How to best learn the math you need?

Use six steps to learn a math skill.  Our new learning materials supports this recommended process.

-1-   EXPLORE   Develop a genuine, enthusiastic curiosity –  become a true mental explorer. Develop this enthusiasm so you will persist in the mental effort to focus attention, understand connections, avoid confusion,  get help for difficulties and overcome inevitable discouragements.

-2-   INQUIRE   Keep formulating inquiry questions –check on what you know and what you don’t know.  Persist in seeking answers to these questions. Use the 5W2H question stems:  Who -, What -, When -, Where -, Why -, How -, How much -?

-3-   CONNECT    your new learning material items to integrate them with the old material items you already learned. Recognize and master all prerequisites first.

-4-   MODEL   Adapt/create mental models to summarize thr new knowledge, contrast similarities and differences and connect knowledge items. Create these models as schema for effective comprehension and improved recall.

-5-   INTERLEAVE   review topics to focus on summary understanding and of differences and similarities.

-6-   SPACE  practice for active recall of these connection models, summaries, concepts, examples and skills.  Do this for long term retention through repeated, directed self-quizzing of your own (for example, Cornell Notes) or our prepared materials.

Using Q&A NOTES for Study

Please adjust your browser width to view only this column and ____ the answer column on the right. … For desktops adjust the window size. …For tablets or smart-phones pinch-zoom or ____ anywhere in a column to best see it.  … Adjust settings to make the text easily readable.  … Usually landscape mode works best.
hide, double-tap
In our study sessions let us keep a loose leaf ____ in which we:

1)   Date the sheets.

2)   Note the questions that are most difficult to answer.

3)   Practice recall of these to end each session.

4)   Summarize in writing what we have learned.

5)   Record questions we may have and any answers from our parents, other students, our teacher.

6)   Do only a little each day.

In our studies we wish to practice recall of the ____ answers that complete the thought as expressed in the sentences in this left column.
These pages will help us learn & review what we need to know and do in ____ ____.
mathematics education
By repeatedly reviewing these notes the reader will refresh his/her ____  of the mathematics standards – including what teachers, tutors, parents and students must know and be able to do.
When reading the question we want to reflect on what each sentence says and means – to grasp sentences as ____ ____..
complete thoughts
These Q&A Notes are written in a conceptual,  ____  style.
We want to intentionally ___ ____ our reading to ensure comprehension.
 slow down
These Q&A Notes follow a successful note-taking approach  called the ____ ____ approach
Cornell Notes
In Cornell Notes we read and reflect by summarizing what we are to grasp.  Then we ____  ourselves repeatedly until we achieve recall retention.
In our studies we think there are ____ steps worth following.
First, we want to focus our working memory ____  on this left column – we will try to complete in our minds  each sentence to  form a complete thought.
Second, when we have difficulty completing a thought we simply un-hide the ____ ____ in the column on the right.
missing answer
Third, ____ any reading items that are difficult for us and reflect on it while hiding the answer column.
We do this until we can comfortably ____  the thought implied by the sentence.
Finally, we say out loud to ourselves any difficult thoughts. This gets the ____ ____ involved with both visual and text cues.
hearing sense
17    When saying the thought aloud we will be courteous – practicing sub-vocally in libraries or public places thinking there were many opportunities we could be . silently
18    We will learn here: 1) The ____ that define what we are expected to know and do,2) The math concepts needed,3) Explanations for rules that are called out in each standard, and 4) Guidance in practicing needed skills. standards
19    We will learn here:1) the standards that define what we are expected to know and do;2) the ____ ____ needed;3) explanations for rules that are called out in each standard, and 4) guidance in practicing the needed skills. math concepts
20    We will learn here:1) the standards that define what we are expected to know and do;2) the math concepts needed,3) explanations for ____ that are called out in each standard, and 4) guidance in practicing the needed skills. rules
21    We will learn here:1) the standards that define what we are expected to know and do;2) the math concepts needed;3) explanations for the rules that are called out in each standard; and 4) guidance in practicing the needed ____. skills
22    Notice the repetition in the above Q&A Sequence.  Must our learning be this ____? repetitive
23    Yes, we must repeatedly focus ____ ____ ____ on concepts in their native thought structures. working memory attention
24    There will be no ____  until we change for the long term the neural circuits in your brain. learning
25    This repetitive recall procedure will help us learn by changing the neural circuits in our ____ ____memory.  long term
26    However – before ____  concepts and/or rules  you must first understandthem. memorizing
27    To first understand the ____ used we must connect or relate them to prior knowledge – knowledge we are comfortable with. concepts
28    This is exactly like learning a new ____, where we MUST first memorize words, repeatedly translate them and then get experience by using them in a context, in real sentences.. language
29    To best learn mathematics we must understand the new material in terms of what we ____ ____. These connections are all-important. already know
30    We gain experience by using knowledge in ____  exercises. doing
31    We need to mix up the exercises to help us better recognize solution approaches that worked for us.
32    Without a goal to motivate us it will be difficult to repeatedly ____ your self – to measure and verify your ability to recall the learned material. self-quiz
33    We will gain ____ by successfully repeating this recall process. confidence
34    We know that unless we review ____ on a special schedule we will forget almost half of what we are exposed to within 7 days. repeatedly
35    To avoid forgetting and best retain (i,e, master) learned material, use the following recall practice ____ after first exposure: Days 1, 3, 7, 14, Month 1. … To refresh for examinations start a week earlier to refresh and aim for 2 perfect recall sessions. schedule