Todays Discoveries Aid Tomorrow’s Understandings!

According to eSchools News, a study released by the University of Missouri suggests that students beginning first grade with a good understanding of number lines and basic math facts were more successful in math skills over the next five years. This should be no surprise – just as building a house on a strong foundation makes for a stronger home, building new math skills on a strong foundation of math knowledge makes for a more robust understanding.  These recent findings also suggest that teaching ‘a mile wide and an inch deep’ may not fully develop a conceptual understanding of key math concepts. Young students need a lot of modeling, time, and a variety of experiences to practice math skills for true understanding.

One way to help develop these skills at an early age is to incorporate the Quantile Framework for Mathematics in specific math lessons. Utilizing the Framework allows teachers to determine which prerequisite skills are necessary for success with a particular math skill or concept, allowing educators to target struggling math students with the appropriate prerequisite skill.  For example, if a third grade student is working on estimation for sums and differences with whole numbers he/she must first be able to:

  • Make reasonable estimates of the number of objects.
  • Subtract 2- and 3-digit numbers with regrouping.
  • Round whole numbers to a given place value.

These prerequisite skills are necessary for students to understand before they are able to extend to estimation skills when they add and subtract whole numbers.

And the Quantile Framework allows teachers to go even lower: if a student is having trouble making reasonable estimates of the number of objects the knowledge cluster for this skill may indicate that he or she is having trouble with:

  • Use counting strategies for totals to 100 that include counting forward, counting backwards, grouping, ten frames, and hundred charts.

The Quantile Framework allows for the possibility of identifying areas where students are deficient.  Furthermore, for educators looking to differentiate math instruction, the Quantile Framework can serve as a valuable classroom resource by helping teachers target lessons to the needs of the students. Additionally, the Quantile Framework is linked to a variety of free tools and resources that – in addition to providing tools for task analysis – provide access to a host of free targeted resources, including worksheets, online tutorials, videos, websites, literature guides, and classroom activities. 

As we enter the new school year (and as many students are suffering the effects of summer slide), be sure to check out the Quantile Framework as a way to help struggling math students.

Consider the Student: Targeting with The Lexile Framework for Reading

A tip of the hat to last week’s Marshall Memo for pointing to Susan Voorhees latest piece in this month’s The Reading Teacher, ‘Why the Dog Eats Nikki’s Homework: Making Informed Assignment Decisions’ (subscription required).  Voorhees argues that too often students failing to complete homework assignments are seen as incompetent, or lazy, or as academically deficient.  When, in fact, many students may be assigned conceptually dense work, or reading material at far too high a level.

Voorhees goes on to offer a detailed and compelling case for scaffolding, for differentiating based on the reader’s ability.  Voorhees even recommends a checklist approach for determining how much assistance young readers may need with an assignment:

  • Can all students decode the homework material?
  • Do all students have prior knowledge, schema, and vocabulary needed to understand the assigned material?
  • Do all students know how to use text structure?
  • Do all students understand the purpose of the homework assignment?
  • Do all students know how to activate prior knowledge prior to reading?
  • Do all students have sufficient attention and ability to concentrate?
  • Do all students have high self-efficacy toward homework and literacy?
  • Do all students get parental help with homework?

For each of the checklist items, Voorhees offers concrete suggestions on ways to ensure that each student meets the criteria listed above.  One such suggestion, for example, focuses on stamina – a reader’s ability to engage with the text for longer periods of time.  Because a reader’s stamina will influence their success on longer reading assignments, Voorhees recommends taking stamina into account and breaking up longer reading assignments into more digestible chunks.

Voorhees also recognizes that reader level varies across classrooms and that more complex texts will present a greater challenge for struggling readers.  Which is why she recommends that, when practical, teachers focus on providing easier texts for struggling readers.

The idea that an important piece of differentiation is targeting a reader with appropriately matched texts is a well-established idea and in line with many practices that complement the use of the Lexile Framework.  The Lexile scale is an important metric for measuring both reader and text on the same scale.  One of the advantages of a common scale is that by placing reader and text on the same scale, an educator has a clear idea of just how much challenge a text may present.  The Lexile Framework for Reading allows educators to match struggling readers at a targeted level.  Because so many supplemental resources have been aligned to the Lexile metric – including tens of millions of articles on just about any topic – educators have a wide variety of resources through which to target struggling readers.  This sort of targeting jibes well with Voorhes’ suggestion to ‘provide easier text’ in cases where students will struggle with high level material.

Voorhees’ suggestions are worth considering. We’ve seen many of these practices implemented in classrooms around the country and many are a natural complement to using the Lexile Framework to match readers to the right level of text.

Washington Moves Toward Digital Texts

We’ve written at length about the shift from print to digital media in higher education. Many universities are now seeking ways to ease the financial burden of higher education for its students. One route that Washington State has opted to take is to offer more online classes with online resource material. According to this report in The Chronicle of Higher Education, Washington state’s current textbook bill is financed through the state legislature, which has been facing financial hardships. The state currently has a half million students taking courses at their 34 two-year colleges. The idea was to create very accessible and affordable resources for students through online portals. The savings alone made the idea a winner. “We believe we can change the cost of attending higher education in this country and in the world,” says Cable Green, director of e-learning and open education at the Washington Board for Community & Technical Colleges.

The state received a matching grant of $750,000 from the Bill & Melinda Gates Foundation to help begin development on low-cost online resources for the two-year colleges. The state is taking an ambitious approach to providing affordable education to their students, regardless of the obstacles they may encounter along the way. This is probably just a glimpse at what could be a revolutionary approach towards the future of higher learning.  If students are already receiving their texts digitally, it’s easy to imagine younger students receiving individualized texts targeted to their own reading level.  Personalized learning systems offer a world of possibilities to the world of education.  The wide availability of digital texts bring those possibilities that much closer to reality.

Next Generation Assessment: Virtual Tutors & Personalized Learning

Online tutoring sites have been around for a while.  But recent advances are taking virtual tutors to a whole new level of sophistication: Imagine a virtual tutor with a computer generated face, a gender, a voice, and, most strikingly, one that responds to the emotional cues of the student   The New York Times recently reported on remarkable advances in affective computing – computers that monitor and respond to the emotional cues of the students.  Maggie Jones writes about her experience with a virtual tutor, named Isabel:

 On a summer afternoon, Isabel, a math tutor with long chestnut-colored hair and hoop earrings, sat in the lower-right corner of my computer screen as I wrestled with geometry problems. When I answered correctly, Isabel gave me a quick congratulatory smile. When I rushed, randomly guessing at perimeters of triangles and rectangles (geometry was never my favorite), Isabel, inferring from the speed of my keystrokes, wanted to know if I was bored. Was it because of the last problem? Did I want to choose the level of the next problem? “I think that more important than getting the answer right,” she said in words reminiscent of many a high-school teacher, “is putting in the effort and that we can all be good in math if we try.”  

This fall, hundreds of students will experience Isabel and her digital counterparts as part of an online tutoring program, Wayang Outpost. This program uses virtual tutors, or “affective pedagogical agents,” via a game-like interface to read students’ emotional cues, like boredom, frustration, anxiety and nervousness. The students are hooked up to sensors monitoring sweat, pressure placed on the mouse, and fidgeting. A small camera monitors facial expressions. This information is then used to cue the tutor’s responses, whether offering hints and explanation where needed or finding various ways to keep middle and high school students engaged.  Wayang Outpost is not just limited to student interaction; the program provides several teacher tools that allow classroom educators to create new classes, assign lessons for certain days, and see reporting on students’ progress. (more…)

Khan Academy: Education Goes Viral

Salman Khan has an ambitious plan. He wants to create the “world’s first free, world-class virtual school where anyone can learn anything”. Believing strongly that everyone should have access to education he created Khan Academy, a non-profit, educational website. His website has become wildly successful; attracting users and fans from around the globe. Bill Gates called Khan his favorite teacher and uses Khan’s videos to help his own children with math.

Khan, a 33 year-old Bangladeshi-American with three degrees from MIT and an MBA from Harvard, began his academy after tutoring some of his relatives online.   He posted some of his tutorials on YouTube, and the videos became so popular that Khan quit his job as a hedge-fund manager and devoted himself full-time to Khan Academy.  Currently, he works out of his Silicon Valley home in a converted walk-in closet with only a couple hundred dollars worth of computer equipment.

The site features over 1,630 instructional videos covering science and math topics ranging from arithmetic to calculus; but the videos are not limited to the core subjects of math and science. The website now offers instructional videos on History and test preparation for California tests, the GMAT and the SAT. But Khan Academy covers less traditional subjects as well.  For example, there are even instructional videos on subjects like sub-prime mortgages and the Paulson bail out.  Such accessible content allows even non-specialists to tackle the details of issues that were previously far too technical and obtuse.


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