Tag Archives: cognition/learning/understanding

Four Very Basic Addition Worksheets

I’ve been assigned a math class this year. I’m not exactly well-suited to teach math; I struggled with it as a student, and really never made it past pre-algebra in high school. Nonetheless, I’m charged with teaching the subject. My students certainly deserve a better math teacher than I am–something I mention to them a couple of times a week.

In any case, here are four addition worksheets and their answer keys that I wrote for this class. There are a number of things I’m trying to assess with this preliminary work in the subject, one of the most important of which is any given student’s fund of working memory, a cognitive ability simply essential for math. You will see some problems repeat in different orders in an attempt to see if student recognize that they’ve seen the problem before. Also, using the same problem in different order gives students a chance to rehearse the commutative law of addition and teachers a chance to assess students’ understanding of this key concept in basic operations of mathematics.

If you find typos in these documents, I would appreciate a notification. And, as always, if you find this material useful in your practice, I would be grateful to hear what you think of it. I seek your peer review.

Euripides on Learning and Youth

“Whoso neglects learning in his youth, loses the past and is dead to the future.”

Euripides (480-406 B.C.)

Excerpted from: Howe, Randy, ed. The Quotable Teacher. Guilford, CT: The Lyons Press, 2003.

J.B. Sears on the Life of a Teacher II

Systematic living. What is needed by teachers is the application of a bit of system and common sense in their daily lives. Teaching cannot be sedulously followed by young people without sedulously offsetting its inactivity with outside exercise and pleasure. Every teacher should set aside a definite time for exercise, and a definite sum of money of recreation and pleasure. A regular time for a walk, a tennis game, a horseback ride; and a regular monthly allowance for theater, opera, travel, of the entertaining of one’s friends, will take one out into the open air where acquaintance with nature may be renewed, furnish a host of new thrills, and establish new interests and new companionships, which will drive away care, renew one’s mental and physical vigor, and provide a saner perspective for the serious tasks of the days to come.”

Excerpted from: Sears, J.B. Classroom Organization and Control. Boston: Houghton Mifflin, 1918.

J.B Sears on the Life of a Teacher I

Intelligent living. As a matter of self-protection, to say nothing of the wisdom of living a joyous life, the teacher must look to the problem of keeping an adequate margin of good health. This is largely the problem of proper rest and recreation. It is such a simple truth to say that when one is tired and half sick most any sort of work becomes barren drudgery, and yet this explanation is rarely thought of by the teacher who retires in disgust after a long evening spent in the useless task of correcting papers.”

Excerpted from: Sears, J.B. Classroom Organization and ControlBoston: Houghton Mifflin, 1918.

Term of Art: Acculturation

acculturation: The adoption by one society of a trait or traits from another society. The term is usually employed in anthropological contexts, and considers the change from the point of view of the recipient society. cf DIFFUSION.”

Excerpted from: Bray, Warwick, and David Trump. The Penguin Dictionary of Archaeology. New York: Penguin, 1984.

Term of Art: Dyscalculia

“Dyscalculia: Impairment of the ability to do arithmetic.

[From Greek dys– bad or abnormal + Latin calculare to count, from calculus diminutive of calx a stone + ia indicating a condition or quality]”

Excerpted from: Colman, Andrew M., ed. Oxford Dictionary of Psychology. New York: Oxford University Press, 2003.

Term of Art: Synesthesia

synesthesia: A medical (or psychological) term describing the occurrence when stimulating one sense organ causes another to respond. It is as though in eating one were to receive strong visual sensations of color rather than, or along with, sensations of taste. As a literary device, synesthesia has been used in certain types of poetry of the 19th and 20th centuries, especially that of the Symbolists. Rimbaud’s “Sonnet des voyelles,” expressing the sounds of the common vowels in terms of colors, is an excellent use of this device.”

Excerpted from: Murphy, Bruce, ed. Benet’s Reader’s Encyclopedia, Fourth Edition. New York: Harper Collins, 1996.

Term of Art: Action Reflection Process

“action reflection process: A structured discussion held during regular teacher meetings in which participants focus on a limited topic. Leaders of the discussion may begin with a provocative statement or video, which is called an action reflection tool. The action reflection process was created by the Education Development Center of Newton, Massachusetts.”

Excerpted from: Ravitch, Diane. EdSpeak: A Glossary of Education Terms, Phrases, Buzzwords, and Jargon. Alexandria, VA: ASCD, 2007.

Daniel Willingham on Reading and Conscious Awareness

“Being able to hear the sounds associated with letters doesn’t seem like it ought to me all that hard. Isn’t it obvious that a child can do that if she can hear the difference between big and dig in everyday speech? But that’s not quite the same task because in order to learn to read and write, the child must be aware of what differentiates big and dig, so she can think Aha, there’s the letter “d,” and I know what sound that makes! Many mental processes lie outside of awareness, and some seem destined to remain so. For example, you obviously know how to shift your weight to stay upright on a bicycle, but that knowledge is accessible only to the parts of the brain that control movement. You can’t examine that knowledge or describe it. Other types of knowledge are unconscious, but can become conscious. For example, most people speak grammatically—even if they violate some rules taught in school, they speak in accordance with others in their linguistic community. People are unaware of these rules, but can consciously learn them. Hearing individual speech sounds is analogous. Any speaker can hear that big and dig differ and although people aren’t born with the ability to describe the difference, most can learn to do so.”

Excerpted from: Willingham, Daniel T. The Reading Mind: A Cognitive Approach to Understanding How the Mind Reads. San Francisco: Jossey-Bass, 2017.

Aristotle on the Educated and Uneducated

“The educated differ from the uneducated as much as the living from the dead.”

Aristotle (384-322 B.C.)

Excerpted from: Howe, Randy, ed. The Quotable Teacher. Guilford, CT: The Lyons Press, 2003.