Mathematics is the relationship of questions and facts involving magnitude

Mathematics is the relationship of questions and facts involving magnitude.


Which comes first the chicken or the egg?

Which comes first the question or the answer?

Facts in relationship one to another is the very definition of a function or equation.

The answer therefore is the ordered steps needed to solve the question, function or equation.

The Jeopardy page is the question, function or equation.

The Subject Pie page is the ordered steps needed to solve the question.

One can state the two statements above as an equality or equation with both sides equal!

Word problem or equation = facts in relationship.

One can begin with the facts or the questions.  One implies the other except in very special and high order mathematics.

If one has learned to deeply process facts by asking questions.  One can solve questions by evaluating the facts in an orderly fashion.

Learning to learn self assessment and resource video links

I trust the background and method of rapid learning is knowable in part or whole.  What part or whole do you know?  What part or whole can you do?

What are three barriers to rapid learning?
What are the steps needed to overcome each of the barriers?
How can the learner take responsibility for mastering the material to be learned in a lean and effective way?

Were you able to understand and implement a trial of deep processing, distributed practice in your class work?

Have you begun brain training to increase your bandwidth?

What are the results to date on time spent in study?  Test scores?

This video illustrates the value of deep processing.

How to Get the Most Out of Studying: Part 2 of 5 ... - YouTube

This video illustrates the value of distributed practice.

Key Concepts in Spacing Learning Over Time

In my system the traditional class, lecture or reading is merely a DATA STACK of topics and relationships written on the Statement/PIE page  which is the in box for stuff to be learned.  The Jeopardy page is filled with questions that are well formed to show meaningful relationships to use in distributed practice at one day and weekly up to three weeks.  The learning is inherent in question forming and extended by meta level question forming.  Learning is therefore forming questions showing understanding.  The questions are a form of test.  Every review of the question prompt is distributed practice test taking that overcomes or demolishes the forgetting curve.  Reviewing questions does not provoke anxiety like the actual test in class.  The learner who processed the DATA STACK with well formed questions and practiced answering the questions using distributed practice has every reason for the same level of confidence as an open book, open ended test.

Acknowledging that tests increase symptoms of anxiety, what can we change to lower the probability or amount of anxiety beyond being prepared?  Performance is ability minus anxiety, therefore reducing stress and anxiety during performance and testing is desirable.

Often body language and posture either enhances or negates test taking anxiety.  Check out the following video and pay attention to the affect of proper posture or “power posing” in stress and confidence hormone levels.

Amy Cuddy: Your body language shapes who you are …

Below is a video on good posture that will show you how to sit/stand in an “all day power pose.”

Authors@Google: Esther Gokhale - YouTube

By the way, good posture does improve backs, diminish pain, improve confidence and diminish anxiety.

Metacognition: How do we know when we know?

METACOGNITION  is defined as "cognition about cognition", or "knowing about knowing". It comes from the root word "meta", meaning beyond.

How does one know when they know something?

How does one learn something new that they do not yet know?

A common mistake made by students who study and work hard is to conflate review with learning.  DISTRIBUTED PRACTICE or review is not learning, per se, it is actually not forgetting which is entirely different. 

One can learn beyond the known  if one ask "beyond questions" known as meta level questions.  

One can also make a LEAN learning process by STUDYING STRATEGICALLY or purposely  new material and distributing practice to keep the learning forever.

Consider the following metalevel questions about subject X.

What does the presented information DISTILL as the big idea of  X? 

What does the presented information OMIT that is important about X?

What new understanding can I form from the following resources:

      1. The Statement/PIE (proof, information and examples presented); 

      2. The ignored Statement/PIE that is already known

      3. The unknown PIE/Statement that is a priority to know?

TRUTH and Integrity are pillars of learning.

In American jurisprudence the stated aim of inquiry by testimony is "the Truth, the whole Truth and nothing but the Truth."  This is the strategic aim of "Truth, Justice and the American Way."  It is also the basis and aim of learning!

What can one learn from the false 1.0?

What can one learn from a meta level inquiry of "the False, the whole False and nothing but the False" 2.0?

The strong and unadulterated Truth is worth it's weight in gold at all levels because it is dependable, reproducible and scalable.  Not so the weak and adulterated truth.  Everything we know is made up of two parts, known to some degree/unknown to some degree. In effect unadulterated, unabridged AND adulterated, abridged.

How does one know?

What can one know?

What does one need to know that one does not yet know?

With limited time, talent and capability; learning, not forgetting and forgetting must be STRATEGIC.

META LEVEL QUESTIONS

What's the BIG IDEA?

What's MISSING?

What's the SYNTHESIS.

A YOUTUBE video from Samford University about metacognition.

How to Get the Most Out of Studying: Part 1 of 5 ... - YouTube

How do I DEEPLY PROCESS and DISTRIBUTE PRACTICE  in my School work?

Picture your notebook, a spiral notebook open with page 1 to the left and page 2 to the right.

Notes are taken from lecture, assigned reading and discussion with peers on the STATEMENT PAGE, page 2 on the right.

DATA to be learned is delivered in the form of statements.
Usually elaboration upon the statements are given in the form of PIE, proof, information or examples.
This is typically recorded in a bulleted outline form.
   
QUESTIONS are written about the data on the JEOPARDY PAGE, page 1 on the left.
Questions are formulated after 2 quick distributed reviews of the notes.
The optimum timing of this quick review is immediately after class and one hour later between classes.  This plants, fertilizes and waters the data in the mind.
After scheduled classes, one formulates, in a rapid and fun way, questions and writes them naked and without answers on the jeopardy page.

On the FIRST DAY, the good notebook has both a STATEMENT PAGE and a JEOPARDY PAGE.

For example.

JEOPARDY PAGE                                                   STATEMENT PAGE

What are the 5 branches                   O                   american military
of the american military?                  O                      army
                                                          O                       navy
                                                          O                       air force
                                                          O                      marines
                                                          O                       coast guard

The powerful 3rd review occurs after a night of sleep which is powerful because the time and sleep has allowed a weakening of the memory trace.  The powerful 3rd review is cued by the questions with the statement page folded under.  The weakened but recoverable memory trace is cued only by the question and retrieved independent of the statement and therefore with a different context which strengthens the memory trace AND retrieval.

Learners on average who performed distributed practice at  10 minutes, 1 hour and 1 day later remember 94% of the material 3 weeks later.

Every Sunday for 3 weeks perform cued 4th,5th and 6th reviews of the past 3 weeks of JEOPARDY PAGEs in a rolling fashion because we want to remember 100% indefinitely.

If a group of students learn at the pool, half in the water and half on the deck and half of each group are tested in the opposite location, the scores of those taught and tested in the same location do better on the second day but the opposite is true 3 weeks later.  Making retrieval novel and harder strengthens the memory trace and its retrieval remotely.

How do you know when you know?  If you can answer the question without revisiting the statement page, you know the data and can retrieve for use or testing.  You now only study what you can not yet readily retrieve which should be less than 6% of the reviewed material.

How does brain training work?
Brain training is analogous to strength and speed training.

High intensity training stresses a system which responds and becomes positively or negatively enhanced due to inherent plasticity or ability to change in a positive or negative direction.

For example weight lifting responds to the overload principle.  If the one rep maximum is 100 lbs then one lifts 70% or 70 lbs 8-10 repetitions.  During recovery the muscle becomes larger, stronger and mitochondria increase in volume and mass.  To continue to gain strength, size and performance one must keep the intensity, load, reps and recovery in the zone.  One trains generally to failure to repeat a repetition.  One can also negatively un-train with bedrest and degrade potential strength.

In brain training one performs a task of attention, audition or vision on two or more comparator events and is tested on the accuracy of the task.  The time allowed to perform, perceive the task is shortened or the presence of interference is introduced to make the task more difficult (or heavier) for each repetition.  Unlike the muscle, brain failure is not digital but analog meaning the evidence of failure is incorrect perception.  The proper intensity to gain brain speed and accuracy is a failure rate of 20-30 % or a success rate of 70-80 %.  Therefore the training zone of 70-80 % capability appears to be optimum.  Twenty minutes is a recurring duration in published reports of various empirically successful brain training regimens.

Who will brain training optimize?

Humans are born helpless and are self learning in a caring family and community.  They are subject to negative and positive brain plasticity changes.  Development is generally asynchronous with regard to gross motor, fine motor, communication, social and problem solving which comes together around the age of 2 and becomes synchronized or aligned for further hypothesis, testing, learning and re-hypothesizing.
At some point one notices that children are learning at different rates.  WHY?
After peak development at 25-30 years of age, the individual is optimized by complete development of the adult brain and the adult body.
At some point one notices that older adults are slowing down mentally from their highest point.  WHY 2?
Way down the road one notices that the elder is repeating questions and lacking confidence in decision making.  WHY 3?
At every step along the way, various individuals in the group drastically slow down mentally or emotionally below the average of their peer age group. WHY 4?

WHY 1.  Children who can master and fluently speak their language have great brain potential which is blocked by slow sensory brain speed processing, superficial processing cognitive strategies and lack of deep distributive practice skills of review and rehearsal.  Brain training increases BANDWIDTH.  Sensory brain speed and poor cognitive strategies explain learning rate variation.
WHY 2.  Young adults lack the skill of exchanging one item in working memory for the next item. This is evidence of slowing down to improve accuracy.
WHY 3.  The inability to recall objects after 3-5 minutes is minimal cognitive impairment.  This results from slowing auditory and visual processing speeds.  Increasing sensory processing speeds greatly improves short term memory.  High IQ/BANDWIDTH and highly educated persons of age reveal less brain slowing by compensating.
WHY 4.  Traumatic brain injury, emotional brain injury, drug, alcohol, anesthesia, chemotherapy slow down the brain from the optimum.
The Bell Curve (IQ) by Charles Murray can be shifted to a higher mean!
Everyone and every age can be optimized by brain training averaging 135-230 % for speed.

Learning to learn overview Action 3. DEEP PROCESSING

Learning to Learn 
     Athletes train.
     Students train.
     Learners train and self-educate.

The 3 Barriers to Learning.
    
      3. Shallow processing.
      2. Forgetting.
      1. Slow brain bandwidth.

Action 3.  DEEP PROCESSING begins with well formed questions as one interrogates a subject.  Use the Cornell note taking system while actively listening or reading by jotting down questions in real time on the same page that notes are taken.  After reflecting and review of all the notes from lecture, text or article, write well formed Jeopardy questions on the opposite page as the essential tool for distributed practice.

Why.  Questions teach.  Teachers question.  Self learners question.  The best questions teach best.

How.  Write notes from lecture, articles and text on the right 2/3 of the page.  Jot questions on the left 1/3 of the page.  Questions are presuppositions or predictions about the material and the relationship between statements made and the proof, information and examples used.  The best questions arise after the lesson as material and relationships are fresh and familiar and are written on the opposite page in the notebook.  They are called Jeopardy questions because each question has a category or subject, relates to facts given on the opposite page and because answering with a question is fun.

What. Statements, proof, information and examples are boring without understanding.  Questions inform understanding.

Caveat:  Mathematics is the opposite of answers learned by questions; mathematics is questions learned by answers.  The process of answering the question or the proof becomes the question in the study of mathematics.

DEEP PROCESSING has been experimentally shown to increase the average word list retention compared to superficial learning strategies from 33% to 68% which is twice as much learning per unit time.  

If one performs DISTRIBUTED PRACTICE to retain the amount learned and learn the residual unlearned material, the efficiency of learning is greatly increased.

If one has INCREASED BANDWIDTH the average word list retention also increases above the average whether one processes superficially or deeply.

INCREASED BANDWIDTH, DEEP PROCESSING and DISTRIBUTED PRACTICE yield compounded growth in learning rate, retention, retrievability and use in other contexts.

Learning to Learn. Overview and Action 2. DISTRIBUTED PRACTICE limits forgetting

Learning to Learn 
     Athletes train.
     Students train.
     Learners train and self-educate.

The 3 Barriers to Learning.
    
      3. Shallow processing.
      2. Forgetting.
      1. Slow brain bandwidth.

Action 2.  Begin a Distributed Practice routine.  
                    Review questions from the day before at 1 day later.  
                    Every Sunday, review the previous 3 weeks of questions.
                    With every review, learn again any forgotten material to keep                
                                 forever....

Why.  Interval learning is superior to steady state learning otherwise know as cramming.  Retrieval of previously learned material is integral to long term learning.  In fact, retrieval is the evidence of long term learning or not forgetting. If one is able to retrieve or use in a different context then one understands and can apply the lesson learned anytime and any place.

How.  Review questions of learned material after 1 day, and weekly  review questions of learning over the past 3 weeks intervals.  One will review learned material a total of 4 times within the month.  If one ever needs to validate learning, return to the questions again to sort the learned from the forgotten.

What. The key to a computer database is context.  Memory is stored in a retrievable database analogous to flash memory.  

The more context retrievals take place the greater number of keys to remember.  Time, place, emotion, order, importance, novelty and relationship also provide memory keys for retrieval.

Learners remember the beginning and end of list.  Therefore, organize the material to be learned into different lists, ordered lists, relationship lists etc.

Learners test better in the short term if the context of learning is the context of the test.  At the pool, learners in the water and learners on the pool deck retrieved best if tested in the same state as they learned and less well if tested in a different context.  Retrieval in multiple different contexts aids testing in real life where all the important testing occurs. Varying the context removes the context clue making retrieval harder yet stronger due to more keys.

Learners who practice batch basketball shots do not perform as well in games as those who practice varying context shots.  The retrieval and change in context makes the memory stronger, more accurate and enduring.  Same for Golf. Same for other subjects.  Varying the context separates the essential from the frame.