Posted in Teaching mathematics

What is Universal Design in Learning?

This is a perfectly good knob to use. Grab it, turn it, pull (or push), and the door swings open. So it meets your needs. Or does it? Does it meet ALL your needs, your universal set of needs, needs that arise in different situations, different contexts?

Well,  suppose you are rushing down the corridor in your office building, with a cup of coffee in one hand, the other clutching a folder or file. You are late. You run up to the door and see the same round knob as above. Can you open the door with it when both your hands are “occupied”?

Or would this design do a better job:

Because with this, you can lean down a bit, and push the handle with your elbow. If neither hand is occupied, you still grab, turn, push (or pull) as always. The handle meets your diverse needs, needs that rise in different situations. It has, what we call, a “universal design”.

It took a long time for people to become conscious of needs that go beyond those that are mainstream and taken for granted. Like people using wheelchairs. When they first built houses and office buildings, people used stairs or steps to climb up the building to get to upper floors. This alienated a population of people who were unable to use their legs. They used wheelchairs in hospitals. Maybe a few in their own homes. But by and large, they were kept out of office buildings and even prevented to do social visits. They couldn’t pay their bills, draw their money from banks, or perform any transactions. Or see visit relatives and friends.

It has been only 4 decades that their needs were acknowledged. In the beginning, it was expensive to redesign and rebuild buildings and homes for people with such special needs. So ramps were “attached” on the side of the buildings for such “special” people. Like this:

“We” soon became associated with the “normal” population that could use steps, and  “They” with “those” people who couldn’t.  Handicapped people. Those “poor people” who couldn’t walk. This led to the exclusion of a part of mankind to a lower, somewhat lesser conceptual level where the handicapped felt like outcasts in their own midst. They were made to enter from the side rather than from the front, “like the rest”.  It compromised their self-dignity.

The Inclusion Movement rallied against the tradition of “Exclusion”  for decades. Until the day came when leading architects and designers began envisioning buildings in which various options were made available to negotiate higher floors. Technology, too, came to the rescue. So elevators and escalators took over. No side-entrances for special needs was necessary. ALL needs were human needs. And ALL needs had to be equally respected, equally addressed. Everyone deserved to enter from the front. And if ramps were needed to enter a building, then the ramps would be integrated into the design of the building from its very conception. They would run alongside the steps. All who enter a building should enter as equals. And all buildings and homes should be designed for such “universal access”.

This same idea applies as much to education as to buildings and door-knobs. Learners have different needs. And these may vary among individuals of different ages and genders as much as within anyone’s given lifetime.

Can educational courseware be designed in such a way that they address the needs of (a) gifted learners (b) disadvantaged learners (c) and all learners that fall between these two extreme poles?

I have tried to meet the demands of Universal Design in Learning in the educational courseware I share in Karismath Insights Videos.

I suggest you read my two other posts on What is visual mediation? and Teaching mathematics by visual scaffolding to fully appreciate the theory behind the videos.

Shad Moarif
Founder-Developer
Karismath

About Shad:

Shad, a Harvard graduate, has a background in Science, Psychology, Reading and Mathematics. He has also developed a comprehensive theoretical perspective of his Five Stages of Math Achievement that awaits publication. 

His work has been influenced by his 35 years of teaching Mathematics and Language to children (and adults) with Mathematics and Language-learning difficulties in Asia, Canada, US and the UK. He has conducted numerous teacher-training seminars and workshops at conferences  in the US, Canada, UK, Singapore, Bangladesh, Pakistan and Kenya.

Posted in Geogebra

GeoGebra and Learning Mathematics

GeoGebra is a great software for teaching and learning mathematics. It offers geometry, algebra and calculus tools in one environment, a great support indeed for linking mathematical concepts. On top of that it is free and an open-code software. Click here to download the latest version of the software.

 Is it easy to use? Yes and No. Yes, for math teachers because they know the mathematics and can therefore easily understand the ideas and logic behind the tools. Yes, for students who have been instructed on how to use the tools and understand the mathematics and logic behind it. They can use it in solving problems and for investigating mathematical relationships. But, for the majority of students, especially those who have not learned the basic of graphing, equations, and geometric relationships, the use of GeoGebra is limited to manipulating ready-made GeoGebra applets. (Click here for my posts on solving problems about quadrilaterals or here for introducing function using Geogebra applets.) Well, yes, GeoGebra applets are easy to use but most of the time if you do not know the  mathematics behind the construction or can’t construct it yourself, then the learning of the mathematics may be superficial.

Construction of math models using the software is not accessible for many younger students just starting to learn basic Algebra and Geometry. In order for them to construct a model, they  will have to follow a set procedure (constructed by the teacher) without really understanding why they do what they do. So I thought why not teach GeoGebra tools and mathematics at the same time? This is a challenge I set for myself and I have no idea if it will work or not. I am thinking of doing a research of it later in the year. GeoGebra is free and faithful to mathematics so for countries like us that can’t afford to  buy licensed softwares, we get the same quality teaching tool with Geogebra. I think all students need to know how to learn mathematics with it.

Posted in Curriculum Reform

Enduring understanding

To know the big picture ideas, to know the enduring understanding students are supposed to learn are indeed very important in planning and teaching a lesson. However, for teachers to be able to identify and articulate the enduring understanding for a particular content topic requires knowledge of the following:

  1. knowledge of the nature of the discipline;
  2. a deep content knowledge;
  3. knowledge of the connections among the different content topics
  4. some knowledge about the connection of your discipline with other discipline or subject area;
  5. knowledge of the relevance of your discipline to real-life

All these should already be partly articulated and reflected in the standards or curriculum framework to serve as guide to teachers when they design their lesson plans. If the curriculum framework is just a list of topics or some general statements then that’s bad news.

One can argue of course that teachers are expected to already know all these (the 5 items I listed above) and hence know the enduring understanding in their discipline. But the reality in this part of the world is that majority of our teachers still need more help in these aspects. This is my reason why we have to have a curriculum framework or Standards that supports the demands of articulating the enduring understanding expected in each unit before asking teachers to plan their “ubdized” (got this term from one reader of this blog) lesson.

Textbooks, which market themselves as “UbD-based”, or “UbD-compliant” should also be required to state the big ideas for the entire course and for each chapter or unit. Statements of enduring understanding and essential questions can also precede each chapter. Teachers can just add their own or state it in their own way when they make the lesson plans. It is not spoon-feeding the teachers. We just want them to have something to start with especially if the textbooks are their only resource.

Textbooks authors are supposed to have a clear big picture idea of what they are trying to teach in the textbooks and so why not require them to put it there. They have no business writing one if they don’t know the enduring understanding that students are supposed to learn. With all these in place, teachers will have more time to plan and design the lessons targeting these big picture ideas. They will also have more time to study their students’ difficulties and misconceptions about the topic and think of ways of addressing them. Most importantly, teachers will have more time to study the topic they are going to teach and how this content topic relates with previously learned concepts and future concept so they can find the right activity/ task and use appropriate assessment process. These are what can make or unmake a lesson, not whether or not the teachers use the backward or forward design in lesson planning.

This is my fifth post about this topic. Click here to link you to my other posts on UbD and backward design.

PS1. Having identified the enduring/essential understanding does not guarantee you’re going to have a good lesson plan or a good lesson implementation.

PS2. In one of the centennial lectures, part of the activities of the University of the Philippines centennial celebration, the speaker for education-related issues said that no one in this country is paying attention to learning. Indeed. We talk about lesson planning, we talk about curriculum frameworks and syllabus, we talk about multiple intelligences, …. we talk about essential understanding … we talk about everything except how pupils learn specific content topics.

Posted in What is mathematics

Math is not easy to learn – that is a fact.

I think it’s a waste of time trying to make math easy and fun to learn if your idea of fun does not involve challenge.

Mathematics is not an easy subject and it is not easy to learn it. That is a fact. The sooner the teacher accepts this, the better for her students. The challenge to us teachers is not in how we can make math easy to learn but in how we can make it makes sense and how we can make our students love the challenge that mathematics presents. Can math be challenging if students feel that what they are expected to do in the class is to follow the teacher’s method, the teacher’s way of thinking, and the teacher’s way of doing things? Where is the fun in that?

Mathematics is not fun to learn if the idea of fun is like playing bingo! However, if ‘fun’ is a function of the challenge a sport or a game presents, then indeed learning mathematics is fun. We love a sport because of the challenge it presents, the opportunities it gives us to make prediction, analyze, strategize, make our stand and defend it, etc and not because it is easy to play!

Everything in mathematics makes sense. Everything in mathematics is connected to everything else. I think this is where we teachers should be devoting our time to. And this is what this blog is about!