This episode is special because it is our first episode topic that was suggested by a listener. A huge shoutout to our friend Erick Lee (Twitter handle @TheErickLee) who suggested this great report published by OECD. If you are on Twitter, please give Erick a follow!
Here is the link to the report:
Every three years the OECD administers and publishes the Programme for International Student Assessment, better known as PISA, which evaluates 15 year-old students around the world to determine how well their education system has prepared them for life after compulsory schooling. This test is important because it allows the performance of educational systems to be examined and compared on a common measure across countries. Currently 70 countries participated in the latest PISA.
Ten Questions for Mathematics Teachers… and How PISA Can Help Answer Them is a report that takes the findings from analyses of the 2012 PISA and organizes them into ten questions that discuss what we know about mathematics teaching and learning around the world – and how these data might help you in your mathematics classes right now.
The questions encompass four broad categories:
Each question concludes with concrete, evidence-based suggestions to help teachers develop their mathematics teaching practice.
For the next several weeks, Maggie and I will tackle one new question from this report. Of course, we begin with Question #1: How much should I direct student learning in my mathematics classes?
WHERE DOES MATHEMATICS TEACHING FALL IN THE TEACHER- VS. STUDENT DIRECTED LEARNING DEBATE?
For years, the most common teaching strategy has been teacher directed with a small – but vocal – contingent calling for a more student-oriente
d teaching. Which one is better? Unfortunately, it is not a simple “either/or” proposition. It would have been so nice if the data simply said “do THIS and not THAT”. Rather, it is a bit more nuanced.
It depends on the the content and students being taught.
It is a given that most teachers are directly teaching. Student-centered practices are most commonly used within the context of differentiating instruction. The PISA survey indicates that students may be exposed to different teaching strategies based on their socio-economic status or gender. Girls reported being less frequently exposed to student-oriented instruction in mathematics class than boys did. Disadvantaged students, who are from the bottom quarter of the socio-economic distribution in their countries, reported more frequent exposure to these student-oriented strategies than advantaged students did.
The data show that as the instruction becomes more teacher-directed the more student learning relies upon using memorization skills. Conversely, the more student-oriented the instruction, the less students rely upon memorization and are increasingly able to elaborate upon their thinking.
WHICH TEACHERS USE ACTIVE-LEARNING TEACHING PRACTICES IN MATHEMATICS?
From the Teaching and Learning International Study (TALIS) – a different OECD-led survey – four active-learning (student-oriented) teaching practices are identified:
These practices have been shown by many research studies to have positive effects on student learning and motivation. TALIS data show that teachers who are confident in their own abilities are more likely to engage in active-teaching practices – which is the bottom line, really. If a teacher feels comfortable with the necessary pedagogy, content knowledge, and classroom management, then they will be able to flexibly think about how to teach it in a manner other than direct instruction.
If this doesn’t scream “WE NEED MATH COACHES!!!”, then nothing does.
HOW CAN A VARIETY OF TEACHING STRATEGIES BENEFIT STUDENT ACHIEVEMENT?
As stated above, as the instruction becomes more teacher-directed the student learning becomes more reliant upon memorization. Conversely, the more student-oriented the instruction, the more students are able to elaborate upon their thinking.
The data indicate that students are slightly more successful in solving the easiest mathematics problems in PISA when teachers direct student learning. Yet as the problems become more difficult, students with more exposure to direct instruction no longer have a better chance of success. Students exposed to greater amounts of student-oriented teaching are more likely to solve the difficult problems on PISA.
This means that one teaching method is not sufficient to teach all math problems; teaching complex math skills might require different instructions strategies than those used to teach basic math skills. In fact, rather than succumbing to an “either/or” mentality (or a direct-instruction versus constructivist debate), Singapore is using this research to require teachers to use a variety of teaching methods depending on the complexity of the mathematics being learned.
Teacher-directed and student-oriented instruction must work in tandem.
WHAT CAN TEACHERS DO?
So, let’s wrap this up. What are teachers supposed to take from Question 1? Three things…
Make sure each lesson/unit has extension activities for those who can go deeper. (This is the low-floor/high-ceiling concept that Jo Boaler talks about.) Offer support for the struggling learner. And provide a variety of activities and roles for students with different abilities/interests
This requires that the teacher move beyond the textbook provided lessons and homework and add new activities to lessons that allow students to work together or use new tools (technology or games).
Reserve your teacher-directed lessons for simpler math concepts and research other strategies for teaching more difficult concepts.
Please read the actual report! Here…
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“It’s time to rethink the assumption that good teachers don’t use prepackaged curriculum materials.”
Thus began the article that I read recently. FIGHTING WORDS…I thought. I began teaching mathematics in 1989 as the Math Wars was heating up. In the battle between traditionalists versus constructivists, I staked my claim firmly on the side of the constructivists. And, because all the textbooks at the time were most definitely of the explicit instruction variety, I proudly bragged about not using the textbook provided. It was, afterall, a badge of honor proudly announcing whose side I was on.
Then I read How to Partner with Your Curriculum[1], by Janine T. Remillard, which is moving into a realm of thinking that I previously thought of as heresy: the textbook can be good.
It turns out I was a believer in the Good-Teacher Doctrine, as Remillard puts it. This doctrine reveres the teacher as an expert who curates/creates curriculum effectively rendering the textbook unnecessary. Using the textbook would be a sign of lazy teaching. The problem with this belief, however, is it is incredibly time consuming. It also required of me a profound understanding of mathematics, the standards, and how the math I taught fit within the K-12 continuum. Even if I could perfectly uphold the thinking of the Good-Teacher Doctrine, it is unreasonable to expect this of every teacher. Moreover, building a K-12 coherence in what and how we teach is impossible if every teacher followed the Good-Teacher Doctrine.
Remillard suggests we become partners with our curriculum. This now makes sense to me.
When the textbook is a partner, the teacher no longer has to spend an inordinate amount of time on WHAT to teach and can now focus on HOW to teach. The teacher uses her deep understanding of her students – their strengths and weaknesses – to make adaptive decisions essential for student success.
There are four strategies for partnering with the curriculum:
Look for the big ideas.
Before digging into the lesson, take time to read through the entire year or module or chapter…whatever makes sense. This provides perspective that allows the teacher better insight as to when a lesson should be repeated or when it makes more sense to move on.
Pay attention to the pathways.
Curriculum writers have likely already sequenced the curriculum to that each grade perfectly leads into the next. When teachers understand the coherence of the math content and how it fits into the K-12 progression they are better able to recognize when a student needs intervention.
Anticipate: What will ___ say?
Before using the lesson provided by the curriculum, the teacher needs to anticipate student responses and common stumbling blocks. The curriculum writers play an important role in guiding students through the year, but they cannot anticipate every contingency. It is the domain of the teacher to know her students, walk a mile in their shoes, and prepare responses to the questions students are likely to ask.
Collaborate with colleagues.
This is a no-brainer. By working closely with colleagues, teachers will be more likely to look for the big ideas, pay attention to the pathways, and anticipate student responses. Besides, working with a colleague…and reflecting with that colleague, makes our profession much more fun.
Curriculum will NEVER replace the teacher. We’ve seen teachers abdicate their authority to the teacher notes in a curriculum or to a series of video tutorials, which is a travesty. The best scenario is when the teacher uses her considerable knowledge in partnership with a well-crafted curriculum to meet the needs of all students.
What are your thoughts? Leave comments below.
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[1] “How to Partner with Your Curriculum – ASCD.” http://www.ascd.org/publications/educational-leadership/oct16/vol74/num02/How-to-Partner-with-Your-Curriculum.aspx. Accessed 23 Oct. 2017.
]]>After having been closed for 11 days, schools re-opened last week; and the community is now left to rebuild their lives.
In this episode Maggie discusses the fires and how they affected the students and the adults responsible for teaching those children.
We know that students subjected to traumatic stress can exhibit unprovoked anger, classroom outburst, withdrawal, and/or self-harming behaviors^{[2]}. Unfortunately, it is really hard for the teacher to discern whether these behaviors are the result of extended exposure to violence, abuse, or neglect, or if the behaviors are merely the result of students being precocious.
It is not clear to me how the fires themselves might contribute to this sort of stress, since fires are short-term, while the stressors discussed in the article are described as “ongoing”. It is certainly true, however, that the fires may push a family – previously already on the edge – into a season of long term domestic stress, including homelessness, violence, and neglect.
It is important for us teachers to be aware that some students in our class may be experiencing real trauma. We must strive to create safe environments and employ Positive Behavior Intervention and Supports^{[3]} (PBIS).
In the case of Santa Rosa, teachers must do this even when they may find themselves homeless as a result of the fires.
It is truly humbling how difficult it is to be a teacher.
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^{[1]} “Santa Rosa, Sonoma, Napa California fires: Death … – Washington Post.” 14 Oct. 2017, https://www.washingtonpost.com/news/post-nation/wp/2017/10/14/more-californians-ordered-to-flee-as-gusting-winds-spread-wildfires/. Accessed 5 Nov. 2017.
^{[2]} “Schools promoting ‘trauma-informed’ teaching to reach troubled students.” 2 Dec. 2013, https://edsource.org/2013/schools-focus-on-trauma-informed-to-reach-troubled-students/51619. Accessed 5 Nov. 2017.
^{[3]} “California – PBiS.” https://www.pbis.org/pbis-network/california. Accessed 5 Nov. 2017.
]]>What is motivation?^{[1]}
When we are motivated it means we are moved to do something. There are two kinds of motivation: extrinsic and intrinsic. The level of extrinsic and intrinsic motivation can go up and down; and the where that motivation is coming from can vary up and down the extrinsic/intrinsic spectrum.
Extrinsic motivation means you are doing something for an outside reward.^{[2]} Kids who are extrinsically motivated will say things like:
An advantage of extrinsic motivation is that with very little effort or preparation on the part of the teacher, behavior changes are readily produced. On the other hand, extrinsic motivations come with some disadvantages. Attention is often shifted to the actual motivation rather than on the subject at hand. Often, the extrinsic rewards and punishments have to be escalated in order to maintain the effect and rarely work over the long term. Once these rewards are removed, students lose their motivation.
Intrinsic motivation, on the other hand, is defined as the doing of an activity for its inherent satisfactions rather than for some separable consequence. Students who are intrinsically motivated will say things like:
Intrinsic motivation has the advantage of being long-lasting and self-sustaining. Efforts to increase intrinsic motivation are often the same efforts that teachers would use to help students become better learners. These efforts often focus on the subject rather than rewards or punishments.
Fostering intrinsic motivation can be slow to affect behavior and can require special and lengthy preparation. Generating intrinsic motivation in students requires flexibility and adaptability on the part of the teacher as she chooses from a variety of approaches to motivate different students. Attaching an intrinsic motivator to each student requires the teacher to actually know her students and their interests. Also, it helps if the instructor is interested in the subject to begin with!
It is a complex relationship between extrinsic and intrinsic motivations. The relative ease of using external rewards is tempting when confronted with the challenge of instilling internal motivations inside each individual students. These two sources of motivation are often in direct conflict with one another.^{[3]}
Since intrinsic motivation is the true goal for teachers and students, let’s take a look at eight ways to increase student motivation. This list^{[4]} is not ours, but we will add some math-centric suggestions as we go.
You have a much greater chance of instilling intrinsic motivation in your students if you are able to directly connect your subject with topics that are relevant to your students. Use local examples or events in the news to demonstrate the need to learning mathematics. Connect math to student culture, their interests, and even social apps online^{[5]}.
Some math-specific suggestions:
Real World Math: Robert Kaplinsky
Mathalicious Lessons for Middle and Upper Grades
In the TRU Framework for what makes good math teaching, one of its five dimensions is Agency, Authority, and Identity^{[6]}. Students are given choice and agency in building their understanding of mathematics. We know that intrinsic motivation and student voice are directly correlated to each other. Providing choice can be as simple as allowing students to choose where they sit and with whom. Choice can get as complicated as allowing students to participate in self-assessment and self-reported grades^{[7]}.^{[8]}
Some math-specific suggestions:
You’ve heard of the Zone of Proximal Development? It was than junk you had to learn (and then forget) during your student teaching days. ZPD increases intrinsic motivation when students work on tasks that are slightly above their ability to complete the task alone. Tasks that are too easy sends students the message of low expectations. Tasks that are too difficult create anxiety and hopelessness. Artful scaffolding by the teacher creates fertile ground for the student to grapple, experience “productive struggle”^{[10]}, and ultimately to build intrinsic motivation.
Some math-specific suggestions:
Low Floor High Ceiling Activities
Recent research shows that black students who have had at least one black teacher during elementary school are much more likely to graduate high school.^{[11]} Having one black teacher between third and fifth grade reduced a black student’s probability of dropping out of school by 29 percent.^{[12]} Clearly role models is essential for black students, but it is beneficial for others as well. Female students are more likely to enter STEM fields when their mother is already in a STEM field^{[13]}. For some students, teachers can act as role models – certainly there is evidence of this^{[14]} – but a teacher cannot be a role model for all his students. Seeking additional role models is essential. Skype, Google Hangouts, and all the social media platforms make it each to bring role models from all around the world into any classroom.
Some math-specific suggestions:
Get the Math: Interviews of real people in real professions talking about how they use math.
Students learn from each other^{[15]}. Building a powerful collaborative culture in the classroom allows students to self-select peer models^{[16]}.
Some math-specific suggestions:
We’ve heard it before: Maslow’s Hierarchy. That pyramid includes love and a sense of belonging. Students with a sense of belonging to a community have a higher level of intrinsic motivation, stronger academic confidence, and are more willing to challenge themselves academically^{[17]}. Teachers have a tremendous influence in whether students feel this sense of belonging.
Some math-specific suggestions:
First 20 Days by Fisher and Frey
The teaching style that a teacher adopts lies somewhere on the supportive vs. controlling spectrum. A more supportive teaching style allows students to become more autonomous learners, which increases achievement, interest, enjoyment, and engagement^{[18]}. Supportive teachers are more likely to listen to students, support students with appropriate scaffolding, offer encouragement, elicit student-generated questions, an invoke empathy.^{[19]} Cognitively Guided Instruction strategies is a math-specific teaching strategy that involves listening to student thinking and offering appropriate supports and encouragement^{[20]}. Teaching students metacognitive strategies has also been shown to increase student motivation^{[21]}.
Some math-specific suggestions:
Motivating Students: Scroll down to ‘Adopt a Supportive Style’ to see examples of supportive and controlling styles of teaching.
Cognitively Guided Instruction
Metacognitive Strategies
When everything seems to be not quite meeting the needs of a struggling student, it is essential to not give up. Include the student in strategizing a way forward. This teaches the student self-efficacy and demonstrates the teacher’s faith in the student. Make a series of strategies with the student for moving forward: note-taking, tips for completing homework, and effective techniques for preparing for an exam. This is the time to assess (from the latin root word assidere “to sit beside”) different teaching strategies the student would like the teacher to try. This conversation has the added benefit of contributing to a supportive teaching style.
Some math-specific suggestions:
Concrete Representational Abstract (CRA)
Don’t let this big list overwhelm you! Pick one thing and work on it until it becomes second nature. Then add a second thing and work on it until both are second nature. And so on. Eventually, with some ebbs and flows, you will be doing all eight things with your wonderfully motivated students.
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REFERENCES
^{[1]} “Intrinsic and Extrinsic Motivations: Classic Definitions and New … – mmrg.” https://mmrg.pbworks.com/f/Ryan,+Deci+00.pdf. Accessed 2 Oct. 2017.
^{[2]} “Motivating Students | Center for Teaching | Vanderbilt University.” https://cft.vanderbilt.edu/guides-sub-pages/motivating-students/. Accessed 2 Oct. 2017.
^{[3]} “Turning “play” into “work” and “work” into “play”: 25 years of … – PsycNET.” http://psycnet.apa.org/record/2000-05867-009. Accessed 2 Oct. 2017.
^{[4]} “Motivating Students – SERC-Carleton – Carleton College.” https://serc.carleton.edu/NAGTWorkshops/affective/motivation.html. Accessed 2 Oct. 2017.
^{[5]} “Connecting with students who are disinterested and … – SERC-Carleton.” https://serc.carleton.edu/resources/37504.html. Accessed 2 Oct. 2017.
^{[6]} “TRU Framework – the Mathematics Assessment Project.” http://map.mathshell.org/trumath.php. Accessed 2 Oct. 2017.
^{[7]} “Hattie Ranking: Interactive Visualization – VISIBLE LEARNING.” https://visible-learning.org/nvd3/visualize/hattie-ranking-interactive-2009-2011-2015.html. Accessed 2 Oct. 2017.
^{[8]} “What Teachers Say and Do to Support Students … – SERC-Carleton.” https://serc.carleton.edu/resources/37494.html. Accessed 2 Oct. 2017.
^{[9]} “Zone of Proximal Development – Scaffolding | Simply Psychology.” https://www.simplypsychology.org/Zone-of-Proximal-Development.html. Accessed 2 Oct. 2017.
^{[10]} “TRU Framework – the Mathematics Assessment Project.” http://map.mathshell.org/trumath.php. Accessed 2 Oct. 2017.
^{[11]} “With Just One Black Teacher, Black Students More Likely to Graduate ….” 5 Apr. 2017, http://releases.jhu.edu/2017/04/05/with-just-one-black-teacher-black-students-more-likely-to-graduate/. Accessed 2 Oct. 2017.
^{[12]} “Research indicates that black children with black teachers less likely ….” 16 Apr. 2017, http://www.baltimoresun.com/news/maryland/investigations/bs-md-sun-investigates-black-teachers-20170416-story.html. Accessed 2 Oct. 2017.
^{[13]} “Raising STEM Daughters | Working Mother.” 1 Mar. 2016, http://www.workingmother.com/raising-stem-daughters. Accessed 2 Oct. 2017.
^{[14]} “Gender matters – SERC-Carleton.” https://serc.carleton.edu/resources/37491.html. Accessed 2 Oct. 2017.
^{[15]} “Successful Learning: Peer Learning: Enhancing Student Learning ….” http://www.cdtl.nus.edu.sg/success/sl13.htm. Accessed 2 Oct. 2017.
^{[16]} “How Peer Teaching Improves Student Learning and 10 Ways To ….” 7 Jun. 2013, http://www.opencolleges.edu.au/informed/features/peer-teaching/. Accessed 2 Oct. 2017.
^{[17]} “Sense of Belonging in College Freshman at the … – SERC-Carleton.” https://serc.carleton.edu/resources/37489.html. Accessed 2 Oct. 2017.
^{[18]} “Motivating Students – SERC-Carleton – Carleton College.” https://serc.carleton.edu/NAGTWorkshops/affective/motivation.html. Accessed 2 Oct. 2017.
^{[19]} “ERIC – Why Teachers Adopt a Controlling Motivating Style toward ….” https://eric.ed.gov/?id=EJ865122. Accessed 2 Oct. 2017.
^{[20]} “Cognitively Guided Instruction | Partners In Learning | Miami University.” http://performancepyramid.miamioh.edu/node/319. Accessed 2 Oct. 2017.
^{[21]} “Effects of Metacognitive Instruction on Learning and Motivation.” 4 Feb. 2016, http://www.apa.org/pubs/highlights/podcasts/episode-05.aspx. Accessed 2 Oct. 2017.
]]>In 1980 an Australian doctor^{[1]} discovered that (and proved overwhelmingly) that ulcers were not caused by excess acid in the stomach – as had been thought for the previous 100 years – but were caused by the bacteria H. Pylori. This meant that for the first time in the history of the world ulcers were no longer an incurable lifetime condition, but were easily cured with a week of antibiotics. Ten years later only 1% of doctors had given up the old way of treating ulcers (bland food, milk, etc) in favor of antibiotics!
Ten years!
What an incredible shame for the ulcer patients who did not get proper treatment simply because their doctors refused to give up the old way of thinking.
The math community is in a similar situation regarding math anxiety. We now know what it is. We know its causes. And yet we continue with the old way of thinking!
What is Math Anxiety and where does it come from?
It is not entirely clear what comes first – the chicken or the egg? Does math anxiety cause poor math performance? Or does poor math performance lead to math anxiety? There are three theories^{[2]} on the relationship between the two: deficit theory, debilitating/anxiety model, and the reciprocal theory.
Though we are not entirely certain which comes first, we know that math anxiety comes from stress. Brain-imaging technology has provided great insight into how math anxiety affects the brain. Studies have shown that when children are put under stress, they are unable to execute math problems successfully. The stress inhibits the working memory – the area of the brain where math facts are held. Stressful math situations cause worries and stress. The math and the worrying then compete for the same working memory. Math anxiety even impacts students with high amounts of working memory – students who typically might do well in math class.
Other things about math anxiety that we know:
What are the effects of math Anxiety?
As previously mentioned, the physical effects of math anxiety are undeniable thanks for MRI scanning. The amygdala is responsible for emotions, emotional behavior, and motivation. Ashcraft and Krause (2007) found that math anxiety severely impacts student’s ability to enjoy math, motivation to take more math or do well in math.
When a student suffers from math anxiety a typical response is “it is just in the student’s head”. While is is in the student’s head, it is now clear that it is physical. The amygdala is being impacted. The cure will need to be more than just hand-waving and hoping the student outgrows it.
Where does it come from?
There are five major contributors to the stress/math anxiety/poor math performance cycle: parents, teachers, society, a focus on speed, and poor teaching.
PARENTS^{[3]}
Jan Hoffman wrote an article on results of a new study stating math anxiety is contagious between parent and child. Here is her surprising conclusion: Math anxiety is transmitted during homework time at home. The more parents help with mathematics, the more likely math anxiety is transmitted from the parent to the child.
We all have heard adults practically brag about how bad they are with math or how much they hate the subject. Many of those adults identify algebra as the onset of their math anxiety, although much research has shown that it can begin earlier. Regardless of when the onset of math anxiety is, when those math-anxious adults become homework-helping parents, math anxiety is transmitted to the child^{[4]} like a virus. And the cycle continues.
Parental math anxiety^{[5]} has been exacerbated even further due to Common Core Math Standards and schools introducing new methods of teaching and learning math, said Harris Cooper, a professor of psychology and neuroscience at Duke University, who has studied the effects of homework.
TEACHERS^{[6]}
Teachers who experience math anxiety transmit it to their students. Girls are especially affected^{[7]} when a teacher publicly announces math hatred before she picks up the chalk. A study published in the Proceedings of the National Academy of Sciences reported that female — but not male — mathematical achievement was diminished in response to a female teacher’s mathematical anxiety. The effect was correlated: the higher a teacher’s anxiety, the lower the scores.
SOCIETY^{[8]}
We all have experienced an increase in society’s pressure to do well and get into college. Classrooms have become highly competitive environments with an increase in high-stakes testing. High-stakes academic cultures have a dark side by increasing the pressure on students to perform well, which then increases stress, resulting in math anxiety.
TIMED TESTS AND FOCUS ON SPEED^{[9]}
The damage starts early in the United States, with school districts requiring young children to take timed math tests as early as the age of 5. This is despite research^{[10]} that has shown that timed tests are the direct cause of the early onset of math anxiety.
PROCEDURAL TEACHING^{[11]}
Mathematics is rarely taught as a creative endeavor, in which all students can participate in some way. When math is taught as a performance subject – where the focus is merely to get questions correct – math anxiety can grow. Math is even used as a tool for weeding out students – a fact students are aware of – which only increased the stress-anxiety-performance feedback loop. More than any other subject math is about tests, grades, homework and competitions.
How can we prevent math anxiety?
I know this is a load of information. Rather than going the way of the ostrich and sticking our head in the sand, let’s address the issue of math anxiety head on. Begin by informing yourself and others. Start a conversation with teachers and parents. Collaborate on how to make tiny changes in your classroom.
And best of all…watch your students benefit from all this.
^{[1]} “Why it Took Everybody So Long to Acknowledge that Bacteria Cause ….” http://www.jyi.org/issue/delayed-gratification-why-it-took-everybody-so-long-to-acknowledge-that-bacteria-cause-ulcers/. Accessed 2 Oct. 2017.
^{[2]} “Espresso 6 – Cambridge Mathematics.” 31 May. 2017, http://www.cambridgemaths.org/espresso/view/espresso-6/. Accessed 2 Oct. 2017.
^{[3]} “Square Root of Kids’ Math Anxiety: Their Parents’ Help – Math Tutor ….” 30 Aug. 2017, http://mathtutor.sg/math-tuition/kids-math-anxiety-parents-help/. Accessed 2 Oct. 2017.
^{[4]} “Parents Transmit their Own Math-Anxiety to their Kids | ChildUp.com.” 31 Aug. 2015, http://www.childup.com/blog/parents-transmit-their-own-math-anxiety-to-their-kids/. Accessed 2 Oct. 2017.
^{[5]} “Parents’ math anxiety can undermine children’s math achievement ….” 10 Aug. 2015, https://news.uchicago.edu/article/2015/08/10/parents-math-anxiety-can-undermine-children-s-math-achievement. Accessed 2 Oct. 2017.
^{[6]} “OPINION: It’s time to stop the clock on math anxiety. Here’s the latest ….” 3 Apr. 2017, http://hechingerreport.org/opinion-time-stop-clock-math-anxiety-heres-latest-research/. Accessed 2 Oct. 2017.
^{[7]} “Stop telling kids you’re bad at math. You are spreading math anxiety ….” 25 Apr. 2016, https://www.washingtonpost.com/news/answer-sheet/wp/2016/04/25/stop-telling-kids-youre-bad-at-math-you-are-spreading-math-anxiety-like-a-virus/. Accessed 2 Oct. 2017.
^{[8]} “The Math Anxiety-Performance Link – Human Performance Lab.” https://hpl.uchicago.edu/sites/hpl.uchicago.edu/files/uploads/The%20Math%20Anxiety%20Performance%20Link,%20Foley%20et%20al.pdf. Accessed 2 Oct. 2017.
^{[9]} “Research Suggests Timed Tests Cause Math Anxiety – YouCubed.” https://www.youcubed.org/resources/research-suggests-timed-tests-cause-math-anxiety/. Accessed 2 Oct. 2017.
^{[10]} “Tips for Tackling Timed Tests and Math Anxiety | Edutopia.” 11 May. 2017, https://www.edutopia.org/article/should-we-abolish-timed-math-tests-youki-terada. Accessed 2 Oct. 2017.
^{[11]} “Math Anxiety – Evergreen Teaching & Learning.” 20 Apr. 2017, https://epslearning.blog/2017/04/20/math-anxiety/. Accessed 2 Oct. 2017.
^{[12]} “7 Reasons behind Math Anxiety and How to Prevent It.” http://www.homeschoolmath.net/teaching/motivate.php. Accessed 2 Oct. 2017.
^{[13]} “8 Empowering Ways to Beat Math Anxiety – MathFour.” http://mathfour.com/math-anxiety. Accessed 2 Oct. 2017.
^{[14]} “Alternative Ways of Developing and Assessing Fluency with Basic Facts.” 28 Oct. 2011, http://scholarworks.wmich.edu/cgi/viewcontent.cgi?article=3322&context=honors_theses. Accessed 2 Oct. 2017.
^{[15]} “The Myth of ‘I’m Bad at Math’ – The Atlantic.” 28 Oct. 2013, https://www.theatlantic.com/education/archive/2013/10/the-myth-of-im-bad-at-math/280914/. Accessed 2 Oct. 2017.
^{[16]} “Creating a Math-Positive Learning Environment – Inspired Ideas ….” 16 Jun. 2017, https://medium.com/inspired-ideas-prek-12/creating-a-math-positive-learning-environment-8837b0eac7c2. Accessed 2 Oct. 2017.
^{[17]} “Here’s the Proof—Bedtime Math.” http://bedtimemath.org/heres-the-proof/. Accessed 2 Oct. 2017.
^{[18]} “1 Tutor + 1 Student = Better Math Scores, Less Fear : Shots – Health ….” 8 Sep. 2015, http://www.npr.org/sections/health-shots/2015/09/08/438592588/one-tutor-one-student-better-math-scores-less-fear. Accessed 2 Oct. 2017.
Other Links
The Math Anxiety-Performance Link: A Global Phenomenon
Dispelling Myths About Mathematics
Are parents transmitting math anxiety to their children somehow?
It’s time to stop the clock on math anxiety. Here’s the latest research on how.
Stop telling kids you’re bad at math. You are spreading math anxiety ‘like a virus.’
Timed Tests and the Development of Math Anxiety
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In this episode we talk about the article Mathletes: Only for boys?
https://www.sciencenewsforstudents.org/article/math-isnt-just-boys
One of the main topics that the article and the supporting research referenced is that of stereotyping. At very early ages, we are exposed to stereotyping – both for girls and boys. In fact, from the moment people know a baby’s sex, they often treat girls and boys differently — and, much of the time, they aren’t even aware of the unconscious gender biases that are driving their behavior. Pink, pretty dresses, stuffed animals, and dolls for girls whereas boys get trucks, puzzles, shape sorters and the like.
Here’s a snippet from a BBC documentary on Gender and they dressed a little girl up like a boy and a little boy up like a girl. The researchers put typical boy toys out and typical girl toys out and allowed strangers to come play with the kids using any toy they wanted. I bet you can guess what they chose to play with each gender!! They even mentioned how interesting it was that all of the adults chose the spatial awareness toys (sorters, blocks, puzzles etc.) for the boys and the girls were given the stuffies and were spoken to a lot more.
Mathematics and science are stereotyped as male domains (Fennema & Sherman, 1977; Hyde, Fennema, Ryan, Frost, & Hopp, 1990b, Nosek, et al, 2009). Stereotypes about female inferiority in mathematics are prominent among children and adolescents, parents, and teachers. Although children may view boys and girls as being equal in mathematical ability, they nonetheless view adult men as being better at mathematics than adult women (Steele, 2003).
Boys and girls are getting messages from somewhere…it might be subtle, subconscious, or invisible, but the messages are clearly getting delivered. Here’s an example of invisible: In one study, fathers estimated their sons’ mathematical “IQ” at 110 on average, and their daughters’ at 98; mothers estimated 110 for sons and 104 for daughters (Furnham et al., 2002; see also Frome & Eccles, 1998).
Teachers, too, tend to stereotype mathematics as a male domain. In particular, they overrate boys’ ability relative to girls’ (Li, 1999; but see Helwig, Anderson, & Tindal, 2001).
WHAT CAN WE DO?
Teachers can begin by acknowledging stereotypes and biases and then begin the process of dispelling them.
First, these findings call into question current trends toward single-sex math classrooms. Advocates of single-sex education base their argument in part on the assumption that girls lag behind boys in mathematics performance and need to be in a protected, all-girls environment to be able to learn math (e.g., Streitmatter, 1999). The data, however, show that girls are performing as well as boys in mathematics, based on 242 separate studies (Study 1) and 4 large, well-sampled national U. S. data sets (Study 2). The great majority of these girls and boys did their learning in coeducational classrooms. Thus, the argument that girls’ mathematics performance suffers in gender-integrated classrooms simply is not supported by the data.
There is also evidence that we need an increased focus on problem-solving at the DOK 3 and 4 level. Girls are on par with boys with DOK 1-type questions, but there seems to be a bit of a gap in the problem-solving skills. Teachers can address this head on in the classroom by introducing unique problems that are low-floor, high-ceiling.
Also teachers should help all students – boys and girls- see that math is fun. Elham Kazemi, associate professor of curriculum and instruction in the UW College of Education says that math is “alive, joyful and creative. If girls get more messages that math is imaginative, they might identify with it more,” She goes on and says “It’s easy for people to express dislike for math, and to say ‘I’m just not a math person,’ but people do lots of math outside of class.” I think teachers don’t always bring this fun to the classroom because their confidence in the contextual understanding is weak (but that is a discussion for another day on credentialing programs!)
Parents can help kids’ interest in math too, by pointing out the mathematics of daily life, such as in cooking, shopping, saving money toward a goal and playing board games. Bedtime Math is a great example of this. Emphasizing persistence and problem solving—rather than speed and competition—and using open-ended math problems with different solutions and different ways of thinking about each problem could help girls with math.
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A Number Talk is a short, ongoing daily routine that provides students with meaningful ongoing practice with computation. A typical Number Talk takes between 5 and 15 minutes. They provide an opportunity for students make sense of their own mathematical ideas because the expectation is that they will use number relationships and the structures of numbers to add, subtract, multiply and divide.
There are many different flavors of Number Talks, but they all follow the same general format:
A variety of Number Talks is one that uses a sequence of problems that students solve in their heads. Each problem is revealed and solved, such that the sequence of problems strategically lead students to uncover a particular solution strategy.
Number Talks should be structured as short sessions alongside (but not necessarily directly related to) the ongoing math curriculum.
It is stressed by all three of our Number Talk authors that it is super important to make Number Talks short! They are not supposed to replace current curriculum or take up the majority of the time, but rather give a short blast of time to allow kids to practice number sense using mental strategies.
And really that is really the primary goal of Number Talks – computational fluency. Kids develop computational fluency while thinking and reasoning like mathematicians and during a number talk, they are asked to make connections and look for relationships. What’s even more fascinating is that kids are super engaged because they are sharing their strategies with others.
It is important for the teacher to support communication skills, by establishing a safe, supportive community where all students can share out. If students don’t feel like they can share – the Number Talk will fall short no matter how much you prepare and they won’t have the impact that research states they can.
So where does a teacher get the problems for the Number Talk? Start by considering the skills within your unit that your kids need more practice with. Then create a problem (or a string of 3 to 4 problems) and give it to your students. Don’t stress out about the need to choose the perfect problem(s). Just do it. You’ll know if you picked a good problem when the conversation is still going strong after 10 minutes.
Some examples of addition for each grade:
Kindergarten | |
1st grade: | 9 + 7 |
2nd grade: | 24 + 27 |
3rd grade: | 74 + 47 |
4th grade: | 370 + 267 |
5th grade: | 345 + 457 |
Really…choose any problem and see what your students do with it. Just keep in mind that students will be solving it mentally.
Finally, when implementing number talks you can maximize your experiences. Be mindful of all of the strategies students might use to help you decipher what students are trying to explain. You might want to start with easier problems or problems with smaller numbers so the students can understand the math before going on to larger, more complicated numbers. As students share their methods, try to connect the method with a visual representation. This makes the solution method more accessible to all students. Here are four different ways 44+35 might be recorded on the poster. Which method depends on how the student explains her method.
There are tons of Number Talk resources out there. Find one. Read it. Then try one in your class. Just do it. You will see the benefits immediately!
References:
Jo Boaler video on Number Talks
https://www.youcubed.org/resources/stanford-onlines-learn-math-teachers-parents-number-talks/
Making Number Talks Matter by Cathy Humpreys & Ruth Parker
https://www.stenhouse.com/content/making-number-talks-matter
Number Talks by Sherry Parrish
]]>Now what does that mean? How does one do that?
Universal Design for Learning or UDL.
Let’s start with some definitions.
UDL + DI = Success for ALL!
What is the difference between Universal Design for Learning (UDL) and Differentiated Instruction (DI)? How to they complement each other?
Both have the common goal of meeting the individual needs of students such that all students can access the same high-quality content. It is the role of the teacher to assess student progress during learning and then adjust as needed, provide multiple ways for students to develop and express concepts, and to emphasize critical thinking.
There are significant differences between UDL and DI, largely with respect to when and how student differences are addressed. In Differentiated Instruction the teacher modifies content and/or process in response to the student’s needs identified during the instruction. By contrast, UDL is a framework for the teacher to proactively customize/create the lesson for the broadest range of students from the beginning.
In other words, UDL proactively evaluates the classroom instruction and environment and provides access to the content on the front end; DI reactively evaluates individual students and retrofits and modifies on the back end.
This is a good time for a Venn diagram…
There are three principles of UDL. These three principles are in response to potential barriers that might get in the way of our students learning.
Goal: To create purposeful and motivated learners. How: Stimulate interest and motivation for learning. | Goal: To create resourceful and knowledgeable learners. How: Present information and content in different ways. | Goal: To create strategic and goal-directed learners How: Differentiate how students can express what they know |
Increase interest through individual choice and autonomy, relevance, and lowering affective filter Sustain effort and persistence with goals and objectives, appropriate challenge, collaboration and community, and mastery-oriented feedback Options for self-regulation via growth mindset, personal coping skills, and metacognition | Increase the variety in which the content is received by student: visual and auditory Options for language, mathematical expressions, and symbols Strategies to increase comprehension by transforming accessible information into useable knowledge | Provide options for physical action Provide options for expression and communication using multiple-media, creation tools, and scaffolds Provide options for executive functions: goal-setting, planning, graphic organizers, metacognition |
But to implement these principles into your classroom, it does NOT require the teacher to learn a bunch of new techniques. Rather, UDL is a mindset in which the teacher intentionally creates variety and choice by inserting already familiar strategies into in the classroom.
Some classroom strategies of each of the three principles…
Engagement | Representation | Expression |
Recruiting interest Alternative seating Choice boards Socratic seminar Brain Breaks Sustaining effort and persistence Rubric for self-monitoring Flipped learning Think-Pair-Share Peer tutoring Self-regulation Timer Desk dividers Exit tickets | Perception Three-Act math Visual cueing Text-to-speech Language, mathematical expressions, and symbols Word Wall – Cognitive content dictionary Tape diagram Math manipulatives Comprehension Warm-up problem (Application problem) Anchor chart Flashcards | Physical action Act out a problem Use online tools Expression and communication Oral presentation Record on video Math manipulatives Think-Pair-Share Executive functions Goal setting Exemplars Anchor charts Self-monitoring |
Let’s wrap up this brief overview of UDL with the punchline…
It’s important to realize that UDL is not some new idea that you have to add to your plate. Really it is just an intentional mindset in which we are always asking ourselves, “Are we providing students a wide variety of classroom strategies in each of the three areas (or principles) to ensure that all students get their needs met? Moreover, are students given choice in these areas, so that they can do some of the choosing?”
Take a few minutes to explore these links:
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We’ve been taught to start every school year with getting to know you activities and boring lists of Class Rules (Thou shall nots…) but is is possible to do that using your content? Is is that we are saying to our student inadvertently “Math is so boring that we’re better off building culture before we get to the boring stuff.”
Imagine if you were able to both engage students in your content area while at the same time developing a positive classroom culture, establishing norms, fostering school pride, etc. Why not use your content area as the tool of culture-building, rather than a follow-up to culture-building? Does that have the potential to change students’ minds about your content area? According to Geoff Krall, it does. If students see your content area as a place where you can develop these positive norms, that can have lasting repercussions for your students even beyond your classroom.
“And I wonder if it’s the message your students hear: ‘Math is so boring that we’re better off building culture before we get to the boring stuff.’”
-Geoff Krall
That requires getting students engaged in math (or whatever) on Day 1, not Week 2, on a level that gets them working together.
The article that got us thinking for this episode is called “The “Don’t Teach Them Content on Day 1” Myth” by Geoff Krall. You can find the link to his article in the show notes.
In a nutshell…
Setting up the norms: Don’t TELL the norms…BE the norms. Choose a math activity that is somehow directly connected to one of your math content standards. The activity should be low-floor/high-ceiling problem to allow all students access. Discuss your norms within this activity.
An example of this is the Quad Match activity from NRICH. Here are the cards for the Quad Match.
“I’m also not suggesting that you eschew culture-building or norm-establishing entirely, but rather that it be an organic outcome of the student-centered instruction that begins from the first minute of class”, says Krall. This is an important point. Don’t give up establishing norms. Be super intentional about the lessons you take from your curriculum so that you are still able to build up your classroom culture.
So what if you are using programs like EngageNY that seem to have no place for “extra” stuff? Look in the side bars for ideas. For example in Kindergarten, the first module’s first lesson is about looking at similarities and differences. When I was working with teachers, we decided what a great opportunity to practice and introduce partner talk.
I still have questions about the idea of introducing curriculum too soon. Some kids need to build up their trust in you, which goes back to the low floor/high ceiling activities that don’t seem like your normal curriculum. Of course, the trust needs to occur in ALL contexts: non-math and math. We need students to trust us in a math setting, so we might as get started building that trust on Day 1.
In building those classroom routines, establishing norms, and learning names, we can use our official curriculum. But we can also use other mathy sources, most notably Week of Inspirational Math by Jo Boaler on http://youcubed.org
What are your thoughts?
Tweet us at…
Duane: @dhabecker
Maggie: @pelelover1
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You’re a math teacher. You know the deal. You know that they are always coming out with new articles and new research telling us new ways to teach…new ways to think about math education. The problem is…when do you have time to read the article or the research…think about how it applies to your classroom…and then actually do it? You don’t!
That’s where Infinite Insights comes it. Hosted by me – Duane – and by my friend Maggie…
Infinite Insights is a podcast designed especially for all TK-12 math teachers (that includes you elementary teachers!) Every other week Maggie and I will share a new math research study or article, we’ll talk it over, bounce ideas off each other, and think about how to implement it in the classroom.
Essentially…we do the reading and thinking for you and fit it into a 20 minute podcast episode.
20 minutes! That is only HALF of your prep time. You still have time to take a walk…go potty…call a parent…or whatever.
Tell your friends! Hit that SUBSCRIBE button. We’re on iTunes and Google Play.
Look forward to our first episode to come out on Monday August 21.
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