focused on pairing each subject with fun activities and lessons for middle and high school learners.

Using Learning Bird to Guide Your Pedagogy

Joelle and Rebecca knew they needed to include educators working in very different situations when preparing for this webinar. Internet connectivity and access to devices affect what types of resources educators can easily use in their classes. While presenting the webinar, they showcased many activities that did not require technology.

They also stressed that Learning Bird units guide instruction while enabling educators to adapt them to their learners. There is no one-size-fits-all solution, so educators can freely adapt the resources and resource kits in whatever way works best for their learners.

Education Resources

The presenters started by giving a brief tour of the Learning Bird platform’s fresh new look. Community names are up-front, allowing communities to find their resources and other communities’ resources faster and more effectively. They then jumped into subject-specific units to give educators ideas for engaging their learners differently.

The presenters explained that Learning Bird lessons are tools to introduce new topics, encourage engagement, prompt discussion, and check for understanding formatively or summatively. They also provided attendees with a handout with additional activities for each subject. Let’s take a look at some of these ideas.

Language Lessons

Learners nowadays are connected to their phones, tablets, and social media. It’s important to use this technology to rebuild language skills amongst younger generations. Different delivery methods engage learners through individual work, group activities, and role-play. The presenters walked attendees through a Learning Bird unit on the colours of food in Oji-Cree. It demonstrates a framework where educators and learners can alternate between whole-class activities, role-play, and individual work.

Whole-class activities include playing a video and having learners practice repeating pronunciation. Role-play involves the educator providing learners with a text or script and practicing in pairs. Educators can print out handouts or project them to facilitate individual work. The example handout includes fun activities like “Pictionary,” “find someone who,” and “classroom mingle.”

Culture Lessons

The featured unit is about well-being from an Indigenous perspective. It is an important topic to discuss with all learners across different communities. Educators guide learners to examine the spiritual, emotional, mental, and physical parts of their well-being.

The presenter mentioned that it is good to start with a class discussion. Ask learners what they currently do for self-care and discuss why it’s important. Educators can then follow this discussion with a video covering introductory concepts of Indigenous perspectives on well-being. Follow the video with a small group activity. Learners apply their knowledge and understanding of the connection between spiritual, emotional, mental, and physical well-being. Lastly, encourage learners to create their wellness plan. Educators should judge whether or not it is appropriate for learners to share their work, as this is a more personal matter.

The presenters emphasized that these units should frame the educator’s lessons and are adaptable. The handout includes additional open-ended activities that can work well in a culture class. “Tableau” has learners act out traditional activities or stories. Educators can set up an “obstacle course” where learners perform a traditional activity. Educators may consider setting up a gallery walk or displaying cultural materials and pictures for learners to view and respond to.

Math Lessons

Although math is not always the most exciting subject for learners, the presenter pointed out that we can engage learners in various ways. We need to explain to learners why they are learning a particular topic, what it means to them, and how they will apply their knowledge in the future.

The star quilt unit featured is cross-curricular. It starts with a video on the history of star quilts. Educators can play it for the class and follow it with a discussion. If possible or relevant, educators can invite Elders and Knowledge Keepers to share the history of the star quilt within the community. Then, the class can jump into the videos introducing specific mathematical concepts. Learners can follow along on the handout individually or in small groups. Lastly, learners make their star quilts using the step-by-step podcast and instructions on the accompanying handout. It’s easier to engage learners in some math topics than others. You can easily integrate the activities on the handout like “around the block,” “3-2-1 prompts,” and “one-minute problems” into everyday teaching.

English Lessons

The presenters looked at the novel Touching Spirit Bear by Ben Mikaelsen. The presenters reviewed reading strategies and activities. Before reading, learners can make predictions, build anticipation, and create graphic organizers. During reading, learners can complete vocabulary activities, fill out graphic organizers, and predict and ask questions. After reading, learners will summarize and analyze themes and characters. The Learning Bird resources on Touching Spirit Bear feature many of these strategies.

Educators can show the videos from the two units and ask learners to complete the handouts and projects available on Learning Bird. These resources help learners prepare for reading and understand what they’ve read. Educators can check for understanding throughout the novel study. Educators can end with a slideshow that outlines a great cumulative project they can adapt for middle or high school. The presenters added that educators could use these strategies and activities for other novel studies, adapting to the content. Activities on the handout include “graphic organizers,” “save the last word for me,” and “somebody wanted but so.”

Science Lessons

The fascinating thing about science is that it’s everywhere, and we need to expose learners to their surroundings whenever possible. The unit featured in this session is about chemistry in cooking. It follows a similar structure as other subjects. A video and slideshow introduce basic terminology, and handouts and activities include group and individual work. The emphasis is on pacing lessons based on learners’ knowledge level. This unit ends with an experiment that learners can carry out in a lab or classroom. Learners can do this in groups.

Although we might not always think of it, it is quite easy to complete activities and experiments in the classroom with very few materials. The presenter encouraged educators to Google search for experiments they can do in the classroom. Educators can always bring the materials and have learners gather around while they take turns experimenting. The handout mentions activities like “two stray, one stay,” where learners compare/contrast conclusions. Educators can easily apply a KWL chart to any subject area.

Social Studies Lessons

The last unit on sustainability was very interesting. Learners can use the featured resources as a template to learn about their community history and changes in the community. Invite Elders and Knowledge Keepers to share their knowledge and discuss it with learners. Learners then apply the research and knowledge to create a large-scale community map and plan.

The handout mentions activities like “stoplights,” which is an easy way to check for understanding. “Nothing ventured” has learners review material by answering a list of questions individually or in pairs. Educators can use “Timelines” as an anchor chart, or learners can create one from scratch as a project.

Make Activities Routine

The session ended with recommendations based on attendees’ questions. One recommendation was the importance of including activities as part of a routine, so learners become accustomed to specific activities. Eventually, there will be less focus on classroom management and more on learning and engagement. “Don’t give up!” said the presenters, as it will probably fail the first, second, and sometimes even third time. Once you figure it out, it will be worthwhile.

If you missed the webinar and would like a recording and copy of the handout, please reach out to your Education Account Lead or email achieve@learningbird.com.

classroom resources English math science social studies webinar

Decolonizing Math: Creating Culturally-Relevant Resources

Reading scale on a map decolonizing math

Although learners can have trouble with any subject, math is the one learners complain about most. Often this is because learners don’t see the connection or relevance of math to their daily lives. Too often, math problems don’t reflect realistic situations or connect to learners’ realities. That makes it hard for learners to engage with the content. It is especially true for Indigenous learners. Many elements of western math instruction don’t necessarily align with the principles of Indigenous learning. This post will explore ideas for decolonizing math in ways that feel natural and authentic.

Integrating Indigenous Examples

A simple first step in integrating Indigenous perspectives into math content is consistently integrating terminology and examples into math problems. While this is a small change, relevant examples can better help learners understand a topic. For example, introduce probability by showcasing a common Indigenous hand game played in the community. That may help hold the learners’ interest and help them better relate to the topic. A relevant and familiar example enables learners to focus on the new terminology related to the topic rather than struggling to understand other example elements.

Probability in Lahal: An Example of Decolonizing Math

The examples used in instruction must be pertinent, meaningful, and consistent. Ideally, examples come naturally to the explanation. They should also add value to the instruction, not just token names or integrated places to provide loose connections.

Connecting Math & Indigenous Knowledge

Another way to decolonize math content is to focus on the six areas of human activity that are common across all cultures:

measuring
locating
playing
counting
designing
explaining

You will make problems more approachable if you center math problems around these activities and work in relevant cultural terminology and examples. A great example is using cooking to teach fractions. Food is an important part of family culture in Indigenous communities. Suppose you base a math problem around scaling a recipe to make a common dish, such as Fry Bread or Bannock for a large group. In that case, you use a real-world example that may resonate well with learners and translate to the knowledge they will need.

When learning cooking from family members and elders, it is typical to hear terms like “a handful” or “a pinch.” An activity could start by measuring and quantifying local values and aligning them with universal measures, like a ½ cup or ¼ teaspoon. Learners can then learn how to scale the recipe by using proportional reasoning. They can also look at downscaling recipes to feed smaller groups and preserve resources, therefore applying division of fractions.

Decolonizing Math Through Indigenous Themes

To take this concept further, you can also look for ways to connect broader Indigenous themes to math instruction. Say you are teaching the topic of number percentages as part of your grade 8 math program. Instead of jumping into a question, start talking about a theme that resonates with learners, like family and ancestry. Ask your learners to map out their family tree and calculate percentages of different scenarios. For example, learners can calculate the number of females vs. males, the average ages, or other variables. They will see real-world, contextual learning. You can also teach number percentages by looking at resource management, predicted yields, or community profiles. It makes percentages more relevant and enhances numeracy as it includes some data analysis.

Using Stories in Math Instruction

Word problems are a big part of teaching logic and reasoning. However, they do not often align with Indigenous oral traditions. Word problems frame the question and provide more details, but they are not truly story-based learning. The use of storytelling can help frame a topic and provide history and context to learning.

Consider how multiple topics can align to a theme. Weave together a lesson or a series of lessons, and build out learning through stories. We recently worked with a school where learners had trouble with even and odd numbers and skip counting. We decided to build a story-driven set of videos that showcased the tale of three friends playing a game of Willow Sticks. It allowed us to weave in many math concepts to a game that most of the learners in the community play. That made it more relevant and provided a new perspective on how educators could teach the content. Instead of addressing the content by topic, we wove themes into a story related to a familiar situation.

Approaching Math from a Holistic Perspective

Weaving storytelling and providing relevant examples often leads to more holistic math learning. Relating to broader topics and themes provides learning opportunities that bridge home, school, and community. It’s easy to work with math concepts like trajectories, angles, and distance calculations while talking about outdoor activities like ice fishing and trapping. You can also work on math skills when looking at science topics. While teaching learners about trees, it’s easy to work in lessons. Learners can count rings, determine a trunk’s radius or diameter, or predict the volume of sap a tree can generate per year, estimating its syrup yield. There is a natural progression toward math integration into other projects and subjects and a more holistic approach for inclusion.

Decolonizing Math: Steps for Success

Decolonizing math resources does require some planning and structure and support and participation by others. Educators may also need some preparation and education to feel supported and comfortable, including Indigenous examples. An educator may need to do essential research to support a math concept with a relevant example. Let’s say an educator wants to use an Indigenous game to explain a math concept. First, they will need to learn its rules, history, and cultural significance. It may also require the collaboration of other educators to build projects that span subjects or topics to integrate math into overall learning better.

If you would like to explore how Learning Bird can assist you in building decolonized math content, we’d be happy to chat. We can also share some other examples of content with you. Contact us at 1-888-844-9022 or email achieve@learningbird.com.

decolonizing math

Teaching Math in the 21st Century: Changing the Focus from Calculations to Critical Thinking

Math class can be a traumatic experience, and for whatever reason, people tie math closely to intelligence. Many people think you can do math if you’re smart, and if you’re not smart, you cannot.

According to statistics from the Carnegie Foundation, about half of all learners in the U.S. go to two-year colleges. Over half of those learners must take remedial math courses (often for no credit), essentially the same classes they took in high school. About 10% of those learners complete the remedial math courses, while the remaining 90% cannot and drop out of college.

Based on this data, what would you say is the top reason? Are there too many math standards? Do learners not have the ability? Are educators to blame? Is math not for everyone?

Rethinking How We Teach Math

I believe that neither math content nor learners are the problems, but rather the commonly taught method. Math involves logic, reasoning, critical thinking, and tenacity. These are all things that people love to do. Give a riddle to a person, and you will find that many people love trying to solve them. Sudoku puzzles enthrall people for hours. The same is true of board games, video games, etc. The human mind likes thinking, reasoning, and figuring things out. The main problem with mathematics is that it is not taught this way. It is not viewed as a riddle to be solved, and, oftentimes, math problems are not explained in a way that allows learners to thoroughly understand what they are looking for or why it is important. Math is shown as a series of steps to memorize and follow rather than understand and apply to new situations.

The skills needed for mathematics are real-world 21st-century skills that learners will need regardless of what they do with their lives. Many learners believe they “dislike” math because they will never need a particular algorithm or equation outside of school. That is true, but we will always need math courses focusing on reasoning and critical thinking skills.

So, if you were asked the best way to teach math, what would you say? A colleague asked me that very question. This post and video represent my response.

What a Good Math Teacher is Not

A good place to start might be to ask what a good math teacher is not.

Teacher ≠ Teller

Math teachers should not be math “tellers.” Rather than challenge learners to build their understanding of concepts, “tellers” tell learners how to understand.

You may be a math “teller” if you show learners how to solve a problem. Being a math “teller” is almost like giving learners a puzzle already completed rather than having the learners put it together themselves.

That brings up a fundamental issue with understanding what good teaching consists of. Most learners, parents, and even educators think you are a good teacher if you explain concepts clearly and concisely. What this means is that you are a good “teller.” The problem with telling is that learners are not challenged to think mathematically. In essence, the “teller” is doing all of the thinking for them. The learners are more focused on becoming good at calculations instead of discovery.

That is not to say that educators should not be helping learners, but helping learners is not the same thing as showing them how. This notion of educators “making things easier to understand” goes against what education research has shown us. Education research identifies one of the most important things educators do to affect learners’ conceptual understanding. That is to make sure learners are engaged in a productive struggle. It involves not simply telling learners how to make something easier but instead focusing on providing learners with challenges that contain clear instructions and enough time to figure things out. Educators’ biggest role is to promote 21st-century skills, create excitement, and build learners’ confidence in learning and thinking. None of this is promoted if educators are simply the medium in which learners get easier explanations.

Solving a Type of Problem ≠ Problem Solving

Another attribute a good math teacher does not have includes teaching learners exactly how to do a certain type of problem and then repeatedly giving them the same problem with different numbers. A simple computer can do this type of rote, basic skills learning. The last thing we need is learners thinking and acting like computers.

There needs to be a human element to learning. An aspect of discovering new concepts collaboratively, making mistakes, debating answers, attempting completely novel problems, etc., must be present. Doing calculations is not the same as doing math. Unfortunately, most assessments are simply assessing calculations while ignoring the concepts.

Math ≠ Race

One of my biggest gripes about tests like the ACT is that they are timed and more focused on calculations than actual thinking. Math (among other subjects the ACT assesses) is meant to be deeply thought about. Instead, learners learn how to take the test. This system gaming does not provide any in-depth thinking beyond the test itself. Assessments in math classes should not follow the ACT’s lead. It is much more beneficial to concentrate on problems than learners robotically completing problems as fast as possible to finish a test. If a concept is important enough to be tested on, then it is important enough to get the appropriate amount of time to be thought about.

Note: I am not saying that learners should be given as much time as they want on a test, but they should not feel rushed to finish a test. Showing mastery of a concept does not require a race against the clock.

As a society, we do not need speedy executors of processes anymore. Computers can do our calculations. We need mathematical modellers, predictors, justifiers, communicators, and problem solvers. We need more people who program and work with computers than people who act like them. These types of people are those who will take up future STEM jobs.

The heart of math is to deeply understand concepts and how they relate to solving other problems. This type of thinking is the basis of intelligence, and time should not limit this.

Math ≠ Memorizing Algorithms

With the ubiquity of information due to the advancements in technology, memorizing facts, formulas, and equations has become increasingly obsolete. Learners should spend valuable learning time working on higher-order thinking rather than rote memorization.

What Good Math Teaching Looks Like

Learning math can promote cognitive strengths that you cannot find in any other discipline. The kinds of thinking that I am talking about involve logic and reasoning. In this type of learning, numbers take a back seat to thinking.

However, such thinking is not part of most curricula. Instead, we get an unsteady collection of seemingly unconnected skills and procedures, which many educators proclaim to reteach every year as if the learners had never seen them before. Time and time again, research has shown that most learners who are considered to be “good at math” under the traditional math setting often cannot apply a single thing they have learned in a novel setting. As math teachers, we tend to focus on what to teach rather than how to teach. That makes math class more like a checklist of processes and algorithms for learners to memorize rather than mathematical thinking.

So what needs to change?

Inform Students How Learning Works

As discussed previously, an educator’s role is to inspire learners to think and want to think. In my opinion, too many learners think they hate math. In reality, they hate what they think is math. A better way of describing it might be “memorized mathematical procedures.” That makes sense if you know anything about control theory. People tend to focus more on what controls their learning than the learning itself. For example, rewarding learners with points or a grade for their learning tend to shift their focus to the points rather than the learning. I tell learners this on the first day. I explain the psychological ideas behind a lot of the teaching and how it can affect them. That way, learners have enough information to attempt learning in a different, more productive way that focuses on intrinsic motivation.

Provide Clear Instructions

Often, learners are not confused about mathematics. They are confused about the class’s setup, the lesson’s instructions, what they are trying to solve, and sometimes even how an educator’s website is arranged. The biggest confusion in class should be from the mathematics, not the learning environment. When giving learners a challenge, have them repeat the instructions you gave to ensure they understood.

Ditch the In-Class Lecture and Focus on Self-Paced, Collaborative Learning

Self-paced learning provides learners time to create their understanding of the material, while collaborative learning has been shown to increase understanding of concepts due to different perspectives.

Lecturing to an entire class assumes that all learners equally understand the content. It also does not provide a lot of opportunities for collaboration. Videos are a great alternative to lecturing and provide an excellent medium for learners to utilize self-paced learning. They can learn at their own pace, pause, re-watch, collaborate and ask more specific questions.

Learners should complete in-class challenges at their own pace. Often, concepts that they struggle with at the beginning make sense at the end of the course, allowing them to catch up to their peers. Also, mastering all units in a course except a few is much more valuable than understanding each partway.

Be Inspiring and Informative With Feedback

Some learners find math simple, while others find it difficult. However, this does not reflect their potential for future understanding. Learners have been gaining different experiences since childhood. Some of those experiences cause synapses to fire, and others do not. As educators, we need to change the path for learners who never had those synapses. Learners need an environment that is personally challenging. Neuroscience shows that every child can excel in math. The potential of the brain to grow is huge, and despite the belief in fixed math ability, every learning experience can change your math capabilities.

Educators should use fixed ability language as little as possible. That includes saying things like “You’re so smart,” “You’re so good at math,” “You struggle with math,” etc. While it may seem nice to give learners positive fixed ability comments, research shows that once learners do something that they perceive as not smart, they think what you said was incorrect. Instead, the focus should be on effort and actionable feedback. When giving feedback, please make sure learners know that you critique them because you believe in their ability and potential to succeed. Starting any feedback to a learner with a positive statement makes feedback even more powerful. Make sure to praise what learners have done rather than their intelligence.

Timely feedback as needed is best but difficult when educators lecture. Educators must be free to socialize with learners during class to give them retrospective feedback regarding past understanding and constitutive feedback related to future understanding.

As Grant Wiggins said, “Students need endless feedback more than they need endless teaching.”

Focus on Learners Actively Creating their Understanding Collaboratively

Simply put, if you don’t ask learners to think, they won’t.

How something works is vitally important, but the further applications of a concept become more extended when one understands the “why.” Most teachers face the problem that the “why” does not come immediately for most learners. Time is always against educators, and most classes are not self-paced. So, rather than spending time on understanding the “why,” educators give learners the easy way out by telling them what to do. The procedures are learned and then forgotten about easily and, since they were never fully understood, are never connected to new concepts.

That is why mathematics may seem fragmented instead of a connected web of concepts. That is not to say that learners do not need to know how to do basic skills. Instead of telling the learners, I recommend discovering it on their own through activities and problem-solving exercises. Having learners use past understanding of concepts to help them solve new problems helps tie old concepts to the new. That provides a deeper understanding for the learners. It is important to note that not all learners can discover concepts independently. That is where the educator comes into play. By providing hints, you urge learners to understand concepts by challenging themselves at their own pace.

As research shows, learners who participate in informal quantitative reasoning can complete formal math assessments with much greater ease. Similarly, learners who are asked to give reasons for their thinking are better at using logic to explain arguments.

Research has shown that when math focuses on problem-solving skills, logical reasoning, multiple forms of representation of concepts, and question formulation, learners perform at higher levels, take more advanced math courses, and create equitable achievement. When educators promote these aspects of math in class, rather than repeating procedures, learners’ intelligence and ideas are more valued, which leads to higher confidence in math. Furthermore, the main skills that math focuses on are reasoning and justification.

Differentiate

Confidence is a huge factor for doing well in math. Learners need to be completing problems at their level and finding success. When helping individual learners, try not to have predetermined questions. Instead, think about learners’ current understanding, listen to their ideas, and create interesting questions that relate directly to their ideas to push the limit of their understanding.

Avoid routines in questioning and the construction of problems. If you want learners to think outside of the box, you must challenge them accordingly.

Each learner is different, and to help all of them, educators need more passion and patience. Although these help, there need to be well-thought-out strategies for each learner. Educators must consider learners’ prior knowledge, confidence level, and motivation.

Make Sure Learners are Making Mistakes (while learning, not on summative assessments)

Recent brain evidence shows the value of learners working on challenging work and making mistakes. However, many learners are afraid of mistakes and think they are not math people. If mistakes are designed into the learning process rather than the grading process, learners will look to them as a way of learning rather than assessing their abilities. Research shows that mistakes cause more synapses in the brain and more growth.

Provide a Collaborative Work Environment

Feedback also needs to come from multiple sources, including peers, educators, experts online, and most importantly, self. Peer-to-peer feedback has been shown to increase learner understanding in both the learner giving feedback and the learner receiving feedback. Also, collaborative work environments provide for more detail in work produced and expected. Furthermore, collaborative work environments promote the usage of the 21st-century skill of communication.

How Do We Get There?

Don’t Think All or Nothing

Don’t think you have to change an entire course to match the math teaching style described. Chances are you already do a lot of what I described. If you make small changes and add more and more throughout the years, you will have a course that focuses on mathematical best practices. You can choose to modify a unit in a year or maybe one lesson a week. Like learning, teaching in new ways requires self-paced timing for educators. The comfort level and learning curve for teaching the prescribed way are different for each educator.

Have Backup

Make sure you have a support system in place to help you. I’m lucky enough to have an administrator that supports the way I teach and allows me to come to him if I ever need any help or ideas. Other educators (even in other subjects) can also be a great source of support.

Make Mistakes!

Don’t be afraid to make mistakes. Often educators avoid the possibility of making any mistakes not to create an ego disturbance. They view themselves in a certain way and do not want to try something new that would cause this view to be altered. As professionals, we must get over such discomforts for the sake of our learners.

Conclusion

Teaching math this way is rewarding, exhausting, and completely necessary. The world is changing more now than it ever has. We need logical thinkers, creators, and modellers of abstract ideas and concepts. Mathematics provides an excellent way of promoting those skills. We, as educators, need to make sure we teach it that way.

References

Hiebert, J., & Grouws, D. “The effects of classroom mathematics teaching on students’ learning.” N.p., 2016. Web. 21 Feb. 2016.

Bay-Williams, J. “Takeaways From Math Methods: How Will You Teach Effectively?” Edutopia. N.p., 2014. Web. 21 Feb. 2016. Cisco.com. (2016). Retrieved 22 February 2016, from https://www.cisco.com/c/dam/en_us/solutions/industries/docs/education/Multimodal-Learning-Through-Media.pdf

YouTube. (2016). e-Learning Affordance 4a: Recursive Feedback. Retrieved 22 February 2016, from https://www.youtube.com/watch?v=3LOjul-kJyc

Achievingthedream.org. (2016). Retrieved 22 February 2016, from http://www.achievingthedream.org/sites/default/files/resources/PathwaysToImprovement_0.pdf

Sciencedirect.com. “Modelling Reality In Mathematics Classrooms: The Case Of Word Problems.” N.p., 2016. Web. 15 Feb. 2016.

Koretz, D. M., et al. “The Effects Of High-Stakes Testing On Achievement: Preliminary Findings About Generalization Across Tests.”. Eric.ed.gov. N. p., 1991. Web. 15 Feb. 2016.

Wolfram, C. (2016). Teaching kids real math with computers. Ted.com. Retrieved 28 February 2016, from https://www.ted.com/talks/conrad_wolfram_teaching_kids_real_math_with_computers

Moser, J. S., Schroder, H. S., Heeter, C., Moran, T. P., & Lee, Y. H. (2011). Mind Your Errors Evidence for a Neural Mechanism Linking Growth Mind-Set to Adaptive Posterror Adjustments. Psychological Science, 0956797611419520.

Dweck, C. (2006). Mindset: The new psychology of success. Random House.

Youcubed at Stanford University. (2016). When You Believe In Your Students They Do Better. Retrieved 28 February 2016, from https://www.youcubed.org/think-it-up/when-you-believe-in-your-students-they-do-better/

Xkcd.com. (2016). xkcd: Forgot Algebra. Retrieved 28 February 2016, from https://xkcd.com/1050/

Mangels, J. A., Butterfield, B., Lamb, J., Good, C., & Dweck, C. S. (2006). Why do beliefs about intelligence influence learning success? A social cognitive neuroscience model. Social cognitive and affective neuroscience, 1(2), 75-86.

21st century critical thinking math mathematics problem solving teacher

Celebrating Pi – A Transcendental Number

The most beautiful thing we can experience is the mysterious. It is the source of all true art and science.”

– Albert Einstein

As an educator, I like to find as many reasons to celebrate knowledge as possible. So when I learned that March 14th is internationally recognized as Pi Day – because that date is 3/14, as the rounded pi number 3.14 – I was a little perplexed, to be quite honest. Why is a simple number being celebrated by so many people?

Sure, it’s always a good time to eat pie in school, which many educators already do every Pi Day. Most people are familiar with pi as the constant π derived from dividing the circumference by the radius of any circle. Pi helps us find the circumference and the area of circles; that’s useful. But is that all pi is good for – circles and a reason to delight in some delicious pies?

Dear reader, you’ll want to take a moment and brace yourself for this.

In mathematical calculations, we often use the shortened 3.14 instead of the irrational and infinite string of digits that π rebelliously is. Did you know it has over 1 trillion digits after the decimal point? Thanks to the invention of the computer (which stemmed from the root word compute because it performs calculations), mathematicians could get that far. However, they are still trying to find the next unpredictable digit in the sequence. Just as a teaser, here are the first 500 digits for you:

First 500 digits of pi

Facts About Pi

Before I give educators any ideas for pi-inspired activities to do with their learners, let me tell you a few amazing facts about pi that will be sure to enlighten you in a way no number ever has.

One doesn’t need to be a physician in signal processing to appreciate the usage of a cell phone. You should know that when your cell communicates with the local cell tower, it performs something called a Fourier transform. The equation for the Fourier transform is this:

the fourrier transform includes pi (Yes, that’s right. The value of π lives on in the innermost workings of your smartphone, somewhere, somehow.)

As human beings, we deal with the world on a large scale, often without knowing what is happening on an atomic and subatomic level. Frankly, we don’t always need to know how particles behave to live fulfilling lives. But many scientists do care and want to understand why things are the way they are, from the smallest possible details, and here is where quantum mechanics comes in. Quantum mechanics is the science of relating to the very small. In it, there is something called a Schrodinger equation, which describes how the wave function of a physical system evolves, represented as:

(Notice anything familiar? Intriguing, isn’t it.)

I’ll casually throw in one more mathematical equation about the General Theory of Relativity. Einstein’s “field equations” describe the gravitational effects produced by a given mass, represented as:

(Do you see what I see? Alas, it is π once more, creeping in here and there in unexpected ways. It’s everywhere!)

Could pi be a part of the universe’s fabric itself?

Celebrate Pi Day in Your Classroom

I could go on, but I think this is enough to spark your amazement at how a commonly used number like π is so incredibly mysterious. It’s enough of a reason to have an international Pi Day! And so, if you want some ideas on how to celebrate it with your learners in an educational manner (worry not, this does not replace the pie-eating component), here are a few suggestions:

Have learners measure circular objects in the classroom & calculate an experimental value for pi. You can use a string to measure the circumference and then align it to a ruler for the actual measurement before dividing the circumference over the diameter of each object. Don’t tell them what the theoretical value should be. Let them discover the pattern on their own!

Learners can experimentally find the value of π by graphing a line of best fit, calculating for the slope to find pi. Let them plot several coordinate points, with x being the diameter and y being the circumference. It is an opportune moment to bring linear regression lines and correlation coefficients to life!

Since the first six values of pi are 3.14159, on 3/14, at exactly 1:59 PM, sing a song about pi or make up your own!

Work on percentages by asking learners to solve a problem finding the percent increase in the area of a circular edible thing (pizza or pie) if the radius increases from 22 to 25 centimetres.

Talk about Albert Einstein!

You may be wondering, why should we talk about Einstein on this particular day? Besides the fact that pi is found in the Einstein field equations, suffice to say that Einstein was born on Mar.14, 1879. That’s right, folks: coincidentally, Pi Day falls on Einstein’s birthday.

Share the joy that only comes from celebrating the transcendental number pi.

Have a lovely Pi Day!

—–

References

http://mathforum.org/te/exchange/hosted/basden/pi_1001_digits.html

https://ck022.k12.sd.us/specialevents/piday.htm

http://scienceworld.wolfram.com/physics/SchroedingerEquation.html

http://mathworld.wolfram.com/EinsteinFieldEquations.html

http://curtiscenter.math.ucla.edu/content/pi_applications

Albert Einstein math mathematics pi pi day

The Mobile Mathematician: Math Apps to Multiply Success

How can math apps help learners multiply success?

It is not new knowledge that math is a hot topic in the 21st century. School boards have put forth great effort through professional development and curriculum resources to shift the direction and purpose of math education. When designing any lesson based on the curriculum, educators need to consider content knowledge, building, thinking, communicating, and applying knowledge. Over the past century, mathematics education has focused heavily on content knowledge building through rote learning practice. Learners then apply this knowledge through worksheets or standardized tests. Educators have exposed learners to math manipulatives for a long time, but these learning tools only supported learners’ success with standardized tests.

Mathematical Thinking and Communication Skills

Of course, math content knowledge and application have their place in learning and are important for learners to be successful. You can consider this knowledge as a building block towards high-order thinking. However, in the 21st century, the education system is seeing a dynamic shift from rote learning practices and tests to recognizing, encouraging, valuing, and assessing learners’ mathematical thinking and communication skills. With an importance placed on thinking and communicating, math in the 21st-century classroom looks a lot different. Educators are now encouraged to focus on learners’ development of new knowledge in math. This knowledge is not necessarily new to everyone. However, it is specifically a new understanding of math for the learner that developed it.

Tweet, “We should focus on learners’ construction of knowledge instead of just the consumption of knowledge.”

Problem-Based Learning

Educators are now implementing more inquiry-, project-, and problem-based instructional methods to support learners’ knowledge instead of just focusing on the consumption of knowledge. Problem-based learning seems to be one of the more prominent choices for collaborative mathematics instruction. It begins with educators posing a question or problem that learners then work in pairs or small groups to solve. Problem-based mathematics aims for learners to construct their own methods and strategies for solving problems. It leads to new knowledge within the group. After learners develop strategies to solve the problem, educators usually hold a whole class congress. Learners share and compare their different strategies and discuss ways to improve each other’s strategies.

As you can probably see, mathematics education focuses more on the learning process than the product. Educators assess learners throughout their math strategy development and large group explanations. While this type of mathematics learning is progressing, learning resources need to fit the 21st-century learner. Learners today respond and are motivated differently than their predecessors, and educators need to consider this when developing their mathematics lessons. The current generations of learners have developed skills to manipulate technology to support their learning. Today’s learners are more motivated by and prefer to learn through interactivity and multimodality within digital technologies.

Tweet, “Today’s learners are motivated by interactivity and multi-modality within digital technologies.”

Digital Touch-Based Technologies

Research has also demonstrated the unique affordances of digital touch-based technologies like tablets to enhance 21st-century learning like problem-based learning. Apple iPads are specifically unique in their lightweight portability, the wide array of apps, unique touch-screen interface, simplicity, intuitive design, speed, and affordability compared to other tablets brands. With these features, tablets can enhance a blended learning approach by making learning accessible anytime, anywhere. Moreover, digital touch-based mobile technologies, like tablets, can support multimodality and learners’ development of 21st-century literacies and skills.

The following provides an overview of mobile technology apps that enhance mathematics instruction in the 21st century with this context in mind. It is time to produce Mobile Mathematicians!

Math Apps for Problem-Based Learning

It is common practice for educators to give out chart paper as a platform for learners to work out problems and record their strategies. However, since most classrooms have 20 to 30 learners and one educator, it can be difficult to go around the room and record learners’ thinking and communications. The educator may miss important conversations between learners and does not always capture the full process of how learners work through problems collaboratively. It can also be difficult to capture how learners are testing different strategies and finally settling on a strategy to solve the math problem.

Screencasting Apps

Different apps have been developed with mobile technologies like tablets to capture learners’ thinking and communications. These apps are commonly referred to as screencasting apps. Screencasting apps resemble mini interactive whiteboards within the tablet. Learners can use multiple modes within the screencasting app, such as drawing tools, picture uploading options, typing tools, and an audio recording tool. Now, this does not sound much better than what you could capture by just viewing learners’ work on chart paper. However, screencasting apps capture these modes throughout the process as learners use them.

Educators can have learners press the audio record option right away. The app captures learners’ conversations and screen interactions simultaneously. The screencasts playback to educators like videos as learners progress towards their final product. Educators can play the combined audio and video file with screencasting tools to see learners’ whole progression towards their final product. That can be extremely helpful when assessing learners’ thinking and communicating.

Furthermore, since learners usually share their work in a whole class congress, learners can play the screencasting videos for other groups to watch. With this type of technology, learners do not need to try and recount everything they did to form a math strategy and solve the problem. Rather, other learners can see the whole process in action. For shy learners, screencasting videos provide an additional opportunity to share their voices without the intimidation of speaking in front of a large group.

Here are some examples of great screencasting apps:

Apps as Math Manipulatives

Hands-on learning is imperative throughout learners’ learning process. However, hands-on learning does not always mean manipulating concrete objects in the digital era. Many educators use concrete manipulatives to demonstrate concepts and further have learners practise these concepts. However, keeping in mind that learners today have a natural and intuitive ability to manipulate and respond to technology, it seems more appropriate to have learners practicing and working through problems with digitally enhanced manipulatives. Digital manipulatives provide learners with the opportunity to touch, slide, and tap in a hands-on manner. However, this process happens in a digital environment potentially better suited for digital natives.

With mobile technologies such as tablets, learners can move more fluidly between screencasting apps and readily accessible math manipulatives while solving math problems. The portability of the tablet also enhances the use of these digital manipulatives. Learners can easily rotate the tablet to show what they have done with manipulatives. They can easily carry the tablet to the educator or another peer to inquire and ask for feedback on what they have done. This process would be much more difficult with regular concrete manipulatives.

Here are some fantastic math manipulative apps:

Manipulatives have gone digital! Furthermore, many math manipulative apps have built-in lessons to enhance self-directed learning through a blended learning model (i.e., Brainingcamp math apps). Learners can use these apps to support strategy development and problem-solving within groups during problem-based learning activities.

Apps to Support Math Content Knowledge Building

Educators mustn’t eliminate the components of math content knowledge building. Learners need to be equipped with general knowledge and understanding of math content to have the tools to tackle different math problems. Math content knowledge building is a prerequisite for math knowledge construction. Tablet app developers have developed a slew of rote learning apps to support general math content knowledge.

However, educators need to take a step back and not be too eager to download these different math apps. Educators need to look for certain features to support a blended learning model for math education. Math apps for content knowledge building need to ensure self-directed learning through scaffolding and immediate feedback features. Furthermore, personalization features like setting up separate student accounts enhance the educator’s ability to modify math instruction for varying levels. Built-in reward systems will further encourage student motivation and self-directed learning.

Educators need to ensure that the features mentioned above are built into math content-knowledge building apps so that effective 21st-century instruction can happen. Educators can spend less time teaching content through traditional teacher-directed methods with more self-directed and personalized apps. Rather, educators can spend more time encouraging student knowledge construction, strategy development, and problem-solving skills. In junior, intermediate, and senior grades, learners can access and use content knowledge building apps at home so that even less teacher-directed instruction happens in the classroom. Math content-knowledge building apps include games, instructional videos, or instructional videos with built-in math manipulatives and interactive activities.

Here are some examples of math content-knowledge building apps:

Prodigy

Prodigy app is an interactive math game that resembles Pokémon for primary, junior, and intermediate learners. The app learns learners’ math skill levels and provides appropriate math questions based on learners’ math abilities. It also has personalized student accounts, built-in manipulatives for learners to access when answering questions, reward systems, and immediate feedback to scaffold learners’, correcting their answers and learning from their mistakes.

Check out this blog post on Prodigy: Are YOU Ready to Make Math Magical?

MyBlee

MyBlee is an interactive app for learning math content within instructional videos. The instructional videos, however, go beyond traditional videos. Learners learn through a gradual release of responsibility by watching demonstrations, practicing with digital math manipulatives, and applying knowledge through rote learning activities. MyBlee also provides immediate feedback to scaffold and correct student learning. It has multiple reward systems, personalized student accounts to support differentiated levels, and extra manipulatives for learners to access when needed.

Check out this blog post on MyBlee: Self-Directed Math with MyBlee

Math Planet by Playpower

Math Planet is a math game app where primary and junior learners can learn through different levels based on different math strand concepts. Each level comprises fractions, number operations, geometry, and other number sense and numeration activities. As learners work through the activities, they move on to different levels or ‘planets.’ This app has a great reward system and motivating features. However, there are limited scaffold features and no readily accessible manipulatives for learners to support learning.

Check out this blog post on Math Planet: 1, 2, 3…BLAST OFF to the Math Planet App by Playpower

Learning Bird

Learning Bird is a mobile-friendly web app offering a wide variety of instructional videos on all curriculum strands for learners in grades 6 – 12. There is an abundance of math instructional videos that you can connect to the curriculum directly. Educators can group math videos on specific concepts into playlists for learners to watch anytime, anywhere. Learning Bird provides each student with their own account, and the variety of videos you could choose for a playlist can support differentiated instruction. Furthermore, educators can assign learners working at different math levels resources geared towards their math abilities.

Conclusions

Learners need to understand the why and how of mathematics and its real-world application to become 21st-century mathematicians. Therefore, 21st-century math classrooms must utilize tools that encourage learners’ engagement in problem-based learning activities, scaffold student learning and provide the math content knowledge needed to build new knowledge. Mobile technologies like tablets will equip learners to build 21st-century skills like critical thinking, collaboration, communication, computer and digital technology skills, and creativity. Essentially, learners will become 21st-century Mobile Mathematicians!

math mobile tablets

Why Pop Culture has a Place in the Classroom

Comic books can bring pop culture into the classroom.

Incorporating pop culture and media into the classroom is a divisive issue amongst educators, and not without reason. While pop culture has its benefits, it could be distracting if integrated inappropriately. It can also be intimidating for an educator to relate to learners of a different generation without feeling out of touch.

However, the benefits of teaching using popular media are substantial. It helps engage learners, brings lessons off the page, and addresses controversial topics. Furthermore, it could be a fun lesson for the end of the semester or a light distraction during tense academic periods.

Why should educators include pop culture in the classroom?

“We cannot sit back and let our students passively digest the material. No, instead, teachers should actively engage students in discussions about the controversial material bombarding them,” Mark Hauser wrote in EducationWeek, rallying educators to stare down music with inappropriate themes rather than shy away from it.

Hauser notes, correctly, that “clean” versions of popular songs mask the profanity but don’t modify the inappropriate themes that come with the chosen language.

The net result is that learners believe the moral shortfall is in specific profane terms. However, the overarching theme of the content is more damaging to a student’s life view.

Pop culture provides a great jumping-off point for discussions on ethics, morals, and current world events regarding controversial themes.

Music, movies, and entertainment inspire richer discussion than news articles. Articles require a reader to see a rolling coverage to understand and engage on the topic.

The educational consultant’s other resounding point is that pop culture lessons help educators meet learners in the middle. They relate to each other in ways learners understand. Educator Clay Morgan endorses this point.

“Lucky I know about zombies,” he petitions before detailing how he used the 2009 film Zombieland to explain the Morgenthau Plan. This strategy made a bored class come alive.

The Morgenthau Plan sounds like something dry in a heavy textbook, perfect for closing and taking a nap. Introducing the topic through the Zombieland rules of zombie apocalypse survival, in this case, Rule #4, “The Double Tap,” as Morgan does, can draw more interest from the outset.

How should educators include pop culture in the classroom?

Would Benjamin Franklin be a Facebook user? How would Abraham Lincoln’s presidential campaigns look on social media? What would the Great Fire of London or the toppling of the Roman Empire look like on Twitter?

Teach learners a lesson about digital media while deeply exploring historical figures and events. Have learners create social media accounts for important figures and events.

The task calls upon digital literacy and storytelling elements that they feel comfortable with while challenging them to think critically about history and social media.

It can be daunting to incorporate music lyrics and movie references for an educator from a different generation than their learners. Educator Tim Weedon, however, provides a three-step framework for educators using pop culture in their classrooms.

Stage 1: Prep

Weedon begins by casually asking learners about their tastes in music (his pet area of interest). He then analyzes the responses from his learners for relevance to topic areas covered in the curriculum course. Weedon pays close attention to lyrical content and themes, ensuring they fit the class’s age.

Stage 2: Development

Using pop culture in group activities is a great way to break the ice in a new class. Weedon suggests assigning learners reading and developing song lyrics/poems in groups. You can read a full breakdown of his lesson plan on Development Education.

Stage 3: Practice

Primarily useful in teaching literature analysis, Weedon asks learners to analyze their favourite song lyrics and how they would be relevant to the course.

The educator subscribes to the same view as Hauser on any inappropriate subject matter. He says, “It is better to discuss the text rather than avoid the subject matter without offering any educational choices or advice.” He does, however, state that he looks closely at the chosen songs and doesn’t guarantee their use.

Once they have decided on their topics and songs, they break down the song structure through vocabulary, spelling, grammar, punctuation, sentence structure, and linguistics.

A popular and effective format for lessons is song. Educators use the melodies of well-known songs or match a popular style to teach a lesson. It takes confidence, but it is fun for educators and makes content incredibly catchy and memorable for learners when done well. I’ve been singing math lessons in my head all day on more than one occasion!

There are many resources to guide you through using pop culture in your teaching. It’s an element of pedagogy that can give an edge to your teaching and provide a deeper reference to content. Join one of the many communities online, connect with educators on social media, or dive into music, movies and tv. It isn’t as intimidating as it seems.

These are some great resources for you to explore incorporating pop culture in the classroom:

Browse Tim Weedon’s full series here: https://developmenteducation.ie/feature/exploring-popular-culture-in-education/

Visit the Popular Culture Pedagogy Facebook page: https://www.facebook.com/popculturepedagaogy

classroom edtech education English history lesson plan math music pop culture school social media

Blogging as a Cross-Curricular Teaching Tool

As technology increasingly becomes a part of schools and classrooms, we must use these tools in the best possible manner. One of these practices, becoming more and more popular, is blogging as a teaching tool.

The Practical Applications of Blogging

There are many reasons why an educator would start a class blog and many insights a learner could gain from the practice. Blogs can help boost literacy & critical thinking skills. They can bolster a learner’s digital skillset, be a hands-on lesson on navigating the online world, and foster deeper learner engagement with a topic.

There are many platforms your classroom can use, from WordPress to Weebly to Tumblr. However, before you get to that stage, you need to create a code of ethics for your learners online. You can create the code of ethics collaboratively with the class and sticky the post to the top of your blog, which acts as a lesson hub.

Okay then, let’s dive right in!

Whether you teach English, math or science, elementary or high school, you can be creative in having your learners blog to enhance their learning experience. In particular, blogging emphasizes cross-curricular, outside-the-box thinking. Here are some suggestions.

English language arts

Reflections on Readings

During class discussions, you probably have a handful of very eager learners discussing the book or article you assigned. What about the quieter learners? Some learners are not comfortable sharing their opinions out loud. Further, this can be a paper-free way to keep track of learners’ assignments & journal entries.

Essay of the Month

Miriam Sullivan & Nancy Longnecker studied class blogs as a teaching tool to promote writing and student interaction. According to their study, most learners agreed that they write better when they know other learners will read their posts. Why not use this (positive) peer pressure to motivate learners to write well? An essay can be highlighted as “essay of the month” and shared with the wider community!

Cross-Curricular Idea

There are oh-so-many possibilities for an English class to get creative with blogging. Just check out this awesome blog about idioms blending ELA, Art and ICT competencies by Jenny Young!

Science

Scientific Papers

A key part of the scientific process is for scientists to communicate their findings with peers through scientific papers. This “communication to other scientists ensures that new findings become part of a growing body of publicly available knowledge that informs how we understand the world around us.”

But what about your learners who write papers? What is their end goal besides a grade? If it’s not published in a journal, how can the educator motivate learners to increase their science literacy?

The answer you may have guessed is to go ahead and publish it on a blog. It is also the perfect way to practice and demonstrate the peer review process, a crucial stage of scientific publishing.

Lab Reports

If your learners have a lab exam at the end of the year, you want them to recall the experiments they did over the year and understand them. While handwritten or typed lab reports are the norm, another possibility is to have the learners write them up on their blog. The additional factors of other learners in the virtual world being able to access their results and upload step-by-step images of the experiment make their experiment more repeatable. It is a great opportunity to get into how the scientific method is carried out in the real world, that “scientists must be able to read anyone else’s report, follow the steps exactly the same way, and compare their findings to the original test.”

Cross-Curricular Idea

Use blogging as one means of using art in the science classroom. Learners learn the names of so many scientists, like Einstein, Coulomb and Newton, but who were these people? Have learners use their digital literacy skills and learn some interesting history by creating a video or recording a song about these great minds, then posting it online!

Math

All in Order

There is nothing like a blog to share your digital lessons with learners and caregivers. Use blogging to keep them all easily in the loop about upcoming assignments, recommended links for extra practice, and even share fun videos to enhance the learning experience!

How else would you use blogs as a teaching tool? Let us know in a comment below or tweet @learningbird!

Blogging classroom edtech education English math science students teachers teaching wordpress