CG50 – What Are All Those Apps?

As many of you know, I post quick videos in the blog to show different things about the Casio calculators or math or teaching. Many of these are posted on my YouTube Channel. I will occasionally get comments from viewers asking questions, and I do my best to answer them. If I can’t answer the question, I find someone who can, or research until I do have a response. Just the other day, when I was asked “how do you use the constants on the CG-50 calculator”, I was not quite sure what was being asked, since I tend to use the calculator from a mathematics teaching perspective, and hadn’t explored using constants (from a science perspective) and wasn’t even sure what was meant by the ‘constants’ in this particular question (as it could mean the constants in a given equation).  Turns out the viewer was asking about the Physium Menu/App on the calculator, and how to get the constants from these tables and values into calculations. This is something I have honestly never used because I am not a science teacher and therefore rarely, if ever, have need for this app. But – it got me curious and seeking out an answer (which I did find and explore so I could give a reasonable answer).

In my ignorance, I realized that there are many apps on the CG50 (and other Casio graphing calculators) that I have never really explored, not just the Physium App. Mostly I focus on the most-used menu items – Run Matrix (to do calculations), Graph (to work with functions and graphs), Table (functions using table representations), Equation (solving equations), and Picture Plot. But there are a lot of other menu items that I need to explore and learn to utilize since they all are useful for different contexts and applications. This is now a goal of mine – to try to learn and explore the basics of the other menu items (apps) of the CG50 (and other) graphing calculator, starting with the Physium Menu/app. Here’s what I have discovered:

The Physium application has the following capabilities (so science teachers, take note!!)

Periodic Table of Elements

  • You can display the periodic table of elements
  • The table shows the elements atomic number, atomic symbol, atomic weight and other info
  • Elements can be searched for by element name, atomic symbol, atomic number or atomic weight

Fundamental Physical Constants

  • You can display fundamental physical constants, grouped by category to make it easier
  • You can edit the physical constants and save them as required
  • You can store physical constants in the Alpha memory and use these saved constants in calculations in the RUN-MAT menu/application

Now, I am still not a science teacher, so this would not be a menu item I will use often, but I wanted to do a quick video of what I discovered in my own exploration.  And – there is a link to the how-to guide for the Physium Menu/App for those of you interested in exploring more. If you have a CG10 or other graphing calculator from Casio and don’t have the Physium menu/app, you can download it here.



Elevators and Number Sense

Number sense should develop early, and what simpler way to do it then to start with elevators?

Elevator, Vicenza, Italy

Why elevators you ask? Well, I just returned from 2 weeks in Italy. Partly for work: training elementary math teachers in Vicenza, Italy on College & Career Ready Standards for UT Dana Center International Fellows and Department of Defense Education Activities; and partly for leisure: touring Venice, Cinque Terre, Florence, Tuscany and Rome with my husband, sister, and brother-in-law. The first thing I noticed was the elevators have negative numbers to indicate those floors below ground zero (i.e. what we usually call floor 1 or Lobby in the U.S.)   It’s not the first time I’ve noticed this – in England, in Paris, in Germany – all these other countries indicate on their elevators the ground floor to be 0, the floors above ground 0 are 1, 2, 3…. and the floors below ground zero are -1, -2, -3….

This way of numbering elevators makes sense. Much more sense than Floor 1, or Lobby and then Basement, Basement2 (or LL1, LL2) – which is our typical way of indicating the ground floor (1) and the floors below ground level (Basements/Lower Levels). If you were a young child living in these countries and taking the lifts (or elevators), you are regularly exposed to integer numbers – with a contextual connection that the ground floor of a building is ground 0, and the floors below the ground are negative numbers, and the floors above the ground are positive numbers. It may not even be explicitly explained to young children, though they would be using the terms ‘negative 1’ or ‘negative 2’ to go down below the ground floor. They will have this repeated exposure so when they are ‘officially’ taught about negative numbers in school, they have an immediate connection to prior knowledge about the numbers in an lift/elevator and can make a real-world connection. Negative numbers won’t be new or hard to understand because it’s just the numbers in the elevator. Or – the numbers of the temperature, because let’s not forget, these countries also use the Celsius temperature scale, where freezing is 0, and anything above 0 degrees is above freezing and getting warmer (positive) and anything below 0 degrees is getting colder (negative). The further from 0 in either direction, the warmer or colder you are – again, real-world connection and a contextual understanding of integers.

Number sense. Number lines. Integers. Real-world connections. Just from elevators and temperature scales.

This repeated exposure, informal as it may be, is developing an intuitive understanding of numbers and their real-world meaning. And when students are then exposed to number lines and positive and negative numbers more formally, in a school setting, they already get what that means because it is familiar to them. They can apply what they already know to ‘mathematics’. The formalization makes sense, and connections make sense, and understanding is that much deeper.  This is different in the U.S., where students often struggle with the idea of ‘negative’ numbers and number lines and the distance from zero because we are teaching them something new.  We don’t have a real-world exposure to negative numbers because we use LL or B1 to represent lower than 0, our ground floor is never called 0, it’s 1 or Lobby or G (ground). Our temperature doesn’t have 0 as the freezing mark – it has 32 degrees Farenheit. Think how much easier it would be to connect negative numbers (those numbers smaller than zero) to negative floors or negative temperatures. Freezing makes sense at 0. Negative temperatures are colder than freezing. Positive temperatures are warmer than freezing. 32 degrees – not quite the same one-to-one connection to a number line, is it?

Anyway – my point is that something as simple as changing the numbers on an elevator to integer representations would go a long way in helping young children develop number sense early on so that by the time they get to school, they already have a natural understanding of positive and negative numbers. Early on they would be exposed to the idea of 0 being the ground level, positive numbers mean higher floors or farther away from ground zero, and negative numbers mean lower floors, below the ground, and the further you go below ground, the more negative you get, the farther away from zero you are. Number lines would then be ‘recognizable’ because there’s a contextual connection. (If we could change our temperature scale to Celsius that would be great too, though that one is a lot harder to do).

Relabel elevator buttons to reflect numbers on a number line – a simple change that could go a long way in developing informal number sense in children.



Graphing How-To – Hyperbola & Asymptotes on the CG50 Prizm

I realized I haven’t posted a ‘how-to’ video in a while, and, with this being the end of summer, there might be some students and/or teachers out there trying to learn some new skills before the school year starts up, hence this post. Why hyperbolas? No reason other than it helps highlight the Conics menu and I love the way it looks! My plan is to try to do some more how-to’s on a monthly or bi-weekly basis, especially as school starts up, so if there is a specific topic you want to explore, please let me know, as well as a specific Casio Calculator. There are several how-to videos out there already on my YouTube channel and Casio’s YouTube Channel, but if you have a specific content/calculator in mind, I will do my best!

The video below models one of the problems in our free Quick Start Guide for the CG50 (our newest version of our colored graphing calculator) on how to graph a conic section, in this case a hyperbola, using its equation, and then from that, finding its asymptotes, coordinates of the vertex, and the coordinates of the foci. This will be a nice example of how to use the Conic Menu option on the CG50 graphing calculator as well as our other graphing calculators, since the steps are the same.


Problem: Construct the graph of the conic section given by this equation: . Once graphed, find the asymptotes, the coordinates of the vertices and the coordinates of the foci.

Access & Equity in the Classroom – A Teachers Role (Equity, Equality, and Access to Quality Education -Part 3)

This is the 3rd installment in my 3-part series on equity, equality and access to quality education. Here are links to Part-1 and Part-2, where I first define these terms and then I talk about funding issues that impact access and equity. As noted in Part 2, funding is a huge component of why schools and districts don’t provide equitable access to support student needs, and why low-economic areas tend to have inequitable education experiences and poor access to the supports and resources needed to help all students learn and achieve, based on their individual needs.

As a teacher, school funding is out of our hands for the most part (except for the personal funds we all spend to make sure the students in our classroom have resources and support). Parents and community leaders need to take a really close look at the money teachers spend out of their own pockets to address some of the inequities within their own classroom and school – it’s not right, it’s not fair and there needs to be more push-back on education policy and more support from local businesses, community advocates, and state and local school boards to ensure that schools that need funding and resources are getting those in an equitable fashion (remember, not equal, but equitable – all schools do not need the same). Teachers will spend their own money, even when they have very little, because they care about their students and what happens in their classroom, but they shouldn’t have to.

But, I digress.

What I want to talk about in this post is what teachers can do in their classrooms to address equity and access to quality education. Teachers, even without adequate funding, resources and support, are the most able to provide equity and access for the students in their classroom because that is where the learning happens. And it’s the learning, it’s the teaching strategies, it’s those interactions and learning experiences that can provide equity and access for all students. Let’s remind ourselves about what equity and access means – it means each student getting what THEY need to learn, meaning they have access to rich learning experiences and teaching that provides them with the support they need to understand the content, to think, to make connections, to apply that learning, and to achieve to their potential. To learn, despite their gender, their race, their socio-economic status, or their disabilities.

I can only speak from what I know, so I am going to take a mathematical approach to equity and access in the math classroom, but even if you are not a math teacher, these ideas and processes work in your classrooms as well, with the only difference being in the content.

NCTM (National Council of Teachers of Mathematics) has a position for what it means to have equity and access in the math classroom, so I am including it here (this links to the full article):

Creating, supporting, and sustaining a culture of access and equity require being responsive to students’ backgrounds, experiences, cultural perspectives, traditions, and knowledge when designing and implementing a mathematics program and assessing its effectiveness. Acknowledging and addressing factors that contribute to differential outcomes among groups of students are critical to ensuring that all students routinely have opportunities to experience high-quality mathematics instruction, learn challenging mathematics content, and receive the support necessary to be successful. Addressing equity and access includes both ensuring that all students attain mathematics proficiency and increasing the numbers of students from all racial, ethnic, linguistic, gender, and socioeconomic groups who attain the highest levels of mathematics achievement.

This means that all students should be engaged in real-world learning, problem-solving kids-girl-pencil-drawing-159823experiences, and applications of the content. These types of learning experiences are not just for those ‘advanced’ students. This means providing opportunities for students to engage in collaborative learning, where they are communicating their thoughts and ideas with others, where they are taught and allowed multiple approaches and multiple solutions, where they have supports (i.e. questioning by the teacher, partnering with others, hands-on materials, technology/visuals, etc.) that might help them make connections or get to that next ‘aha’ moment.  Lower-performing students shouldn’t be relegated to doing drill & kill worksheets and ‘remedial’ math classes where the focus is on test-taking strategies and memorization, but rather should be exposed to the same challenging problem-based, inquiry approaches as the high performing students, but with different supports to help address their needs (so scaffolded questions, or suggestions on strategies, or working with a partner, etc.).

A large part of this equity and access means teachers need to BELIEVE that ALL students can achieve and learn, with the difference being that some need more supports than others. I can’t tell you how many times I hear, “well, my lower-level students can’t do that” or “my students won’t talk or show me different approaches” or “my students will just wait for the ‘smart’ ones to do all the work’ or “my students have a hard time reading so we don’t do word problems” or “my students will just give up or just ask me to show them the answer”. I could go on, but I think you get the point (and have perhaps made those same comments yourself). It becomes a self-fulfilling prophecy if you think this way, try something once and it ‘fails’, and therefore you don’t do it again – and then you and the students believe they can’t learn, or they can’t talk, or they can’t solve problems, etc. This is where inequity becomes a huge issue in classrooms – because we then resort to teaching students the ‘one way’ to do things (i.e. often the ‘way that’s on the test), and those students who need a different approach or who can’t memorize, can’t ‘perform’ or ‘achieve’ because they are NOT getting what they need to learn, and the cycle continues. To promote equity and access within your own class, you need to do some planning, some hard work up front, and be consistent – but it can change how you teach and how students learn so that all your students are getting what THEY need to learn. As a teacher, this is your responsibility within your own classroom.

cute-children-drawing-teacher-preschool-class-little-40195392Here are some suggestions:

  1. Starting day one, begin creating a classroom culture that promotes communication, collaboration, and respect. Students need to ‘learn’ how to talk with each other and listen to each other – so practice getting them in and out of groups, sharing ideas (start with non-academic sharing first, like ‘what’s the best movie you saw this summer and why”), working with partners and presenting their thoughts. Practice respectful listening. Practice and model appropriate responses when someone might make a mistake (mistakes should be accepted as part of the learning). There are several places to go to help you learn some collaborative teaching strategies – this is a nice list of articles with good tips.
  2. Learn to ask questions instead of giving answers or telling students they are right/wrong or yes/no. Simple questioning skills force students to start thinking, communicating, making connections, asking their own questions. Again, many resources out there to support questioning skills and provide some sample questions (“Why” is always a good one, or “Can you explain?”). Here’s one resource.
  3. Set high expectations and be consistent with those from day one. Expect students to not only show their work, but to explain their thinking (write out in words or draw pictures or explain verbally). Model this when you teach or show things to students (think-out-loud is a great way to model this type of behavior in mathematics class). Consistency is important!
  4. Provide problem-solving strategies from the beginning so that students realize that they have multiple ways to approach an unknown problem or situation. These are great strategies to incorporate in those first couple weeks of school and then to reference as they come up the rest of the year. And yes – even elementary students need problem solving skills.  (Notice & Wonder should become a habit of mind for all students, no matter the age because it provides that ‘think time’ and that ability to try and connect to prior knowledge and use what you know). The Math Forum is a wonderful resource for learning about the strategies and for getting problems to use in class.
  5. Expect and allow for multiple ways to approach math problems. As long as students can justify what they did and it is mathematically sound reasoning/thinking, it should be okay. This is probably the single most important piece to equity in the math classroom – allowing students to solve problems multiple ways, using the strategies and methods that work for them, and allowing for multiple solutions/solution pathways. This is the hardest thing for teachers i think because we ‘know’ the ‘right’ way – but the right way is not the only way, and some students may never get the ‘right’ way, but they have a way and it gets them there and that should be okay AS LONG AS THEY EXPLAIN THEIR THINKING (see #3). To make this work, see #4.
  6. Provide interesting learning experiences that promote thinking, multiple pathways to a solution, even multiple solutions. You will not get students working and communicating if you give them a worksheet with 30 process/skill based problems. You need to find interesting, relevant, problem-solving experiences that engage all students, that allow all students, no matter their ‘ability level’, a way to start thinking about solving. These types of problems should require previous math content knowledge and/or applications of new math content, require some analysis… think rich tasks.  There are many resources for interesting problems out there – content-related too – (Math Forum, Mathalicious, YummyMath, Illuminations, links to other resources)
  7. Less lecture, more inquiry, student-based learning. Hands-on, visualizations, student questioning, student explanation. This does not mean you need to have a different activity for every student – that would be exhausting. You need to find learning experiences that address your content that allow all students a way to ‘enter’ the learning from whatever level they are at.

Teaching one way and expecting the ‘same’ approach for all students, no matter the level, will always leave some students behind and others stagnating.Our teaching should always be focused on the standards and content, with the way we structure the learning and the way we allow students to demonstrate their understandings providing the differentiation that will let all students achieve – those who are ‘behind’ learning to catch up and those stagnating able to move ahead and explore. The more students can connect with, engage in, and explain mathematics using what they know  and building on this knowledge, with the teacher guiding them to deeper understanding through questioning, modeling, and supports as needed, the more equitable the learning becomes.

Solar Eclipse 2017 – Resources and Links to View (and Use in Math/Science class….)

I think by now most American’s are aware that there is a full solar eclipse coming on August 21. I have friends traveling to different parts of the country (Wyoming, South Carolina) just so they can see the complete eclipse instead of just a partial. It’s big deal. There has been a lot of talk about how to view the eclipse safely – yes people, you can damage your eyes and/or go blind if you look at the eclipse without some type of protective eye wear unless it is in complete totality (i.e. the sun is completely covered by the moon). If there is even a sliver of sun showing, eye damage is possible, so why risk it? Apparently there is a shortage of eclipse glasses – and regular sun glasses don’t cut it. Later in this post I will provide a way to make a device to see the eclipse without looking directly at it for those of you who did not jump on the eclipse glass ordering craze!

This is a rare occurrence and there are many sites and resources out there to help collect data, track the eclipse, watch it live streamed. I’ve compiled a list of sites and resources that provide lots of options that you can use personally or use with students. Lot of math and science questions and connections that can be made!

  1. Space.Com – lots of links here to where to see the eclipse, how to track it, how to livestream, safety, etc.
  2. State-by-State Map – also Space.Com but the slide show focuses on time and where to see the eclipse by state
  3. Also shows where, when and how, with some great visuals and suggestions for safety
  4. A great resource – click on the different links to prepare, find maps, discussions on what an eclipse is, etc.
  5. Science Space Institute – they have an app that will allow you to explore real-time images of the solar eclipse
  6. Astronomy Magazine – 25 facts about the solar eclipse – (good resource to use with students!)
  7. – very cool map that if you click on it (path of eclipse) it will show date, time, location
  8. USA Today – lots of resources here, with an important one – the FAKE eclipse glasses that have gone on the market – beware!
  9. The Washington Post – some fun facts about the sun, moon, eclipse – great for students
  10. Sky & Telescope – lots of links to where, when, education resources all connected to the eclipse
  11. Eclipsophile – interesting facts about each state in the path of totality – great math/science stuff here!

As you can see, there is a plethora of information on the solar eclipse out there to explore, much of which for you teachers out there, can become some really interesting math and science exploration and discussion.

Let’s end with some links to making your own SAFE eclipse viewer, because again, you do NOT want to look directly at the eclipse, especially partial, with the naked eye. Indirect viewing (or watch it livestream via some of the links above). Here are a few different links that show different ways to create your own eclipse viewers, and I have included a video at the end as well.

  1. NASA – using things from around your house (well, only if you have binoculars)
  2. National Geographic – uses stiff pieces of white cardboard. This is designed for use with students.
  3. – pinhole box (so need a box, duct tape, scissors, white paper…)
  4. – this involves carboard and a camera (those of you wanting to take pictures)
  5. USA Today – this involves a cereal box, aluminum foil, scissors, white paper – simplified pinhole box
  6. Exploratorium – this has several methods, and even has the same scientist from the NASA as one option
  7. Youtube – lots of videos on youtube on how to make an eclipse viewer.  I liked this one because it was simple and efficient.

Below is a video on making your own eclipse viewer. I chose this one because it was simple and uses items easily found around the house:

The Access Formula – (Equity, Equality, and Access to Quality Education – Part 2)

In last weeks’ part 1 of this series on equity, equality, and access to quality education, I defined access to quality education as “the ways in which educational institutions and policies ensure—or at least strive to ensure—that students have equal and equitable opportunities to take full advantage of their education. Increasing access generally requires schools to provide additional services or remove any actual or potential barriers that might prevent some students from equitable participation in certain courses or academic programs.” Access then encompasses many aspects of education, from funding, to resources, to programs and services that help ensure that all students are getting an equitable education (what they need to support learning).

Obviously, all school districts and schools strive to provide access to needed services and supports for their students. There are federal laws in place designed to ensure that all students are getting access to equitable education and getting supports they need. The Individuals with Disabilities Act (IDEA) is a law that all public schools must adhere to, which ensures that students with disabilities (including learning disabilities) have access to the least restrictive educational setting, have rights to ensure they get the services they need to support their learning, and parents can have a say in the educational decisions made regarding their students. An example of this from my own teaching is having an interpreter in my math classes that signed for the deaf students in my classes, or a student with an IEP (individual education plan) who needed copies of my notes because they had a learning disability that interfered with their ability to take their own notes. There is also Title I Laws and Funding, specifically designed to address low-income and disadvantaged students and ensure that schools that serve these students are getting the funds they need to support achievement, through things like extra academic supports for reading and writing, pre-school and after-school programs, with the goal to improve achievement on state standardized testing. I won’t go into all the details (link provided gives more information), but the idea here is to provide additional academic supports to low-income& disadvantaged students who are struggling academically. There are no federal laws that pertain to gifted students needs, though there are individual states and local schools that provide resources and supports for gifted education, but it varies by state.

As you might surmise, there is definitely an attempt to provide access to equitable education. But what’s the reality?

From my own experiences, access is NOT equitable. I would wager in most school districts, there is a huge disparity between what resources are available and the quality of education received at various schools within the same district and between districts within the same state. I have worked in many urban school districts where one middle school has low-achieving students at computers every day in math class, working on computer programs designed to support their mathematical skill development, and the other middle school down the street barely has enough rulers for the 42 students in the class, with a teacher who just has one computer and projector and a room full of ELL students speaking 5 different languages. Same school district. Not equitable access to resources. Not equitable learning environments or supports.

This is NOT an isolated situation, as I am sure many of you have experienced similar situations personally, whether as an educator or as a parent. Why is there such disparity when there are laws designed to ensure access to equitable resources and education opportunities?

The obvious answer is funding, which is a huge factor in access discrepancies. While everyone thinks funding for schools comes from federal money, federal funding makes up only 8% of public schools funding, so those TitleI funds and IDEA funds only accounting for a very small portion of education funding overall.  92% of funding for public schools comes from the states themselves, from taxes, lottery receipts and other sources, and a large portion from local property taxes. This means two school districts next to each other, one with a lower-economic base and less property tax, and one with a higher-economic base and more property tax, are going to have vastly different educational funding and resources. High-poverty schools spend less per student, and often have a more difficult time keeping quality teachers because of the disparity in available resources and services. It’s a vicious cycle. Many of the problems come from the way states/school districts apportion school funding, using different funding formulas that from the outset are ‘unfair and unequal’:

In a separate report, “Is School Funding Fair? A National Report Card,” the Education Law Center answered its own question with a resounding “No.”  Among the findings:

  • Fourteen states, including Texas, Pennsylvania and Illinois, have “regressive” school funding, defined as providing less money to schools with higher concentrations of students from low-income families.
  • In 19 states—including California, Florida, Colorado and Washington—the funding systems are defined as “flat,” meaning they “fail to provide any appreciable increase in funding to address the needs of students in high poverty districts.”
  • Only four states have school-funding systems that earned “fair” ratings: Minnesota, Massachusetts, New Jersey, and Delaware. But “these states have a sufficient overall level of funding and provide significantly higher amounts of funding to high poverty school districts,” according to the report. (from

If we go back to what equitable education means – students should be getting the resources, supports and instruction that supports their individual needs. With the type of funding described above, this is clearly not what is happening (nice graphic here by state showing the difference by state in funding for poor school districts vs. wealthy school districts). Poverty and all that it entails, seems to be a huge factor in the access to equitable quality education. It impacts parental support (hard to be there to help with homework or pay for tutors if you are working two jobs to make ends meet), access to educators and schools support personnel such as school counselors and nurses, access to technology, education supplies (paper, manipulatives, textbooks, calculators, etc.), school safety, and all the myriad of other components that make up quality education.

When thinking about education and how to provide access to the resources every student needs, we need to restructure how states and school districts distribute school funding and resources. Districts need to do a true evaluation of what each school in their district has in terms of education resources (materials, technology, personnel), and most importantly, what they need to support those students in those specific schools. If the two schools down the street from each other in the same school district have math classes in one school of 20, with students at computers, and the other school with math classes of 42 and no computers and not even enough seats or rulers for students, there is clearly a problem. The first step is to really do an inventory of what schools have, what class rooms and sizes look like, what personnel resources are and really identify the glaring discrepancies. You can’t fix something if you don’t even know where it’s broken – once we see the vast difference in access within school districts, then we can take that next step of thinking about ways to reapportion some of those resources in a more equitable way.



Equity, Equality, and Access to Quality Education – Part 1

Back-to-school is already upon some, and for many will be starting up in the next few weeks. With that in mind, and especially with the very public conversation around school choice and ESSA and accountability for schools, I’ve decided to do a 3-part series on equity, equality, access and quality education. These are ‘buzz’ words that are thrown about in news stories and education settings, but I think often times these words or terms are used incorrectly, or interchangeably, with many people not really understanding what is really being said or what the meaning behind these terms actually might be. With that said, this first part in my series is going to focus on defining these three terms so that we are all on the same page and have a common understanding in which to move forward.

Quality Education

This term is loaded. Everyone wants a quality education for their child and schools and states strive to provide quality education for all their students. But what does this mean? What does this look like? I am going to define it here and in later follow-up posts we will dive more deeply into this.

There are many definitions out there for what quality education means. I actually had a hard time finding an ‘official’ definition, but found the term ‘quality education’ used frequently in vision/mission statements from many education organizations and school districts. Which is interesting – we use the term, yet we don’t define it, so how are we ensuring that students are indeed getting a quality education?

Here is a definition of Quality Education from ASCD (Association of Supervisors of Curriculum Development) and EI (Education International) which I think provides a strong common understanding that will connect to equity, equality and access.

A quality education is one that focuses on the whole child—the social, emotional, mental, physical, and cognitive development of each student regardless of gender, race, ethnicity, socioeconomic status, or geographic location. It prepares the child for life, not just for testing.

A quality education provides resources and directs policy to ensure that each child enters school healthy and learns about and practices a healthy lifestyle; learns in an environment that is physically and emotionally safe for students and adults; is actively engaged in learning and is connected to the school and broader community; has access to personalized learning and is supported by qualified, caring adults; and is challenged academically and prepared for success in college or further study and for employment and participation in a global environment.

A quality education provides the outcomes needed for individuals, communities, and societies to prosper. It allows schools to align and integrate fully with their communities and access a range of services across sectors designed to support the educational development of their students.

A quality education is supported by three key pillars: ensuring access to quality teachers; providing use of quality learning tools and professional development; and the establishment of safe and supportive quality learning environments. (retrieved from

Equity and Equality

The definition of equity in the dictionary is “the state or quality of being just or fair”. The definition of equality is “the state of being equal, especially in status, rights and opportunities”. So what does this mean in terms of education, especially as these two terms are often used interchangeably, when they are very different when it comes to education? Let’s look at each separately in terms of education.

Equality in education would mean that all students are treated the same and are exposed to the same opportunities and experiences and resources. This is deemed as fair because everyone is getting the same instruction, the same assessments, the same resources, the same access to teachers. However, if students are coming into a classroom with different capabilities and different backgrounds – which is the reality no matter where you are – (this means educational knowledge, socio-economic status, family support, etc.), then treating them equally is going to disadvantage most students. No one will get what they truly need to learn – most will not get the appropriate supports and opportunities they need to be successful and to learn to their full potential (as examples, those with special needs would not get the additional supports needed and ‘gifted’ students would not be exposed to more challenging learning experiences they might need).  Everyone gets the same and so everyone suffers to some extent.

Equity in education means that all students get what they need from education, meaning instruction, assessments, resources are distributed so that every students individual needs are met in a fair way so all students can be successful. This relates to the statement above, under quality education, that students have access to personalized learning so that their educational needs are supported, allowing them to be prepared for future success, whether that be a career, college or some other aspiration. So unlike equality in education, equity in education is not the same for everyone, rather it supports everyone with what they need. A students socio-economic status, gender, race, or ability level do not prevent their access to education resources and opportunities. Equity does NOT mean equal. Equity implies an education for each child that meets their specific needs,  both pedagogically and developmentally, so they can be successful in their future endeavors no matter where they live or what their economic status might be.


Access to education is closely tied to equity and equality. I almost didn’t separate it out, but I do think it is a key component behind why many students do NOT get equitable education opportunities. The goal of providing quality education to all students means we are providing them with equitable access to resources and learning opportunities – i.e. students with learning disabilities are getting the extra services and supports they need to be able to learn; students from low-income areas are getting the technology and materials and qualified teachers needed to address their instructional needs; students who excel at math or science are provided with technology and resources that allow them to explore and expand their understandings; students who are artistically or musically inclined are provided with teachers and courses that let them learn and create.

It was hard to find a ‘definition’ for access, because it’s really a process of ensuring students get what they need. I found this nice summation of access on the Glossary of Education Reform that I am going to use to inform our discussion going forward:

 “The term access typically refers to the ways in which educational institutions and policies ensure—or at least strive to ensure—that students have equal and equitable opportunities to take full advantage of their education. Increasing access generally requires schools to provide additional services or remove any actual or potential barriers that might prevent some students from equitable participation in certain courses or academic programs”.

As you can see, all these terms and ideas are related, and it is often hard to think of them in isolation. Hopefully now you have a better understanding of each, and in our follow-up posts, we will explore issues surrounding these using our common understanding.