Students must know their Facts before Practice!

Recently on a social media platform I noticed a post along the lines of:

"I have students in my class who are still doing repeated addition and other approaches to do their tables!  What are some good practice activities both to help these children with their tables?"

The concern I have with this question is that if students do not know their tables giving them practice examples will not help them learn them, they will just keep using the method that they know.

We as teachers need to make sure that students "know" the tables before asking them to practice them.

Imagine a Sports Coach who says, "I know I have not taught you how to pass the ball correctly but just go and practice the correct way anyway. I will call you back in 5"

As a Mathematics Adviser years ago we talked about:

New Learning

Practice

Maintenance

New Learning as the label suggests is the new skills, methods, procedures that a student has not previously learnt
Practice is the activities used to  help ensure New Learning is committed to memory etc
Maintenance is the long term practice of previously learnt skills concepts etc.

I can remember being corrected after using the oft quoted phrase, "Practice Makes Perfect". I believe it may have been a Physical Education Adviser who said, "NO! it has to be Correct Practice Makes Perfect"

To me this must be at the back of our minds as we set activities for students to do, 

is it the correct practice they are doing? 

(I used this regularly when working with teachers from the 80's to 20's)

Mastery of a fact is indicated by the students’ ability to: 

•Show it with materials, talk about it and write or draw about it
    This demonstrate, record and explain stage is vital for the initial development of understanding.              This is done by presenting the fact in a meaningful context and having the  student model it with a variety of materials and record in a way appropriate to their level.

•Have instant recall
    Students need to have memorisation routines to achieve instant recall.  This is not rote                 learning, rote learning implies a lack of understanding.
    The goal is for the students to internalise the facts so that the recall is quick and effortless.      

This can only happen once the concepts behind the facts are understood.
    Explore possible strategies for helping to organise information in a 

table to make memorising easier

    • Practice is needed to make the facts automatic “PRACTICE IS ESSENTIAL”

 
    • Allow time each day/week for it to happen.
    The routines suggested below will have two purposes a) self assessment and by finding a     method         that works for them.
Routines you might choose to use with the students to help them memorise a basic fact.....

1.    Identify the fact to be learned
    Correctly record the fact
    Look at it say it, write it with your finger 5 times
    Look at it say it write with your pencil 5 times
    Cover it, write it, check that it is correct
    Repeat the routine if necessary

2.    Write the fact in big numbers on a piece of paper
    Trace it with your finger saying it out loud
    Close you eyes and say it
    Turn the paper over and see if you can write it
    Check it, give your self a pat on the back if you were correct.

3.    With older students explore how they can best    
    memorise the basic facts, let them try their method
    and test a partner to see if it is successful

Expect/demand that the students learn their facts.  

They are capable of it-just look at the way they memorise moves in computer games

• Use facts when solving problems
    Can be done through a variety of activities such as mental problems, games and quizzes

Knowledge of single digit number facts is essential, mental arithmetic is a 

valuable skill and both enhance “NUMBER SENSE”


TO COMMIT BASIC FACTS OR TABLES TO MEMORY STUDENTS SHOULD:
•    begin to memorise basic arithmetic facts soon after they have
    demonstrated an understanding of symbolic statements
    students should be able to demonstrate their understanding of the 

mathematical concept with equipment, verbally and in writing.
•    participate in practice activities with intent to memorise
    using fingers, tally marks etc as aids is not practicing memorisation
•    practice during practice sessions
    short and snappy, not time for explaining or teaching.  

Give instant feedback of correct fact.
•    be involved in short practice sessions every day when possible
    5-10 minutes is long enough. Keep students enthusiastic
•    try to memorise only one fact each session
    keep the task realistic and manageable
•    constantly review previously memorised facts
    we all forget!!! especially add/subt once students move on to mult/div

•     be praised and reminded of what they already know, by the teacher
    express confidence in the students ability to memorise.  

Capitalise on the pleasure they feel with success

•    be involved in verbal practice activities and receive immediate    
    feedback use full class response drills cautiously.  

It is difficult to tell what individual students are saying or    

 whether they are participating.
•    be exposed to a variety of activities
    have a pool of activities and change frequently to maintain interest
•    be praised for good efforts and keep a record of their progress
    be enthusiastic, praise students ability to memorise rather than ‘clever practices’.

DON’T CONFUSE TESTING WITH TEACHINGTimed tests emphasise speed where the emphasis should be on persistence and understanding.  Those students who do well under time pressure get to show off their skills and they are the ones who DON’T need the practice.  The students who have difficulty, work more slowly and run the risk of reinforcing wrong practices under pressure and develop fearful and negative attitudes to math’s learning.
    Prior to ‘Tomorrow’s Schools’ (1989) the School Inspectorate noted that they found a great deal of testing of tables and very little teaching of tables.

I leave you with this thought, 

"Is the anguish and energy over Basic Facts Learning and Memorisation 

as important as we think it needs to be?

Should we be helping students to explore processes and thinking?"

It is interesting to note that many Mathematicians, and Leading Math's Educators 

(Jo Boaler included) do not know all of their Basic Facts yet have succeeded mathematical