1. Information is passed from the sensory memory into short-term memory via the process of attention (the cognitive process of selectively concentrating on one aspect of the environment while ignoring other things), which effectively filters the stimuli to only those which are of interest at any given time.
Long-Term Memory © 2010 Luke Mastin

2. Unlike with short-term memory, forgetting occurs in long-term memory when the formerly strengthened synaptic connections among the neurons in a neural network become weakened, or when the activation of a new network is superimposed over an older one, thus causing interference in the older memory.
Long-Term Memory © 2010 Luke Mastin

3. Copyright 2015 by Delano P. Wegener, Ph.D. All Rights Reserved.
Initial Learning of Information by Delano P. Wegener, Ph.D. August 2015
Copyright 2015 by Delano P. Wegener, Ph.D. All Rights Reserved.

4. “No matter what you may set your sights on doing or becoming, if you want to be a contender, it’s mastering the ability to learn that will get you in the game and keep you there.” 1 In this Power Point presentation we set our sights on succeeding in a basic mathematics course. For the purpose of this presentation the intent is to learn some basic algebra and to remember it long enough to do well on the final exam.
1. Brown, Peter C. ( ). Make It Stick (p. 200). Harvard University Press. Kindle Edition.

5. In this Power Point presentation we concentrate on learning information, learning facts. Ultimately in a mathematics course we expect students to learn how to use deductive reasoning XXXXXXXXXXXXXXXXXX The learning principles presented in this Power Point presentation are not restricted to learning mathematics. Current cognitive research demonstrates that these principles apply to ALL learning, in and out of a classroom.
1. Brown, Peter C. ( ). Make It Stick (p. 200). Harvard University Press. Kindle Edition.

6. We need to keep learning and remembering all our lives.
SOME BASIC PRINCIPLES
To be useful, learning requires memory, so what we have learned is still there later when we need it.
We need to keep learning and remembering all our lives.
Learning is an acquired skill
The most effective strategies are often counterintuitive.
The most common strategies are often nonproductive.
Learning is deeper and more durable when it is effortful.
Adapted from: Brown, Peter C. ( ). Make It Stick (p. 2-3). Harvard University Press. Kindle Edition.

7. Learning is Hard Work
Learning is hard. Thinking is hard. It’s as exhausting, though in a different way, as physical labor and wears most of us down at a similar rate.
Carey, Benedict ( ). How We Learn: The Surprising Truth About When, Where, and Why It Happens (p. 209). Random House Publishing Group. Kindle Edition.

8. “All new learning requires a foundation of prior knowledge
“All new learning requires a foundation of prior knowledge.” 1 (DrDel) Memorization of stipulative mathematics definitions provides a form of foundational knowledge upon which to build a complete concept. An understanding of place value is necessary for a real understanding of polynomials. A knowledge of the set of rational numbers is required to understand many results in algebra. (e.g. Rational Zeros Theorem). A knowledge of the concept of set is prerequisite to learning about solution sets.
1. Brown, Peter C. ( ). Make It Stick (p.5). Harvard University Press. Kindle Edition.

9. most of our instincts about learning are misplaced, incomplete, or flat wrong. That we invent learning theories out of whole cloth, that our thinking is rooted more in superstition than in science, and that we misidentify the sources of our frustration: that we get in our own way, unnecessarily, all the time.
Carey, Benedict ( ). How We Learn: The Surprising Truth About When, Where, and Why It Happens (p. 213). Random House Publishing Group. Kindle Edition.

10. A baseball consists of a central core tightly wrapped in several layers of different materials. Construction of a golf ball is similar. As a matter of fact many familiar objects, including the earth, have similar constructions.
On a more abstract level, simple mathematics concepts are similarly constructed. It is convenient to think of them as a central core (definition) tightly wrapped in several layers of illuminating information.
Complex mathematics concepts consist of many simple mathematics concepts joined together.

11. we should have developed pretty keen instincts about how best to approach learning. But we haven’t, and the reasons why aren’t at all apparent. No one that I know of has come forward with a convincing explanation, Carey, Benedict ( ). How We Learn: The Surprising Truth About When, Where, and Why It Happens (p. 214). Random House Publishing Group. Kindle Edition.

12. If learning is so critical to survival, why do we remain so ignorant about when, where, and how it happens? Carey, Benedict ( ). How We Learn: The Surprising Truth About When, Where, and Why It Happens (p. 213). Random House Publishing Group. Kindle Edition.

13. From Why students don’t like school – find it
In sum, successful thinking relies on four factors: information from the environment, facts in long-term memory, procedures in long-term memory, and the amount of space in working memory. If any one of these factors is inadequate, thinking will likely fail.
From Why students don’t like school – find it

14. “The fact that you can repeat the phrases in a text or your lecture notes is no indication that you understand the significance of the precepts they describe, their application, or how they relate to what you already know about the subject.” 1 (DrDel) Memorization of stipulative mathematics definitions is essential because of their stipulative nature and because they are the core element around which we construct complete concepts. The above claim from “Make It Stick” does not preclude the necessity, in some instances, to begin the study of an abstract concept with rote memorization of key definitions.
1. Brown, Peter C. ( ). Make It Stick (p.16). Harvard University Press. Kindle Edition.

15. Elaboration
“Elaboration is the process of finding additional layers of meaning in new material.” 1
Elaboration may include illustrative examples, relating it to knowledge you already know, or a visual image.
The more you can elaborate on how new learning relates to what you already know, the stronger your grasp of the new learning will be, and the more connections you create to remember it later.
Elaboration is very important in mathematics. Titles of courses, textbooks, chapters, sections, and subsections are deliberately chosen to promote this last form of elaboration.
1. Brown, Peter C. ( ). Make It Stick (p.207). Harvard University Press. Kindle Edition.

16. Memory is the residue of thought. Willingham, Daniel T. (2009-06-10)
Memory is the residue of thought. Willingham, Daniel T. ( ). Why Don't Students Like School?: A Cognitive Scientist Answers Questions About How the Mind Works and What It Means for the Classroom (Kindle Location 1083). Wiley. Kindle Edition.

17. If you don’t pay attention to something, you can’t learn it
If you don’t pay attention to something, you can’t learn it! You won’t remember much of the seminar if you were thinking about something else. Willingham, Daniel T. ( ). Why Don't Students Like School?: A Cognitive Scientist Answers Questions About How the Mind Works and What It Means for the Classroom (Kindle Locations ). Wiley. Kindle Edition.

25. In this Power Point Presentation: “When we talk about learning: we mean acquiring knowledge and skills and having them readily available from memory so you can make sense of future problems and opportunities.” 1 When we talk about problems: we mean any cognitive work that requires attention. “When we talk about solving problems: we mean any cognitive work that succeeds.” 2 (DrDel) These are examples of stipulative definitions.
1. Brown, Peter C. ( ). Make It Stick (p.2). Harvard University Press. Kindle Edition.
2. Willingham, Daniel T. ( ). Why Don't Students Like School?: A Cognitive Scientist Answers Questions About How the Mind Works and What It Means for the Classroom (Kindle Location 260). Wiley. Kindle Edition.

26. Rereading text and massed practice are the preferred study strategies of most learners and teachers, but they are also among the least productive. (DrDel) Mathematics education has incorrectly focused on massed practice. Retrieval practice (recalling facts or concepts or events from memory) is a more effective learning strategy than review by rereading. When used properly and spaced appropriately flashcards provide excellent retrieval practice.
Adapted from: Brown, Peter C. ( ). Make It Stick (p.3). Harvard University Press. Kindle Edition.

27. Interrupted Forgetting Curve
“Periodic practice arrests forgetting, strengthens retrieval routes, and is essential for hanging onto the knowledge you want to gain.” (DrDel) Notice that after each successive interruption forgetting “tails off” at a higher percentage.
Uninterrupted Forgetting Curve
Interrupted Forgetting Curve
1. Brown, Peter C. ( ). Make It Stick (p.4). Harvard University Press. Kindle Edition.

28. When you space out practice of a task and get a little rusty between sessions, or you interleave the practice of two or more types of tasks, retrieval is harder and feels less productive, but the effort produces longer lasting learning and enables more versatile application of it in later settings. (DrDel) Spaced practice is a very powerful learning tool. Spaced practice is easy to implement with proper use of flash cards. The advantage of spaced practice was first observed by Ebbinghaus in 1885 and no study has ever been able to refute it. My students have successfully use spaced practice since I started touting its benefits around We all want longer lasting results even if only to get through the comprehensive final exam.
Adapted from: Brown, Peter C. ( ). Make It Stick (p.4). Harvard University Press. Kindle Edition.

29. (DrDel) The preferred method of interrupting the forgetting curve is with spaced retrieval practice.
Such practice is achieved with flashcards, interleaved practice exercises, and frequent low-stakes quizzes.

30. Even the most diligent students are often hobbled by two liabilities:
a failure to know the areas where their learning is weak
a preference for study methods that create a false sense of mastery.
Adapted from: Brown, Peter C. ( ). Make It Stick (p.17). Harvard University Press. Kindle Edition.

31. determine how much a student knows.
One of the most striking recent research findings is the power of active retrieval to strengthen memory. Moreover, the more effortful the retrieval, the stronger the benefit. Testing is a form of active retrieval. If a test is used to practice retrieval of knowledge from memory then that test is a tool for learning. Therefore frequent spaced self-tests and other low-stakes tests are powerful learning tools. (DrDel) Retrieval practice is also critical to making knowledge accessible to us when we need it.
Tests can be used to:
determine how much a student knows.
determining what a student must learn.
practice retrieval of knowledge from memory.
Adapted from: Brown, Peter C. ( ). Make It Stick (p.19). Harvard University Press. Kindle Edition.

32. Interleaving practice different topics related topics or skills
As a result of recent research we know simple and practical strategies that anybody can use, at any point in life, to learn better and remember longer:
Retrieval practice
low-stakes quizzes
self-tests
Spaced practice
Interleaving practice
different topics
related topics or skills
Trying to solve a problem before being taught the solution.
Distilling the underlying principles or rules that differentiate types of problems, and so on.
Brown, Peter C. ( ). Make It Stick (p.19-21). Harvard University Press. Kindle Edition.

33. Take charge of your education by implementing the following.
Practice Retrieving New Learning from Memory
Space Out Retrieval Practice
Interleave the Study of Different Problem Types
Other Effective Study Strategies
Elaboration
Generation
Reflection
Calibration
Mnemonics
Avoid massed practice
Avoid excessive rereading
Avoid excessive underlining
Brown, Peter C. ( ). Make It Stick (p ). Harvard University Press. Kindle Edition.

34. Practice Retrieving
First, as we recode and consolidate new material from short-term memory into long-term memory, we must anchor it there securely.
Second, we must associate the material with a diverse set of cues that will make us adept at recalling the knowledge later. Having effective retrieval cues is an aspect of learning that often goes overlooked.
Adapted from: Brown, Peter C. ( ). Make It Stick (p.75). Harvard University Press. Kindle Edition.

35. Practice Retrieving
Aristotle wrote: “exercise in repeatedly recalling a thing strengthens the memory.”
Practicing retrieval makes learning stick far better than re-exposure to the original material does.
The act of retrieving a memory changes the memory, making it easier to retrieve again later.
Repeated retrieval not only makes memories more durable but produces knowledge that can be retrieved more readily, in more varied settings, and applied to a wider variety of problems.
Adapted from: Brown, Peter C. ( ). Make It Stick (p.28,41,43). Harvard University Press. Kindle Edition.

36. Spaced Retrieval Practice
When retrieval practice is spaced, allowing some forgetting to occur between tests, it leads to stronger long-term retention than when it is massed.
The advantage of spaced practice was first observed by Ebbinghaus in 1885 and no study has ever been able to refute it.
Delaying subsequent retrieval practice is more potent for reinforcing retention than immediate practice, because delayed retrieval requires more effort.
(DrDel) It has always baffled me that for 130 years we have known the disadvantage of massed practice and the advantage of spaced and yet all math textbooks and other study materials are based on massed practice.
Adapted from: Brown, Peter C. ( ). Make It Stick (p.32,43). Harvard University Press. Kindle Edition.

37. Avoid Massed Practice
“Faith in focused, repetitive practice of one thing at a time until we’ve got it nailed is pervasive among classroom teachers, athletes, corporate trainers, and students. Researchers call this kind of practice “massed,” and our faith rests in large part on the simple fact that when we do it, we can see it making a difference. Nevertheless, despite what our eyes tell us, this faith is misplaced.” 1
“Cramming for exams is a form of massed practice. It feels like a productive strategy, and it may get you through the next day’s midterm, but most of the material will be long forgotten by the time you sit down for the final. “ 1
Working many problems of the same type at the end of a section is massed practice and is quite ineffective. It is more like training than learning.
1. Brown, Peter C. ( ). Make It Stick (p.47,48). Harvard University Press. Kindle Edition.

38. Avoid Massed Practice
“In math education, massing is embedded in the textbook: each chapter is dedicated to a particular kind of problem, which you study in class and then practice by working, say, twenty examples for homework before you move on. The next chapter has a different type of problem, and you dive into the same kind of concentrated learning and practice of that solution. On you march, chapter by chapter, through the semester. But then, on the final exam, lo and behold, the problems are all mixed up: you’re staring at each one in turn, asking yourself Which algorithm do I use? Was it in chapter 5, 6, or 7? When you have learned under conditions of massed or blocked repetition, you have had no practice on that critical sorting process.” 1
1. Brown, Peter C. ( ). Make It Stick (p.53). Harvard University Press. Kindle Edition.

39. Interleaving
“Practice that’s spaced out, interleaved with other learning, and varied produces better mastery, longer retention, and more versatility.” 1
“The learning from interleaved practice feels slower than learning from massed practice. Teachers and students sense the difference. They can see that their grasp of each element is coming more slowly, and the compensating long-term advantage is not apparent to them. As a result, interleaving is unpopular and seldom used.” 1
“A significant advantage of interleaving and variation is that they help us learn better how to assess context and discriminate between problems, selecting and applying the correct solution from a range of possibilities.” 1
1. Brown, Peter C. ( ). Make It Stick (p.47,50). Harvard University Press. Kindle Edition.

40. Reflection
“Reflection is the act of taking a few minutes to review what has been learned in a recent class or experience and asking yourself questions.” 1
Reflection adds layers to learning and strengthens skills.
Questions you might ask after a math class or study session.
Is this an object, operation, or relation?
How does this material relate to previous knowledge?
Did the examples illustrate the concepts?
Can I create additional examples?
What kind of problems will this help solve?
What makes this concept important?
Is this a generalization of a known concept?
1. Brown, Peter C. ( ). Make It Stick (p.209). Harvard University Press. Kindle Edition.

41. Generation
Generation is an attempt to answer a question or solve a problem before being shown the answer or the solution.
Fill in the blank test questions are simple examples of generation.
Using known concepts to devise a solution to an unfamiliar problem without being told how to solve the problem is an advanced form of generation we expect students to achieve in math classes.
Adapted from: Brown, Peter C. ( ). Make It Stick (p.208). Harvard University Press. Kindle Edition.

42. Calibration
“Calibration is the act of aligning your judgments of what you know and don’t know with objective feedback so as to avoid being carried off by the illusions of mastery that catch many learners by surprise at test time.” 1
“Calibration is simply the act of using an objective instrument to clear away illusions and adjust your judgment to better reflect reality.” 1
Flashcards provide a ready quiz. Read side one and then WRITE (without looking) precisely what is on side two.
In mathematics if you cannot WRITE a definition, property, rule, or procedure precisely, then you do not know it.
Brown, Peter C. ( ). Make It Stick (p ). Harvard University Press. Kindle Edition.

43. Calibration
Use quizzes and practice tests to see whether you know as much as you think you do.
It is very important that you write the answers to questions in a self-quiz.
It is natural to look at a question on a practice test and say: Yup, I know that, and move on to the next question without making the effort to write the answer.
If you don’t write the answer, you may be giving in to the illusion of knowing, when in fact you would have difficulty rendering an accurate or complete response. This is extremely important in mathematics because mathematics demands precision and completeness.
Adapted from: Brown, Peter C. ( ). Make It Stick (p.210). Harvard University Press. Kindle Edition.

44. Calibration
Treat practice tests as tests, check your answers. Be a harsh grader.
Focus your studying effort on the areas where you are not up to snuff.
Adapted from: Brown, Peter C. ( ). Make It Stick (p.210). Harvard University Press. Kindle Edition.

45. Mnemonics
“Mnemonic devices help you to retrieve what you have learned and to hold arbitrary information in memory.” 1
I do not recommend mnemonic devices for mathematics because:
What you are trying to remember is not arbitrary.
The mnemonic device obscures the math concept.
The mnemonic device obscures connections and context.
The mnemonic is harder to remember than the math.
1. Brown, Peter C. ( ). Make It Stick (p.211). Harvard University Press. Kindle Edition.

46. Practice Retrieving New Learning from Memory
Current research has yielded at least three keystone and five supporting study strategies which can be implemented for significant benefit. That same research identifies at least three strategies to avoid.
Practice Retrieving New Learning from Memory
Space Out Retrieval Practice
Interleave the Study of Different Problem Types
Other Effective Study Strategies
Elaboration
Generation
Reflection
Calibration
Mnemonics
Avoid massed practice
Avoid excessive rereading
Avoid excessive underlining
Brown, Peter C. ( ). Make It Stick (p ). Harvard University Press. Kindle Edition.