Children’s Books That Turbocharge the Math Curriculum

        “Integrating children’s literature into math makes learning more engaging and less intimidating,” says South Carolina educator Candice Brucke in this helpful article in AMLE Magazine. “It can motivate, provoke interest, connect mathematical ideas, promote critical thinking skills, inspire a creating writing experience for students (and teachers), and provide a context that leads to problem solving.” She believes her use of well-chosen books was a major reason for very high achievement in her classes – her class ranked ninth best in the entire state in 2007. Here are some of her suggestions, including one she wrote herself:

• The Grapes of Math (Tang, 2004) and The Important Book (Brown, 1999) to teach number properties;
• A Giraffe to France (Hillard, 2000) for measurement and writing and solving equations;
• The Missing Piece (Silverstein, 2006) for missing-angle measures and sectors of a circle;
• How I Became a Pirate (Long, 2003) to assess students’ prior knowledge on the coordinate plane;
• Sir Cumference and the Dragon of Pi (Neuschwander, 1999) for circumference and π.
• Skippyjon Jones Lost in Spice (Schachner, 2005) for combinations and permutations;
• Wrappers Wanted: A Mathematical Adventure in Surface Area (Brucke, 2009) for surface area;
• Chasing Vermeer (Balliett, 2005) to introduce manipulatives such as pentominoes;
• My Full Moon Is Square (Pinczes, 2002) for the concept of square numbers;
• The Lion King (Disney, 1994) for the concept of slope – students can graph the good/ill fate points for a particular character;
• What’s Your Angle, Pythagoras? (Ellis, 2004) for the Pythagorean Theorem applied to everyday situations;
• One Grain of Rice (Demi, 1997) for exponential growth;
• Cinder Edna (Jackson, 1998) for box/scatter plots;
• Multiplying Menace: The Revenge of Rumplestiltskin (Calvert, 2006) to review fractions.

 

“Connecting Children’s Literature to Middle Grades Math” by Candice Brucke in AMLE Magazine, March 2014 (Vol. 1, #7, p. 23-24), www.amle.org; Brucke can be reached at cbrucke@oconee.k12.sc.us.

 

 

Stephen Anderson

Bringing the Lewis and Clark Expedition to Life

        “Far too frequently, many students find history to be boring, rate it as their least favorite subject, or perceive it as irrelevant,” say Scott Waring (University of Central Florida) and Cicely Scheiner-Fisher (Seminole County Schools instructional specialist) in this Middle School Journal article. But they believe that even tech-savvy adolescents will love history if teachers use primary-source documents and focus on how events affected ordinary people. Waring’s and Scheiner-Fisher’s article is a detailed example of how this played out in a unit on the Lewis and Clark expedition. The big question for the unit: What was it like for Lewis and Clark to travel west? Here is the seven-step SOURCES framework they used:

        • Scrutinize the primary source material. From the Library of Congress collection, Waring and Scheiner-Fisher chose Thomas Jefferson’s letter of instructions for the expedition as the best document (see http://tinyurl.com/7b7wbg6). To scaffold students’ close reading of this document, they used a primary source analysis sheet produced by the Library of Congress.

        • Organize thoughts. Students watched a video providing background, including the fact that Jefferson’s letter went through multiple drafts and incorporated feedback from a number of experts and political figures.

        • Understand the context. Students learned about the historical background of the expedition and Jefferson’s goals.

        • Read between the lines. Using this information, students re-read the primary document with new understanding.

        • Corroborate and refute. At this point, students were asked to examine other primary documents on the Library of Congress website to learn more about the expedition:

http://www.loc.gov/exhibits/lewisandclark/lewis-landc.html.

        • Establish a plausible narrative. Students were assigned the following performance task: pretend you are a member of the expedition and write a journal on how it unfolded.

        • Summarize final thoughts. Students were asked to pull together what they learned and what questions still lingered.

 

“Using SOURCES to Allow Digital Natives to Explore the Lewis and Clark Expedition” by Scott Waring and Cicely Scheiner-Fisher in Middle School Journal, March 2014 (Vol. 45, #4, p. 3-11); www.amle.org; the authors can be reached atScott.Waring@ucf.edu and Cicely_Fisher@scps.us. The full article is rich with details and suggested websites.

 

 

Stephen Anderson

Anger, In Moderation, Is Emotionally Intelligent

        In this intriguing Psychology Today article, Joanne Ellison Rodgers says that anger (mild to moderate, not uncontrolled rage) is an important and functional emotion. “Researchers are amassing evidence that anger is a potent form of social communication,” says Rodgers, “a logical part of people’s emotional tool kit, an appetitive force that not only moves us toward what we want but fuels optimism, creative brainstorming, and problem solving by focusing mind and mood in highly refined ways. Brainwise, it’s the polar opposite of fear, sadness, disgust, and anxiety – feelings that prompt avoidance and cause us to move away from what we deem unpleasant. When the gall rises, it propels the irate toward challenges they otherwise would flee and actions to get others to do what they, the angry, wish.” For example, the anger Americans felt after 9/11 brought people together in a common cause and minimized paralyzing fear.

        Interestingly, when we’re angry, heart rate and testosterone levels rise but cortisol, the stress hormone, falls. Brain scans have also shown that anger activates the left frontal lobe and the left anterior cortex, which control rational, logical, systematic, and positive ways of dealing with a problem. In short, anger works to help us focus on a challenge and think straight – as opposed to avoiding or running away from it. “Anger allows us to detect our own value in any conflicting interaction,” says Rodgers, “then motivates us to get others to rethink our positions, to pay a lot more attention to what it will cost us to get what we want – and whether it’s worth the cost.”

        The most important take-away about anger, she concludes, is that we shouldn’t suppress it but should keep the flame low and use it to help solve problems and deal constructively with others.

 

“Go Forth in Anger” by Joann Ellison Rodgers in Psychology Today, March/April 2014 (Vol. 47, #2, p. 72-79), no e-link available

 

 

Stephen Anderson

Best Practices with Formative Assessment

(Originally titled “Formative Assessment in Seven Good Moves”)

        In this thoughtful Educational Leadership article, Brent Duckor (San Jose State University) says that effective use of on-the-spot assessments is the most influential factor in improving student learning. Duckor recommends the following seven “moves”:

        • Explicitly prepare students. “Unfortunately, the literature on formative assessment provides few accounts of the culture shock many students experience when they’re expected to learn in this new and perhaps puzzling manner,” says Duckor:

• Why is the teacher always answering a question with another question?
• Why is the teacher asking “Why” all the time?
• Why is the teacher using Popsicle sticks to call on us?
• Why is the teacher pausing before taking answers?
• Why is the teacher writing up all the answers, even the wrong ones?
• Why can’t the teacher just solve the problem and write the correct answer on the board so we can move on?

• Pose good questions. Many classroom questions are either too simple (“Can someone give me the definition of mitosis?”) or too open-ended (“Why did the French Revolution occur?”). “An effective question sizes up the context for learning, has a purpose related to the lesson and unit plan and, ideally, is related to larger essential questions in the discipline,” says Duckor. For example, in a high-school civics class discussing a segregated skating rink: “Should the integration of public facilities extend beyond the ruling on education addressed by the Brown v. Board of Education decision?”

• Give students time to think. Some teachers feel uncomfortable with silences. Giving adequate wait time for students to process their answers requires planning, patience, and complementary moves – turn-and-talk, think-pair-share, journal writing, polling. All these help the teacher gauge the level of understanding and guide next steps.

• Probe student responses. Many standard classroom questions lead to staccato exchanges with students – “Does everyone understand?” “Can we move on now?” Standard Who? What? When? Where? How? Why? questions have one correct answer, and as soon as a student provides it, there’s no need to follow up since “we” all know the correct answer. Probing, on the other hand, means there’s always more to know. For example, in a lesson on buoyancy, a teacher might ask, “So who thinks things float because they’re hollow? Can you say why? Turn to your partner and ask for an example of a hollow thing that might sink.” “The more one learns about how real students in a particular classroom approach the material,” says Duckor, “the better one can guide them through the bottlenecks, cul-de-sacs, and eddies that will inevitably mark a student’s progression toward an understanding of conceptually difficult material.”

• Question all students. “Feedback is about generating a loop,” says Duckor. “Too often, the loop is too small, occurring mostly between the teacher and a few eager students.” This can give the teacher an inaccurate sense of whole-class understanding and allow most students to rest on their oars. The solution: cold-calling with popsicle sticks or all-class response systems. This is particularly important for low-achieving students and English language learners.

• Use tagging to generate a wide range of responses. For example, the teacher asks the class, “What is the first thing that pops into your head when you hear the word ratio?” and has students jot their ideas, turn and talk to a partner, and then creates a word web on the board. Some teachers are uncomfortable entertaining incorrect answers, but, says Duckor, “If teachers don’t create a space for students to express both their understandings and their misunderstandings, students who are too embarrassed to express a potentially incorrect answer will simply remain silent.”

• Sort answers into “bins.” As students answer questions, the teacher mentally sorts them – correct, misconception, proficient, etc. “A teacher needs to know, through practical training and rich classroom experience, where kids get stuck and why,” says Duckor. For example, teaching a science unit on why things sink or float, teachers need to know common misconceptions about mass, volume, density, and relative density.

 

“Formative Assessment in Seven Good Moves” by Brent Duckor in Educational Leadership, March 2014 (Vol. 71, #6, p. 28-32),

http://www.ascd.org/publications/educational-leadership/mar14/vol71/num06/toc.aspx; Duckor can be reached at brent.duckor@sjsu.edu.

 

 

Stephen Anderson

Chester Finn Finds the Middle Ground in U.S. School Debates

        “Modern U.S. politics leave scant middle ground where compromise or synthesis can be forged,” says Chester Finn Jr. in this sweeping Education Gadfly article. “But it should be the job of serious education reformers to plant their policy banners – and themselves – on whatever demilitarized territory can be found.” Finn examines a number of perennial “debates and dichotomies” in American education and argues for a sensible middle ground in each one:

        • Skills vs. knowledge – The Common Core standards appear at first to be skills-centric, he says, but they also “make clear that success hinges on the deployment of a rich, sequential, content-focused curriculum.”

        • “Sage on the stage” vs. “guide on the side” – It’s not students’ job to figure out for themselves why the Civil War was fought or what atoms make up a molecule of water, says Finn. “It’s their job to internalize much that has been figured out by others – and to use it themselves, both for purposes of their own devising and for purposes that adults place before them.”

        • Who should be in charge, parents or the state? Education is both a private and a public good, says Finn. We need to balance students’ preferences/needs/aspirations (as gauged by parents) and “a set of needs, priorities, and capacities determined by the larger society…”

        • Evaluate teachers by student results or peer judgments? Each approach has serious limitations, says Finn, and the best way to compensate for them is to use a blend of both approaches, augmented by student surveys and other data.

        • Assess achievement via test scores or pupil “performance”? Standardized tests, for all their deficiencies, can gather important information, he says, but performance assessments go deeper, measuring creativity, understanding, and the ability to apply knowledge and skills. Use both, says Finn.

        • Gauging pupil progress by grade level or competency? Instructing students at their assessed levels seems more efficient, but it wreaks havoc with the traditional structure of schools and is confusing to many parents (my child is at fifth grade level in math and seventh grade in writing?). Finn advocates working toward an amalgam of both.

        • Learning with technology or humans? Online education seems efficient, “But what about socialization?” asks Finn. “What about music and phys. ed.? Basketball and Christmas pageant? How about children’s relations with adults and other kids – and the teacher’s role not just in answering their curricular questions and helping them understand the lesson but also seeing what excites their minds, how they’re behaving, and what may be going awry in other parts of their lives?” Yet the traditional model is expensive, depends heavily on the quality and character of individual teachers, tends to be boring to fast learners and frustrating for those with learning difficulties, and harms students who are stuck in subpar schools. Once again, a blend works best.

        • Diversity vs. uniformity? Finn is for a body of shared knowledge, with reasonable variations for the marvelous diversity of America.

        • Is education run best by professionals or laypeople? “We need them working in tandem,” he says. Political leaders need to set broad parameters, but shouldn’t be micromanaging at the classroom level.

        • Local or centralized control? Finn believes governance needs a “top-to-bottom renovation” to bring a 19^th-century structure up to speed with a 21^st-century world of geographic spread, increasing diversity, charter schools, and more.

 

“Education’s Endless, Erroneous Either-Ors” by Chester Finn Jr. in The Education Gadfly, March 6, 2014 (Vol. 14, #10), http://bit.ly/1qcNo5L

 

 

Stephen Anderson

An Informative High-School Student Survey

        In this article in Independent School, Amada Torres (National Association of Independent Schools) reports on her organization’s three-year pilot of the High School Survey of Student Engagement (HSSSE), which is designed to measure three aspects of students’ life in school:

• Engagement of the mind – Cognitive, intellectual, and academic;
• Engagement in the life of the school – Social, behavioral, participatory;
• Engagement of the heart – Emotional.

Here is a sampling of questions with the stem, “How much has your experience at this school contributed to:

• Writing effectively
• Thinking critically
• Reading and understanding challenging material
• Learning independently
• Developing creative ideas and solutions
• Speaking effectively
• Using technology to gather and communicate information
• Acquiring skills for a job after completing high school
• Developing career goals
• Applying school-based knowledge to everyday life
• Understanding why what you learn in school will be important after high school.

To see a sample HSSSE survey, go to http://ceep.indiana.edu/hssse/HSSSE_ForResearch.pdf; for general information, see http://ceep.indiana.edu/hssse.

 

“Assessing Student Engagement” by Amada Torres in Independent School, Spring 2014 (Vol. 73, #3, p. 16-18),www.nais.org

 

 

Stephen Anderson