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Jill Bergeron

Mathematical Mindsets: Unleashing Students' Potential - 0 views

  • So often mathematics instruction has focused on the “right” answer as opposed to the process of getting an answer. As a result, many educators and most students have a lack of understanding of how mistakes in math should be viewed and how mistakes can actually enhance the brain’s development.
  • Mathematics is a cultural phenomenon: a set of ideas, connections, and relationships that we can use to make sense of the world. At its core, mathematics is about patterns.
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    This is a book review of Mathematical Mindsets which builds off of Carol Dweck's work on mindsets.
Gayle Cole

teaching/math/culture | I research mathematics teaching and learning in secondary schools - 0 views

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    workshop with Gary Stager at Willows - Reinventing Mathematics
Jill Bergeron

The Marshall Memo Admin - Issues - 0 views

  • “While people usually gain power through traits and actions that advance the interests of others, such as empathy, collaboration, openness, fairness, and sharing, when they start to feel powerful or enjoy a position of privilege, those qualities begin to fade.”
  • Behaviors like these undermine leaders’ effectiveness by depressing the performance of those around them, and are ultimately self-defeating.
  • power puts us in something like a manic state, making us feel expansive, energized, omnipotent, hungry for rewards, and immune to risk – which opens us up to rash, rude, and unethical actions.” But it turns out that simply being aware of those feelings – “Hey, I’m feeling as if I should rule the world right now” – and monitoring impulses to behave inappropriately helps keep those behaviors in check.
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  • When Keltner works with up-and-coming executives, he counsels them to remember and repeat the virtuous behaviors that helped them rise in the first place and develop three essential practices: empathy, gratitude, and generosity.
  • To practice empathy: -   Ask a question or two in every interaction, showing genuine interest in the subject. -   Paraphrase important points made by others. -   Listen with gusto, orienting your body and eyes toward the person speaking and verbally showing interest and engagement. -   When someone comes to you with a problem, don’t jump right to judgment and advice but say something like, “That’s really tough” or “I’m sorry.” -   Before a meeting, take a moment to think about the person you’ll be with and what’s happening in his or her life.
  • The alternative mindset is that people can grow professionally and managers can change the way people perform through effective coaching, management, and intrinsic rewards like personal development and making a difference.
  • “From Silicon Valley to New York, and in offices across the world, firms are replacing annual reviews with frequent, informal check-ins between managers and employees.”
  • One observer called the traditional performance evaluation a “rite of corporate kabuki” that restricted creativity, generated mountains of paperwork, and served no real purpose. It was also an incentive to put off bad news until the end of the year, at which point both manager and employee may have forgotten what the problem was.
  • There’s one more reason: once-a-year reviews focus on past performance rather than encouraging current work and grooming talent for the future.
  • To practice gratitude: -   Make thoughtful thank-yous a part of how you communicate with others. -   Send colleagues specific and timely e-mails or notes of appreciation for a job well done. -   Publicly acknowledge the value that each person contributes to the team, including support staff. -   Use the right kind of touch – pats on the back, fist bumps, high-fives – to celebrate success. • To practice generosity: -   Seek opportunities to spend a little one-on-one time with people you lead. -   Delegate some important and high-profile responsibilities. -   Give praise generously. -   Share the limelight – give credit to all who contribute to the success of your team and your organization.
  • employees, especially recent college graduates, learn faster from frequent, detailed feedback from mentors and superiors. Second, companies realized they needed to be agile to survive and thrive in the competitive, ever-changing marketplace and real-time performance monitoring and feedback led to more rapid adaptations. And third, managers saw that teamwork was key to innovation and productivity and moving from forced annual ranking to frequent individual accountability was more conducive to teamwork and better results.
  • Studies of the workplace show that the time employees spend helping others is as important to their evaluations and chances of promotion as how they do their jobs. And Grant’s own research on “givers” (who enjoy helping others) and “takers” (who are focused on coming out ahead) shows that givers consistently achieve better results.
  • on the most difficult part of his exams – the multiple choice section – if a student was unsure of an question, he or she wrote down the name of another student who might know the answer – like asking for a lifeline on “Who Wants to Be a Millionaire.” If the classmate had it right, they both earned points; one person’s success also benefited a classmate. Grant reports that this made a big difference – more students joined study groups, the groups pooled their knowledge, and the class’s average score went up 2 percentage points compared to the previous year. Why? Because one of the best ways to learn something is to teach it to someone else, and that’s what was going on in the groups.
  • There was something else going on in the lifeline idea: transactive memory, or knowing who knows best and taking advantage of their knowledge. It’s easier to get help if you know where to look.
  • In this Chronicle of Higher Education article, Ellen Boucher (Amherst College) says the “pressure of perfection” is causing lots of stress for students in their teens and twenties, contributing to the rising suicide rate in this age bracket.
  • The burden of multiple obligations can seem insurmountable.”
  • Sociologists have shown that students from less-privileged backgrounds often have trouble understanding the unwritten rules of college life – the so-called hidden curriculum… [A]sking a professor for an extension doesn’t always come naturally. It might not even occur to them as an option.”
  • all students can elect to take a two-day grace period on any paper, with no questions asked.
  • “Since changing my policy, I’ve seen higher-quality work, less anxiety, and fewer cases of burnout.
  • Rebrand. A more inviting name for these perennial meetings is “progress conferences.” This is more positive and doesn’t seem to exclude foster parents and guardians.
  • Finesse the childcare issue. “To pay a babysitter to watch your three younger siblings so a parent can attend a conference is not going to happen,” says Ohio high-school teacher Allison Ricket. She invites parents to bring along other children and provides crayons and paper in an area at the back of her classroom where they can entertain themselves during conferences.
  • Accommodate. Some parents need an interpreter (children shouldn’t be asked to translate) and support with disabilities.
  • Change the dynamic. It makes a difference if a teacher sits side by side with family members and doesn’t hold a clipboard or pad of paper; open hands suggest an open mind.
  • Involve students. Progress conferences are much more helpful when students are at the table reporting on their progress, challenges, and goals. Advisory group meetings focus on preparing students to lead parent conferences and lobby their parents to attend.
  • • Listen. “Parents usually come in having an idea of what they want to talk about, so I like to be open and ready for whatever they need,” says Ricket. Although she has students’ grades and portfolios on hand, she lets parents go first and is careful to empathize with any concerns they have.
  • “mathematics is better taught when everyone shares in consistent language, symbols and notation, models and schema, and rules that support developing learners. The idea behind this comprehensive agreement is not unlike a schoolwide behavior management policy – whereby children hear the same phrases, share identical expectations, and experience practices that are common and consistent year after year across classrooms and throughout the school.”
  • Language – Moving from less conceptual language – borrowing, carrying, reducing fractions, the “Ring around the Rosie” property – to more mathematically appropriate language – regrouping, simplifying fractions to the lowest terms.
  • Symbols and notation – For example, writing fractions with a slanted bar 3/8 may confuse students who think the bar is the numeral 1 and think it’s 318.
  • Models and schema
  • Number lines or graphics should be consistent through the grades, for example, a graphic showing two parts next to one whole.
  • Rules
  • “This unified approach is particularly helpful for students who struggle,” conclude Karp, Bush, and Dougherty, “as it provides a recognizable component to new content. Additionally, all learners in a school can make connections among ideas in a unified and collaborative culture that promotes stronger learning in mathematics.”
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    "Online Resources for Teaching About the Presidential Campaign             In this article in Education Week, Madeline Will shares five free classroom resources for teaching and discussing this year's election: -   Letters to the Next President 2.0 www.letters2president.org - Students' letters to the 45th president will be published by PBS member station KQED and the National Writing Project. -   Teaching Tolerance Election 2016 Resources www.tolerance.org/election2016 - These include a civility contract, civic activities, and PD webinars. -   iCivics www.icivics.org/election_resources_2016 - Materials on the basics of democracy, with an interactive digital game in which students manage their own presidential campaign. -   C-Span Classroom www.c-spanclassroom.org/campaign-2016.aspx - Primary sources with historical and contemporary video clips and related discussion questions, handouts, and activity ideas. -   Join the Debates www.jointhedebates.org - Curriculum materials for collaborative discussions on issues in the campaign and debates.   "Educators Grapple with Election 2016" by Madeline Will in Education Week, September 14, 2016 (Vol. 36, #4, p. 1, 12-13), www.edweek.org "
Jill Bergeron

The Marshall Memo Admin - Issues - 0 views

  • students who have four years of art score 91 points higher on the SAT than students who don’t.
    • Jill Bergeron
       
      This seems correlational.
  • Danny Gregory applauds the arguments made for the importance of art and music in schools: they improve motor, spatial, and language skills; they enhance peer collaboration; they strengthen ties to the community; they keep at-risk students in school and improve their chances of ultimately graduating from college; and
  • In middle school, the majority start to lose their passion for making stuff and instead learn the price of making mistakes.
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  • In short, every child starts out with a natural interest in art, but for most it is slowly drained away until all that’s left is a handful of teens in eyeliner and black clothing whose parents worry they’ll never move out of the basement.”
  • As of 2015, only 26.2 percent of African-American students have access to art classes.
  • Gregory has a startling suggestion: take the “art” out of art education and replace it with creativity education. Why? Because creativity is something that almost everyone agrees is vital to success.
  • Solving problems, using tools, collaborating, expressing our ideas clearly, being entrepreneurial and resourceful – these are the skills that matter in the 21st century, post-corporate labor market. Instead of being defensive about art, instead of talking about culture and self-expression, we have to focus on the power of creativity and the skills required to develop it. A great artist is also a problem solver, a presenter, an entrepreneur, a fabricator, and more.”
  • We need to make sure that the kids of today (who will need to be the creative problem solvers of tomorrow) realize their creative potential and have the tools to use it.
  • A total of 21 percent of students said they had been bullied in the following ways: 13 percent made fun of, called names, or insulted; 12 percent subject of rumors; 5 percent pushed, shoved, tripped, or spat on; 4 percent threatened with harm; 5 percent purposefully excluded from activities; 2.5 percent told to do things they didn’t want to do; and 2 percent had their property purposefully destroyed. Girls reported more online harassment (16 percent) than boys (6 percent). These were the locations where students said the bullying occurred: -   42 percent in hallways or stairwells (similar for boys and girls); -   34 percent in classrooms (perhaps mainly during entry, transitions, and exit); -   22 percent in cafeterias; -   19 percent outside on school grounds; -   12 percent online or by text; -   10 percent on school buses; -   9 percent in bathrooms/locker rooms.
  • hallways and stairwells, taken together, are nearly twice as likely to be the source of the problem as the cafeteria, playground, or buses and bathrooms. Supervision and vigilance in those fluid spaces between classes is likely to benefit vulnerable students disproportionately.”
  • dance, gesture, and other forms of movement can improve motivation, engagement, and learning.
  • students in classrooms that integrated movement were “significantly more excited by, engaged in, and focused on the lessons” than they were with conventional teaching methods.
  • Dancing to memorize information
  • Moving among stations
  • Applying movement to assessments
  • Forming lines, rows, or other groupings – Each student gets a card with a punctuation mark or a word and students silently arrange themselves to form a complete sentence.
  • Representing terms or ideas with actions – After reading a book about emotions, students stand and act out furious, satisfied, courageous, and other words.
  • – The teacher gives each group of students sets of fraction cards and they take turns moving to another group in search of equivalent fractions, bringing possible matches back to their group to see if they’re correct.
  • – To test knowledge of synonyms and antonyms, pairs of students jump straight up and down three times, then choose to land on either their right or left foot; if both land on the same foot, they must come up with synonyms for a word on the board; if they land on opposite feet, they must name antonyms.
  • – Doing a dance skip-counting numbers (5, 10, 15, 20…) to the “Macarena.”
  • Many teachers assigned tasks with complex instructions and procedures, but little higher-level thinking was required of students
  • How many of these do schools teach? Just three, say the authors, even in schools where students get high state test scores: application, recall, and (sometimes) analysis.
  • a synthesis of the skills they believe adults need for successful lives: Cognitive skills: -   Recall -   Application -   Analysis -   Evaluation -   Creative thinking Interpersonal skills: -   Communication -   Cooperation -   Empathy -   Trust building -   Service orientation -   Conflict resolution -   Negotiation -   Responsibility -   Assertiveness -   Advocacy Intrapersonal skills: -   Flexibility -   Adaptability -   Appreciation of diversity -   Valuing learning -   Cultural appreciation -   Curiosity -   Forethought -   Self-regulation -   Self-monitoring -   Self-evaluation
  • Most teachers presented students with complex content, but the tasks students were asked to perform were simple recall and application
  • interpersonal and intrapersonal skills almost never showed up.
  • These exceptional instructors created “a harmonious environment,” say the researchers, “demonstrating an understanding that doing so is a prerequisite to academic learning.”
  • It was the teacher, not the subject. This level of intellectual and affective demand cropped up in different subjects, grades, and classes with different student achievement levels. The variable was the teacher.
  • In a 10th-grade honors humanities class, for example, students were asked to invent questions to guide their study of Western imperialism in China (having just finished a unit on the colonization of Africa). Guided by the teacher, students brainstormed possible questions, decided which were most important, and edited questions until the questions were intellectually stimulating and open-ended.
  • These outliers managed to weave rigorous instruction of content across the cognitive, interpersonal, and intrapersonal domains, putting to rest the notion that content- and skill-focused instruction precludes higher-order thinking – and vice-versa.
  • Teachers adapted their teaching to the moment.
  • to teach a deep and broad range of skills while also addressing disciplinary knowledge – requires intelligence and years of practice.”
  • Instruction was tied to complex assessments. Often designed by the teachers themselves, these checks for understanding stood in contrast to the test-prep oriented assessments in other classrooms.
  • Teachers built strong relationships with students.
  • First, Nehring, Charner-Laird, and Szczesiul suggest that schools need complex, high-level assessments to make all classrooms accountable for teaching the full range of adult skills. Second, “excellence requires highly skilled teachers with finely tuned radar and improvisational ability.” And third, “good teaching is about caring relationships, a parental affection that gives and receives, that honors the fundamentally human nature of our work as educators.
  • Thomas Guskey (University of Kentucky) stresses the importance of professional development starting with clear outcomes.
  • “In education, getting better generally means having a more positive influence on the learning of our students and helping more students learn well,” says Guskey. “Knowing our destination provides the basis for determining the effectiveness of our efforts.”
  • Polly details the 5E approach, in which students spend most of a lesson exploring mathematical tasks with limited support from the teacher, and some students get individual or small-group support: -   Engage – The class is given a math task or activity. -   Explore – Students have time to work on the task with their partner or a small group, with the teacher giving only instructions and circulating, sometimes posing questions to support students’ exploration. -   Explain – The class comes together to discuss the problem and how different students solved it. The teacher facilitates the discussion, perhaps choosing a main focus based on what was observed during the work time, and provides direct instruction as needed. -   Elaborate/extend – For the rest of the class, the teacher gets students working on activities, math games, and small-group activities that deepen understanding of the concept and zeros in on students who seem confused or off track. -   Evaluate – Students solve a final task or participate in a discussion of concepts, allowing the teacher to assess learning and plan for future lessons.
  • “Looking beyond the intended goals to the broader array of possible outcomes is an important aspect of evaluation and vital to judging effectiveness,”
  • What sparks robust discussions in PLCs is looking at variations in students’ responses to individual items on common assessments and writing prompts.
  • “The primary purpose of this collaborative data analysis,” says Guskey, “is to guide these teachers’ professional learning experiences so they can improve the quality of their instruction and help all students learn well.”
  • One additional cautionary note: PLCs tend to jump into “debating new ideas, techniques, innovations, programs, and instructional issues,” says Guskey. “While these are important issues, we must remember that they are means to an important end that must be determined first. Our journey always begins by deciding our destination… Ninety percent of essential questions in any evaluation are addressed in the planning process, before the journey begins.”
  • “When a teacher models and provides direct instruction at the start of a lesson, it rarely enables students to explore mathematical tasks or engage in productive struggle,” says Drew Polly (University of North Carolina/Charlotte) in this article in Teaching Children Mathematics.
  • researchers have found that if students grapple with a task before the teacher explains and models it (and receive appropriate follow-up), they’re more engaged and learn better.
  • What student learning outcomes do we aim to accomplish? -   What evidence will tell us if we met the goal? (ideally more than one source of data) -   What unintended consequences might occur, positive or negative?
  • “[T]he size of a person’s vocabulary is one of the strongest predictors of his or her reading comprehension,” say Tanya Wright (Michigan State University/East Lansing) and Gina Cervetti ((University of Michigan/Ann Arbor) in this article in Reading Research Quarterly.
  • Students who enter school knowing fewer words are likely to continue with relatively small vocabularies and struggle with text comprehension throughout school. Students who start with larger vocabularies, on the other hand, have broader general knowledge, need to spend less time accessing memory of words (which frees up working memory to grasp the meaning of a text), read and enjoy their reading more, and build stronger vocabularies – a reciprocal relationship that tends to widen the achievement gap.
  • Teaching word meanings almost always improved comprehension of texts containing the words taught. • Teaching word meanings doesn’t seem to improve comprehension of texts that don’t contain the target words.             • Instruction involving students in some active processing was more effective than dictionary and definition work at improving comprehension of texts containing the words taught. One caveat: researchers don’t know how much active processing is enough.             • Teaching one or two strategies (e.g., context clues or morphology) for solving word meanings doesn’t seem to improve generalized reading comprehension.
Jill Bergeron

Conrad Wolfram: Teaching kids real math with computers | TED Talk | TED.com - 0 views

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    "From rockets to stock markets, many of humanity's most thrilling creations are powered by math. So why do kids lose interest in it? Conrad Wolfram says the part of math we teach - calculation by hand - isn't just tedious, it's mostly irrelevant to real mathematics and the real world. He presents his radical idea: teaching kids math through computer programming."
Gayle Cole

Cybraryman Internet Catalogue - 0 views

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    My STEM/STEAM (STEAM - Science, Technology, Engineering, Arts, Mathematics) page: http://t.co/0tcPMAZA #STEMchat
Gayle Cole

Wolfram Cloud Document - 0 views

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    from workshop at Willows, Reinventing Mathematics
Jill Bergeron

'The Capacity for Connection' | Teaching Tolerance - Diversity, Equity and Justice - 0 views

  • For instance, examples to teach mathematics principles can be developed around social justice issues, such as rates of unemployment and disparities in incomes. Critical reading skills can be honed by critiquing biased and incomplete news reports.
  • Only 14% of white students, for example, attend multiracial schools. How might such isolation affect white students' ability to develop healthy racial identities?
  • Ironically, in more racially diverse educational settings, assumptions of white superiority are often reinforced by "ability" grouping and tracking. Thus, simply being in more diverse school settings is not a guarantee that white children will develop non-racist attitudes and behaviors, unless their teachers intentionally work with them on these issues.
Jill Bergeron

Making Stuff Safer Project Guide | Science | Document | PBS LearningMedia - 0 views

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    Design challenge: Build an earthquake proof structure.
Jill Bergeron

6 ways to bolster STEM education for the future | eSchool News - 0 views

  • Recent results from the National Assessment of Educational Progress, for example, show that 43 percent of white students and 61 percent of Asian students score at the proficient level in eighth-grade math, compared to 19 percent of Hispanic students and 13 percent of black students. Eighth-grade students with disabilities and students eligible for free or reduced-price lunch scored nearly 30 points below their peers in science and mathematics; English learners scored nearly 40 and 50 points below their peers in these two subjects.
    • Jill Bergeron
       
      These stats point to a real disparity among diverse groups of students.
Jill Bergeron

The Marshall Memo Admin - Issues - 0 views

  • “It’s not just effort, but strategy. Students need to know that if they’re stuck, they don’t need just effort. You don’t want them redoubling their efforts with the same ineffective strategies. You want them to know when to ask for help and when to use resources that are available.”
  • the key to schools succeeding with all students is prioritizing – isolating and focusing on “only the most vital, game-changing actions that ensure significant improvement in teaching and learning” and then sustaining a disciplined, laser-like focus for a significant amount of time.
  • Teachers should have clear, specific direction on which skills and concepts to teach – the what and when – with discretion on the how to and some room each week for teachable moments and personal passions.
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  • Of paramount importance is ongoing checking for student understanding (minute by minute, day by day, week by week) and adjusting instruction based on assessment insights. This is especially important for project- and problem-based learning.
  • “To succeed, students simply need vastly more time to purposefully read, discuss, and write about worthy, substantive literature and nonfiction across the curriculum (as often as possible, in the interpretive and argumentative mode)
  • “this should occur in a climate that emphasizes helpfulness and growth, rather than evaluation.”
  • “Nobody has a growth mindset in everything all the time,” says Dweck. “Everyone is a mixture of fixed and growth mindsets.
  • When students fail, teachers and parents should say things like, “Okay, what is this teaching us? Where should we go next?”
  • With praise, focus on the process that led to success – hard work, good strategies, effective use of resources. “Be matter-of-fact,” advises Dweck, “with not too strong or too passive a reaction… Effective teachers who actually have classrooms full of children with a growth mindset are always supporting children’s learning strategies and showing how strategies created that success.”
  • U.S. elementary teachers spend an average of about 32 hours a week with their students, secondary teachers about 30 hours, out of a 38-hour contractual week. Daily planning time ranges from 12 to 80 minutes for elementary teachers, from 30 to 96 minutes at the secondary level. The paucity of contractual planning time in most schools pushes a lot of teachers’ work into late afternoons, evenings, and weekends; including that time, the typical teacher’s work week is about 52 hours.
  • Teachers need two types of planning time, Merritt believes: (a) Individual time every day to prepare materials for upcoming lessons, assess student work, and communicate with specialists and parents about their students; and (b) common planning time once or twice a week with same-grade/same-subject colleagues to plan, implement, reflect on, and modify instruction.
  • The 30-32 hours U.S. teachers spend with their students each week compares to about 20-21 hours in other countries.
  • Shorter days for students
  • No-student days embedded within the school year
  • The number of such days ranges from two to 18 per school year.
  • Increased staffing – Core subject teachers can be given more planning time within the school day if their students go out to additional physical education, art, music, science, environmental education, and other specialty subjects – and also by increasing supervised recess and using instructional assistants and parent volunteers.
  • “we should trust teachers who are asking for more time, and make planning time a high priority in budgeting decisions. Instead of implementing costly interventions that yield minimal results in schools, we should pay more attention to the repeated requests from teachers about how to support them in their daily work… They need more time to identify problems they see in their schools or classrooms and work individually and collectively on solutions.”
  • Using inquiry protocols, they asked each other What do we want students to get out of the curriculum? and How can we get them there? -   They collaboratively developed model curriculum units and adapted them as needed; -   They used a fishbowl approach to observe colleagues teaching new curriculum materials; -   They watched outside curriculum experts modeling appropriate classroom strategies. -   They looked together at student work as students grappled with the new expectations and thought about the implications for unit and lesson planning; -   They jointly figured out ways to support students in material that at first seemed too hard.
  • Meaningful data – Static assessment results from benchmark assessments are not enough. To have truly high-quality discussions about their work, teachers need (a) open-ended assessment items from their ongoing instruction to identify student strategies and uncover their mathematical reasoning; (b) feedback from classroom observations; and (c) video clips of their own instruction and that of colleagues.             • Supportive tools – These include classroom observations and videos and having a facilitator with deep pedagogical content knowledge. It’s also crucial that the PLC sinks its teeth into one or two substantive and actionable math concepts or strategies.
  • • Supportive colleagues – Dissonance is not enough, say the authors. To truly improve instruction, teachers also need a collegial group that will hold their hands as they deal with their students’ struggles and criticism from observers:
  • “It is likely,” say the authors, “that repeated video recording and written feedback motivated Ms. Walker and other teachers to try out new instructional strategies and continuously  assess and refine them so that they could demonstrate improvement in subsequent observed lessons.”
  • -   Within-class grouping (teachers differentiating instruction among several small groups) had moderately positive effects.
  • -   Cross-grade grouping (students from different grade levels brought together to learn a particular subject or unit – e.g., the Joplin Plan for reading) had small-to-moderate benefits.
  • -   These two forms of grouping benefited students with high, medium, and low achievement.
  • -   Special grouping for gifted students (pullout or honors programs) was very helpful for those students.
  • -   Acceleration (students skipping a grade or taking courses at a younger age than their peers) was the most beneficial of all.
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    "1. Mike Schmoker on three focus areas 2. Carol Dweck on fine-tuning the growth mindset 3. Maximizing high-quality teacher planning time 4. Effective and ineffective teacher teamwork in the Common Core 5. What gets professional learning communities working well? 6. Research findings on ability grouping and acceleration"
Jill Bergeron

SMART Exchange - USA - Search lessons by keyword - 0 views

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    SMART technologies lesson and game plans.
Jill Bergeron

Mathalicious - 0 views

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    While you need a membership to join this site and access all of the resources, there are great real world examples of math that correlate to many different concepts taught in middle school and high school.
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