Online Learning


 

Students are different in interest and abilities, some need more repetition and some need hardly any. An interactive, self paced option can offer advantages to all types of learners. 

New technology is here to help us. As dedicated teachers and tutors, we would love to be the proverbial octopus that can tailor instruction to 8 different learners at the same time, but in reality it’s not working and our national math achievement is not something to be proud of. I am ready to accept the helping hand of technology as long as it is truly research based and the student is not left on his own when he stumbles, but gets immediate constructive feedback. 

Internet programs are very convenient, can be used anytime in school and at home and will help bridge the long summer holiday, when many newly learned math abilities are forgotten. 

Interactive Math learning software should have attractive, but not overpowering graphics: the attention is still on the mathematical content instead of on the comic or movie part. The progression from one concept to another should be clear and logical so students do not get frustrated with questions that are still too hard for them, and teachers/parents/tutors should be able monitor progress and still be able to step in where needed and last but not least: cheer the successes! 

There are numerous good websites for classroom and individual use:

For example, the Illuminations website by the National Council of Teachers of Mathematics (NCTM) provides a great number of tried and proven lesson plans and online activities. For several of the activities you will also find a link to the activity on iPad. You can search on level and type of activity. An invaluable resource for each math teacher and tutor!   

The NASA website has a list of engaging math activities and lesson plans per grade band. The GeoGebra website can be used both in the HS classroom and by individual students.

Have a look at the SHODOR.org website, a National Resource for Computational Science Education. They maintain a great website, under Activities and Lessons you will find Interactivate’showing students over 100 math concepts in a novel interactive way. 

The additional advantage of websites for individual use is differentiation. Many programs just provide drills for arithmetic. We are now aware that speed drills for math facts can cause math anxiety. Luckily there is a growing number of websites that presents concepts in a novel and interactive way that is hard to do with text books alone.

A few suggestions from the long list of math oriented websites that can be used for individual learning for younger students with dyscalculia are the Number Race and the Number Sense website. Websites that offer all levels are the Khan Academy and the BBC ‘Bitesize’ website. Middle and High school students can use Connected Math and SchoolYourself.org. Also check out the Mind Research Institute (you can try several activities for free).

The Number Race was developed for ages 4 – 8 developed by Dr. A.J. Wilson in collaboration with Dr. S. Dehaene from the Unicog Institute (INSERM) in Paris and is available for free from SourceForge in several languages. It uses recent research in neuroscience to specifically target youngsters with dyscalculia.

The London Knowledge Lab developed the Number-Sense website, with five highly acclaimed activities for students with dyscalculia: Learn Time, Number-bonds, Dots2Track, Number-line, and Chicks Test. (This website uses Flash, so not suitable for Apple Pc’s). The Number-bonds is a tetris like game where you combine the well known Cuisenaire rods to make ten. Different levels ultimately leading to the abstract notation. You will also find the contact to the Low Numeracy Network and can sign up for regular updates and new information on the topic.

The Khan Academy has super clear lessons presented on a ‘blackboard’ with oral explanations in all levels, from simple addition to multivariate calculus. There is a built-in progression, that takes students on a journey through the areas of Math and a progress monitoring system. Teachers can connect with their students using the Coach function. Unlike many educational computer programs that span only elementary, middle school or high school level, this one spans many levels, so the student on the verge of one of these school borders does not need to wait till graduation day…

Word problems area a huge stumble block for many students with dyscalculia, in particular those who also have dyslexia. Thinking Blocks, by Math Playground, is based on the Singapore way of using strips to represent numbers. Students are guided step by step through the process of problem solving. You can choose from word problems focusing on Addition-Subtraction, Multiplication-Division, Fractions, and Ratio-Proportion. It is available as PC game and on iPad.

The BBC Bitesize website has a wealth of interactive and fun Math games and learning activities. The games and activities are grouped according to level: KS stands for Key Stage. KS 1 and 2 are for elementary, KS 3 and 4 for middle and high school, and GCSE stands for General Certificate of Secondary Education (UK). Most of the lessons have three parts 1. Revise: the explanation how it works,  2. Activity: using novel ways to learn the content, with immediate corrections, and 3. Test: after doing the test, you can print your answers with guidance for correcting answers.

The Connected Mathematics Project for Middle School at the University of Michigan offers a lot of information, not only math content for students, but also a section with in depth explanations for parents, who like to help their teenagers and interactive resources, including online math games using Java: Connected Math 

A newer website for Middle and High School is SchoolYourself.org It offers great oral explanations and clear visuals. Students are asked to participate in various points during the explanations and hints are provided to go to videos where you can brush up the required basic knowledge. 

Check out the Mind Research Institute, a neuroscience and education-based non profit corporation: www.mindresearch.net. They developed a math game where students help penguin Jiji to bridge a gap using mathematical concepts: the kids love it and it is effective too!!

Happy calculations!

Dyscalculia Movie: Sorry, wrong number


 

Professor Brian Butterworth is a world authority on the problems associated with dyscalculia – the inability to recognise numbers – and we are delighted to have him working with the Educating Together team as a consultant. The problem is as severe as for those who suffer from dyslexia, affecting approximately 7 per cent of children in the UK. If identified early on, children can be supported with their learning difficulties with maths by intervention and remediation. We, at Educating Together, know only too well that dyscalculia is a serious problem for a child’s development unless it is addressed, but help is at hand. We have made a film – ‘…Sorry,wrong number’ with Professor Butterworth and Alex Gabbay, which we will be launching in August 2012. Here is  a sneak preview.


Download our free fractions booklet


 

Understanding Fractions

Introducing fractions in the traditional abstract way (a/b) has the risk that the concept is not connected with your child’s previous daily life experiences. The new concept is ‘hanging loose’ and it will be almost impossible to access and apply it later on.

If this sounds like what is happening with your child: read on, there is a simple cure:

Like with many other mathematical concepts, we overlook that most children already have a basic idea about fractions. Storybooks tell about dividing treasures and kids see things being dived at the kitchen table and in school all the time, so they have formed an understanding in their mind about what dividing something into fractions is.

This is a valuable developmental step and a child feels really proud when we acknowledge that her understanding of how you can share and divide things into smaller parts is important.

The boxed conversation starters do not put the child on the spot and do not add to the usual math anxiety. Your child’s answer shows us the key to the preferred type of examples, that will help your child link the new knowledge to what she has already anchored in her long term memory. It tells you how to guide your child to the proverbial door knob that will open the door to deeper understanding and successful application of the fractions concept in different types of questions.

How to use the Fractions Booklet

What does it mean to share? How do we use fractions in our daily lives? Asking questions makes learning interactive and fun. Time and again it is proven that engaging in a conversation or an activity is the most effective way to learn!

 

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Title: My Fractions Book

  1. Do you know family and friends to share with?
  2. What are things you can share? What is the name for a part or fraction?
  3. How can you divide something to share it?
  4. How do you know you divide evenly so you have equal parts? What is a fraction?
  5. How do you know how big your part is?
  6. How do you tell somebody else what her part is?
  7. What are ways to divide a round item, like a pizza?
  8. What are ways to divide a rectangular item, like a chocolate bar

The boxed suggestions are communication starters. Be sure to ask questions on the go like: what is the best example and how would you say that? Use these examples and wording wherever you can.

The answers to these questions give you insight in your child’s thinking and progress so you can give as many specific compliments as possible and you can help exactly where needed. The written answers or drawings will show your child’s understanding. If you see a glitch, do not rush through the book thinking that it will magically ‘click’ later on, but take the time to ask more guiding questions and redo difficult pages before going on. When completed, staple the book together with a nice cover as a keep sake. Give ample praise.

Math Anxiety


It hurts teachers to see students struggle with Math. Clearly, those students come into the classroom anticipating to go through an hour of discomfort or outright stress.

Those clear verbal explanations, colorful graphs, and easy to understand formulas or diagrams that work for the majority of students go over their head.

Starting the lesson with the mindset that it will be another ‘failure’ becomes a self fulfilling prophesy.

Heartfelt encouragements are met with disbelief.

Obviously, you are trying to break the downward spiral of Math Anxiety. Emphasize a positive attitude and minimize student embarrassment.

Unfortunately, just as in reading, students come to the classroom with different independent, instructional and frustration levels in math. Here are some suggestions for differentiation that might be helpful:

  • Math teachers need readily available tools to evaluate the level and possible gaps for the individual student and time to do this.
  • Knowing your students’ abstraction level and learning style allows you to choose or design assignments to fit the ‘rule of thumb’: every five questions can have one hard one, or four compliments can balance one comment/correction.
  • Temporarily going back to a level just below where the student is really proficient has worked wonders. It gives the student the feeling that he can do math, it’s even easy!
  • Textbooks that have built in differentiation in content and workload are time efficient and can help your students regain their confidence and start trying again.
  • To explain a new concept or guide a student through a given problem, it can be amazingly effective to backtrack one or more levels in the developmental sequence of mathematical abstraction:
  1. providing stories about numbers and concepts and asking the student to tell about it
  2. providing concrete manipulatives to represent the problem and modeling or having the student ‘act out’ the problem
  3. providing pictorial representations and having the student make drawings
  4. providing abstract representations and having the student write numerical answers to problems
  • The golden rule still applies that it is best to minimize the time between an error and a correction or to explain every mistake as quickly as possible to prevent that the misconception can take root. For older students providing the answers (not the procedure) to homework can be helpful. Even better than giving the explanation is having the student explain to you why he thinks it’s not the right answer and how he can correct it. Ask the student to write down what went wrong next to the problem and what he can do to prevent it.
  • Working in pairs or small groups gives you the option to team up a student who needs help with a more advanced student.
  • Allowing more time and quiz or test corrections for half or a third of the regular credit is another way to focus on working towards improvement instead of being stuck with a failing grade. Recent research suggests that timed tests are related to the early development of Math Anxiety. Ref: Jo Boaler in Teaching Children Mathematics, NCTM, Vol 20, #8, 469-74, April 2014.
  • Keeping a record of error corrections in her/his math journal that also highlights accomplishments is highly effective to boost self confidence in math.
  • Making a graph of personal progress is very motivating and eliminates the negative comparison with other students in the class.
  • When personal tutoring is not an option, consider online math tutoring programs, they can be very economical and beneficial.

Teaching is often a time balancing act and it is obvious that this approach takes a lot of extra time from both teacher and student, but you can expect great leaps and to have happy faces in your classroom.

What is dyscalculia?


How often did you hear adults say: “I always struggled with math in school” or even worse “I am just not a math person” basically accepting that it will always be hard for somebody to do things such as keeping a checkbook and other important math related activities?

Were you one of those kids struggling and giving up on math? You could well have dyscalculia or Math LD yourself.

Do you like to prevent your child from struggling with math in the same way? Read on: Recent research shows that learners can be confident and successful in Math with an individualized approach from early on! Even love it!! Much like we know that children with dyslexia benefit from special dyslexia instruction using sequential structured phonics lessons and can become good readers and even love to read!

 

What does the word dyscalculia mean?

The word dyscalculia has Greek and Latin roots: dys (the Greek part) means badly and calculia (the Latin part) comes from calculare: making calculations, so dyscalculia is ‘badly calculating’ or having trouble with making calculations, or ‘dyslexia with numbers’. Compare dyslexia ‘badly reading’.

Dyscalculia is a Specific Learning Difference or Disability (Sp LD) involving all sorts of numerical tasks. It is listed in the DSM IV.

Dyscalculia in children often involves struggling with one or more of the following:

  • simple mathematics  memorizing and applying math facts: addition and multiplication
  • the order of operations
  • the ability to visualize a small or large quantity
  • to mentally connect a number with a size or quantity (number sense)
  • learning to tell time

Dyscalculia in adults often involves one or more of the following difficulties:

  • uncomfortable with all sorts of number related activities
  • mistakes in copying and memorizing numbers  trouble with everyday calculations like estimating shopping total or change given
  • difficulty keeping a checkbook and managing a bank account  getting directions and using a map is often confusing
  • time related issues

The brain of a person with dyscalculia is wired slightly differently and a mathematical stimulus is processed differently. This is pictured with functional MRI: when a child or adult with dyscalculia does a math problem the areas in the brain that are best equipped for numerical tasks are bypassed and other less efficient areas are used instead. We also know that that the brain can be trained to unleash that previously hidden capacity.

 

Watch a ten minute youtube video by one of the leading experts in dyscalculia, Prof Brian Butterworth

click here to watch