Category Archives: Uncategorized

More Cartoons on Teaching and Learning Math in and out of School

Cartoons about teaching academic subjects have appeared in this monthly feature many times. Teaching and learning math in and out of school, it seems, gives cartoonists’ pens ample subject matter to make fun of. This month is no exception. Enjoy these!






























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Part 6: Summit Rainier Teachers Integrating Technology: Chemistry

After spending six years working for pharmaceutical companies, Edward Lin who had tutored students while working as a chemist, decided to change careers. He went to  University of California, Berkeley and secured his state teaching credential. Attending various career fairs for teachers, Lin heard about Summit, researched the school, garnered an interview and was hired as a chemistry teacher. He has been at Summit Rainier for two years.

On March 16, 2016 I observed Lin teach from 11:25 to 1:00 a lesson on metals (including a Lab) to 17 students sitting two to a table facing the “smart” board at the front of the portable classroom. A Periodical Table hung from one wall of the classroom. A sink in the back of the room students used to wash hands, vials, and get water for experiments. Tubs of equipment, goggles, test tubes, and other paraphernalia, rested on tables also at the rear of the classroom.

Lin has prepared a series of activities, beginning with the Warm Up, on slides and shows them to students as he segues from one task to another over the course of 95 minutes.

One slide lists the items today’s lesson will cover:
*Project Introduction
*Molecule Selection
*Is it a metal? Lab
*Are atoms in your molecule metal or nonmetal?

The Warm Up (see slide 2 here)  which introduces the unit asks students to identify common tools used in kitchen and around the house and answer questions about them.   Students pair up and generate examples such as knives, wrenches, pencils, etc. in response to Lin’s request. Discussions engage each table as I scan the room. Teacher then asks students to answer three questions about each tool they identified: How does the tool’s shape allow it to do the job? What material(s) is the tool usually made of? Why is the tool usually made from the material(s)?

A whole group discussion of these tools ensues for about 10 minutes. Lin calls on students by name. Few raised their hands. As I scanned the classroom, most students were listening and responding to the teacher’s prompts. A few were not. Those who were not looked at their cell phones which were lying on their desks or were quietly chatting with table-mates. The teacher stops talking, motions to one of the chatterers and she stops. He continues to guide the discussion and makes the central point that these tools students identified are made of metal and other materials containing molecules with certain properties allowing the tool to do its work as a tool. The discussion continues until Lin moves to the next task of reviewing the entire project.

The teacher goes through a series of slides (see here, slide 3) covering what students have to do (e.g., choose a molecule they want to work on; produce a 2-D or 3-D model of the molecule each student chooses that can be made out of clay, drawn, crocheted, etc.; make an oral presentation (e.g., write and read an essay, present a comic book, do a PowerPoint lecture). Lin gives many examples for each of the tasks students need to complete and then asks students at each table–usually two and sometimes three–to choose a molecule in the next 15 minutes from the list that they have in a handout. Students use their Chromebooks to look up particular metal and non-metal molecules and ask Lin questions as he circulates around the class. Some of the students have quickly glommed onto the task and tell the teacher immediately which molecules they want to focus on. Lin takes down names and the molecules they chose. There is a flurry of activity when two different tables of students chose the same molecule (e.g., silicon). The teacher negotiates agreement between tables competing for the same element one team choosing another one.

Lin then segues to the handout labeled “Is It a Metal?” (see here) that will guide the Lab they do. The teacher had prepared samples of elements (e.g. lead, magnesium,calcium, copper, silicon) arrayed on two front tables. The Lab directions ask students to test each element and determine whether the element is a metal, nonmetal, or metalloid. Pairs of students are to get samples from the array of elements lying on the tables, test each one at a time, and record data, making observations of what they see happening (or not happening). Each element, say copper or aluminum, has certain properties (e.g., appearance, conductivity, brittle or flexible, reaction to acid). These properties are listed in handout. Students are to check the reaction of each element to hydrochloric acid and copper chloride. Based on the data students collect and the properties these elements have, they are to determine whether, for example, silicon, carbon, magnesium are metals, non-metals or metalloids.

Most of the students go to the rear of the portable where I am sitting and pull from various tubs of equipment, pairs of goggles and test tubes, return to their table and then go up to where the elements are arrayed at the front of the room and begin testing the properties of each one. A few students hang back and as they see others engaged begin to take part in Lab. Lin walks around the room answering questions, offering hints to puzzled students, and monitoring those less engaged in the Lab. Most of the students are working on the task. They carry their Chromebooks with them to record data and confer with one another in their group about what they see.

From time to time, Lin reminds students how much time is left to complete filling up the sheets and recording the data. One group of five students dip into and out of the Labwork as they do the operations chatting and laughing. The teacher sits down with a few of them to see how they are doing on the tasks. Other students have completed the Lab and ask Lin what they should do and he directs them to push ahead with otherparts of the unit that he had previewed earlier in the period.

At 12:45, the stop watch is at 0:00 and Lin tells students to clean up. Students line up at sink to wash out test tubes, dry their hands, and at their tables compare what they have found with other groups of students.

Lin then convenes the whole class–he counts down from 5 to 1–and says: “Let’s chat a bit.” He asks which of the elements are metals. Students call out answers: “copper,” zinc.” Lin follows up and asks what are the properties of these metals. More call-outs from students (e.g., “you can bend copper,” “when acid hit, bubbles came up in test tube”). One student is puzzled over silicon and Lin notes that and elaborates on the element. He then asks class about carbon. He clicks away on his laptop and student answers about each of the elements they examined appear on the screen. “Nonmetals are brittle, dark, not shiny, and barely conductive.” He then goes to Periodic Table and asks students to look at how metals, nonmetals, and metalloids are aligned on the Table. This is a mini-lecture with a handful of minutes remaining. Restlessness rises in the room. Lin concludes the summary and students pack up and move toward door of portable. In a few moments, the teacher releases the class to go their next one.






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Cartoons on Computers in Our Lives

Trite as it is to say, but interacting with computers in work, social media, and other parts of our lives is pervasive for readers of this blog. So for this month’s cartoon feature, I have picked a few that tickled me. Enjoy!






























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Summit Charter Teachers Integrating Technology: Part 3–Precalculus

There are eight Summit charter schools in the San Francisco Bay area (and two in Washington state). They serve over 2,500 students of whom nearly half are Latino, 20 percent are white, 11 percent are Asian, seven percent are multiracial and six percent are African American. Just over  40 percent are poor (the proxy measure for poverty are those students eligible for free and reduced price lunch). Ninety-eight percent graduate and attend at least one four-year college. Summit Prep, where Precalucus teacher, Ethan Edwards teaches, was the first school (2003) in the charter network. Ninth through 12th grade, Summit Prep has 400 students chosen through lottery who seek to attend college. Like other Summit schools, Prep has a similar demography of diverse population and rate of poverty to the rest of the schools in the network.

The Block 2 Precalculus class in Redwood City began at 10:40 and ended at 12:15. Ethan Edwards is in his third year of teaching at Summit. He was a math major at University of California, Santa Cruz and got his credential to teach at the University of California, Davis before coming to Summit. He, like other Summit teachers who have been at the high school beyond one year float to different classrooms in the building; first-year teachers have one classroom the entire day. So at the beginning of the block 2 class, he and a few students are shoving tables into rows facing the front to get ready for his class. Four tables sitting two students each in three rows accommodated the 24 students who arrived. Like all Summit classrooms, there was an LCD projector and screen at front of room that showed slides as the teacher clicked keys.

The agenda for the day is on the screen.

“* Warm Up Analysis

* Essay Overview

*Independent work time + workshop

*Goal: finish paragraph


Since the class will be visiting University of California, Davis for the next two days, Edwards flashes slides of buildings at Davis that they will see. He asked students to turn in forms for trip later in the day. He explains the housing arrangements–4 students to a room. There were ripples of excitement and nervousness about the trip, especially after he announced that there will be four students to each car in driving to Davis. Students look around, start signaling one another to share same car. Edwards says:  “I can feel the tension in the room over who I will be with in car for the trip.” That lowers the murmuring and tension. There were a few questions from students. He reassures students by saying that it is a short car trip to the university. Teacher then segues to lesson.

“I want to talk about how we are going to predict tuition increases through 2020 from the data set I gave you. We will be doing scatter plots and writing different regression equations.” Edwards proceeds to explain the making of regression curves (linear, exponential, and polynominal)–the central point of the lesson–using the white board as he writes down key concepts. He goes over “key features” of such data and equations and how it gets displayed as outliers, intercepts,slope, rate of growth, and residuals. In every instance, he defines them and brings into the explanation particular students who respond to his choral questions (these are questions directed to the entire class and have no student name attached either before or after the question is asked).   Students do contribute. Teacher draws on the white board examples of each concept thereby defining the terms for class. He brings the explanation of what students will work on to a close, saying: “So, I just talked a lot about some high level stuff.” He asks, “Are there any questions?” No one asks a question.

Teacher then turns to spread sheet of data on tuition costs for two schools. “So you are going to look at how to use this spreadsheet to come up with functions to predict increases in tuition costs through 2020.” He passes out data set and asks students to pair with partner to go through the data.

Before students open their Chromebooks to look at spreadsheets and begin work, Edwards goes over with whole group, step-by-step, how they are to create a linear regression equation. Does same for exponential and then polynominal equations. During his explanation, he asks choral questions of class to check for understanding. A few students respond to each query. When hearing one or two responses that match the question, he picks up on the answer and continues the explanation. After he finishes going over the three regression equations, he asks: “are there any questions about how to use the data spreadsheet to create these equations?”

No student asks a question.

He returns to explaining where students should input data. He then directs students to open their Chromebooks.

“I am going to give you guys 30 minutes to start to work in pairs on spreadsheet to make proper equations.” He discusses due date for when they will turn in their work.

For next 30 minutes Edwards moves up and down aisles to answer questions, check on what each student is doing, and help individual students who are having trouble with task. At this point I had leave the classroom because of another appointment elsewhere in the school.





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Cartoons on Digital Life

For this month, I have selected an array of cartoons that slice-and-dice the influence of digital technologies on our daily lives. Enjoy!

























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Zombie Ideas Again: “The Learning Pyramid”

Stories, ideas, and beliefs that have been disproved through scientific studies litter the mind. Professionals across-the-board in medicine, law, architecture, engineering, and business take-for-granted stories that have little to no basis in evidence. Yet they persist.

In earlier posts, I have identified such “zombie” ideas that have scientific-crafted shafts buried in their heart yet arise again and again (see here and here). I offer another one that a viewer of this blog (Pedro De Bruyckere, a teacher educator in Ghent, Belgium) suggested in a recent comment . He and colleagues have written a book about common myths that educators hold and he reminded about the “Learning Pyramid.”


A cottage industry of debunkers have pointed out many times over the past quarter-century that the “Pyramid” has no scientific standing and comes from unattributed sources mushed together in the 1960s and 1970s (see here, here, and here). Although it lives on, seldom, however, in official programs (there are exceptions, see here) the “Pyramid” resides quietly and strongly in the folk wisdom of those many practitioners who believe in their heart-of-hearts that active or experiential learning is far better (and more effective) than teachers talking, showing visuals, or demonstrating concepts. How come?

Such beliefs about knowledge retention exist in the minds of many college educators and practitioners across the professional spectrum–increased by the launching of lecture-dominated  MOOCs and surge in lecture-driven online courses–representing another instance of “confirmation bias.”

Why does the belief in the “Learning Pyramid” persist in the face of so much counter-evidence? The zombie effect about the “Pyramid,”and here is where I am speculating, reinforces the tilt that so many university teacher educators and workplace practitioners have toward student-centered, experienced-driven learning. Such ways of thinking about better ways of teaching were pushed by early 20th century pedagogical progressives, 1960s-era neo-progressives, and now with the explosion of “personalized” and blended learning, many reformers have shrouded themselves in the cloak of student-centered learning. Progressive rhetoric about student-centered teaching and learning abounds.

I have no bias for or against student-centered, project-based, whole child-driven progressive teaching (or whatever label best fits). I have stated my position often that those who teach daily need mixes of both student-centered and teacher-centered practices. They need a broad repertoire of ways of teaching. My histories of how teachers have taught since the mid-19th century make that point in capital letters. I have worked hard to scrub any bias toward one or the other set of classroom practices, always arguing that “hugging the middle” of the spectrum on teaching approaches is both historical and consistent with contemporary practices that I have found in classrooms around the nation. Having said that, I have also found that many teacher educators and practitioners cherish the notions, but particularly the talk, that one way of teaching is better than another and that way is student-centered, however defined. The “Learning Pyramid” while not often referred to explicitly gives such believers aid and comfort because the bottom three strata of the “Pyramid” confirm that student participation retains the most knowledge–even though past and current studies fail to find that to be true.

Consider teacher educators. David Labaree argues that university schools of education became centers of progressive rhetoric about child-centered education over decades (see here) even though the realities of public school organization, curriculum, and instruction tilted strongly toward encouraging teacher-centered instruction. Teacher educators, he says, prepared their charges for classrooms for a workplace where progressive methods should be used but seldom were. Lecturing to students, “direct instruction” and more teacher talk than student talk were negatives to many of these teacher educators. The “Learning Pyramid,” seldom referred to explicitly,  justified language and approaches to instruction that privileged discussion, small groups, and active student participation (see here).

Turn to classroom teachers. In my research of teachers past and present, I have found that primary grade teachers generally adhere to more student-centered, whole-child approaches than secondary school teachers. There does remain, however, even among those upper-grade teachers who see their primary duty to convey content and teach skills a rhetorical embrace of student participation with recognition that such approaches are harder to implement, particularly in times when standards, testing, and accountability are dominant policy prescriptions.

These deeply buried progressive beliefs among so many teacher educators and practitioners feed and nurture the “Learning Pyramid,” I believe, so that it persists well after it has been debunked and buried.





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Cartoons about Winter Holidays–Families, Children, and Schools

For this month with winter holidays upon the nation, I have gathered some cartoons that poke fun at what transpires in homes, schools, and Santa’s place. Enjoy!













Let's stick to 'No room at the inn' and leave out 'Have you tried the internet?'


'In our class's Christmas pageant, I'm playing the department store manager.'






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