Reading Comprehension - Math Problem Solving - The Learner's Edge, Inc.

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Research: Reading/Literacy

"The idea is to constantly learn. You are always taking an examination. There is no end to learning...." quoted in The World Is Flat: A Brief History of the Twenty-first Century (2005) by Thomas L. Friedman

The Learner's Edge, Inc. conducts extensive, ongoing research in the area of reading comprehension and the reasons for poor student performance on today's reading assessments.

The research includes classrooms in large and small school districts and students of all grade levels. The study populations consist of regular, gifted and talented, bilingual, and at-risk students students of all ethnicities and socioeconomic levels.

Significant highlights from these studies indicate that for students to be successful in the area of reading comprehension and on today's demanding reading assessments, they must:

  • Be instructed at grade level because they are evaluated at grade-level.
  • Be taught by teachers who match classroom instruction with assessment formats.
  • Be taught through modeled instruction until they have demonstrated that they can problem solve and write correct answers on a regular basis in all class work.
  • Be aware that tests are timed and that there are no pictures. There is little opportunity to apply word attack skills or to use pictures or context clues. (Such skills are reading enablers rather than the requisites for reading comprehension.)
  • Know how to recognize and respond appropriately to multiple types of assessment questions (multiple choice, constructed answer webbing, etc.).
  • Have an automatic facility with grade-level vocabulary because assessments are written at grade level.
  • Have a working knowledge of reading comprehension skills (main idea, cause and effect, inference, author's intent, meaning of words and phrases, best evidence, etc.), that they can apply analytically to any reading passage.
  • Have the opportunity to show and demonstrate all learned skills daily. (Nothing can be taken for granted.)
  • Not be placed in graded readers in a sequential fashion. (Below-grade level students never catch up.)
  • Avoid books that are more gibberish than common sense.
  • Be aware that correct answers are always dependent on or relative to passage content. (Answering questions with what you think or personal opinion is not acceptable.)
  • Realize that the casual nature of journal writing is a pitfall when writing for precision and purpose.
  • Be taught by direct instruction until they are ready to learn vicariously or through group discovery.
  • Be aware that one-word answers, starting sentences with "because," omitting stems from the question, incorrect punctuation, garbled or contaminated responses, and misspelled words are not acceptable.
  • Be taught through a dyad reading approach when subject material is at a frustration level.
  • Have a "purpose hat" and a "fun hat" for reading and know when to use each one.
  • Have daily opportunities to participate in lively classroom activities that model the problem-solving process both orally and in writing.
  • Learn the penmanship skills to write legibly. (Work that can't be read, can't be scored.)

Based on a careful review of our studies, the Learner's Edge integrated each of the elements identified as essential for reading success into highly effective instructional programs for students from kindergarten through adulthood. The programs include teaching techniques, strategies, interventions, and materials that make a significant, positive impact on student reading comprehension and on performance on today's standardized tests.

Other Voices...

Rapid recognition of frequently used words is not the only factor related to fluent reading but it is essential. Reading fluency and comprehension are directly related to this ability. (Eldredge, 1995)

New vocabulary words are written on small cards which the student uses to practice these new words thus building a word bank. (Perry, "Students At Risk: The Slow Reader in the Middle Grades," Middle Schools Reading, January 1990)

Students benefit from direct instruction, and some cannot learn without it. (Thompson, 1992)

The difficulty of the reading material is irrelevant as long as the material is of interest to the student and read with fluency and interest by the lead reader. (Eldredge and Butterfield, 1986)

Poor readers are involved with reading natural texts in unison with the teacher. Neurological Impress Method (NIM) reported a range in achievement from 0 grade levels to 5.9 grade levels at the end of a 6 week exposure to NIM. (Heckelman, 1969)

Students who are assisted to read difficult materials in a dyad system over a period of time become able to read difficult material independently. (Eldredge and Quinn, 1988)

At any stage of a reader's development, the use of guided reading strategies allows you to model for students the "why and how and the knowledge that you know" of reading. (Mooney, Teaching K-8, September 1995)

Pretests and posttests have their place. Students like to see how much more they know at the end of a unit than they did at the beginning. (Improving Reading Skills in The Content Areas, Jane Keen, ed., 1997)

Provide students a chance to answer comprehension questions without being graded, and time to discuss their answers and the answering process. (Armbruster, The Reading Teacher, May 1992)

Over a period of time, using the dyad reading approach, assisted readers were able to read the regular school material without assistance, and they achieved significantly higher scores in both reading achievement and attitude. (Eldredge, 1990)

Provide demonstration of how to answer the questions. (Armbruster, The Reading Teacher, May 1992)

Vocabulary must be taught, not just assigned and tested. (Carter and Klotz, NASSP Bulletin, 1991)

Use of think aloud strategies helps students understand what kind of thinking is required for a task. (Improving Reading Skills in the Content Areas, Jane Keen, ed., 1997)

Reading fluency affects reading comprehension because good sight word recognition allows students to decode fluently and therefore give their full attention to comprehension. (Labarge and Samuels, 1974)

Decoding and reading comprehension ability are significantly improved when poor readers are helped to read material that is at the "frustrational level." (Eldredge and Quinn, 1988)

The most critical element of reading is vocabulary and conceptual understanding; all effective instruction focuses on the explicit teaching of vocabulary and conceptual understanding. (McREL, Power Teaching, 1990)

Research: Mathematics

"On evolutionary grounds it would be surprising if children were mentally equipped for school mathematics. These tools were invented recently in history and only in a few cultures, and too late and too local to stamp the human genome... mathematics is a noninstinctive invention." Steven Pinker, The Blank Slate (2003)

The Learner's Edge, Inc., conducts extensive, ongoing research in the area of mathematics acquisition to determine how present instructional practices and interventions impact student conceptualization and application—what students know and can do. The studies involve classroom observations, teacher interviews, student input, review of textbook content, the piloting of various instructional programs and interventions, and analysis of assessment formats and content—and finally the development of our own instructional solutions and materials that work!

Fundamental to all of our research were the nagging questions: Why, over the last many years, haven't the majority of our students learned and retained the necessary knowledge or skills required for success in mathematics? And—Why do increasing numbers of students score poorly when confronted with today's mathematics assessments? From a careful review of the literature and our own extensive studies, the fundamental instructional factors required for learning and retaining mathematics concepts were identified, piloted, and integrated into a teaching process that works for all students—at-risk through gifted and talented.

It was found that certain key factors must be present in the successful teaching of mathematics. They are as follows:

  • Take nothing for granted in the area of student competencies until they demonstrate proficiency.
  • Teach grade-level content. Students are assessed at grade level.
  • Align instruction with content standards and assessment formats.
  • Develop the enablers (the ability to add, subtract, multiply, divide. etc.) to a level of automaticity.
  • Model all instruction and problem-solving on a chalkboard or overhead. Students have to see it to learn it.
  • Include the modalities of learning in all lessons: auditory, visual, kinesthetic, and practice. That's how students learn and retain.
  • Develop, use, and stress appropriate math vocabulary, both orally and in written form.
  • Use dyad-reading when reading is a problem.
  • Teach the art of representation to clarify mathematical concepts.
  • Assess/evaluate student progress daily through guided class practice.
  • Teach students to communicate in writing the thinking used to solve problems.
  • Include opportunities in the instructional process for immediate reinforcement and correction.
  • Teach students how to develop and use math dictionaries or journals.
  • Maintain, review, and reinforce all pertinent concepts on an ongoing basis throughout the year.
  • Use cooperative learning and discovery activities only after students have demonstrated that they know and can apply the skills.

The Learner's Edge has carefully integrated each of these key/essential elements for "learning mathematics for keeps" into a highly successful instructional model. This model incorporates proven teaching strategies and techniques with materials designed for efficient learning. Such an approach works and makes a significant positive impact on the acquisition, retention, and continuous application of grade-level and above mathematical concepts.

Other Voices...

To say that school mathematics comes easily out intuitive mathematics is not to say that it comes easily. (Geary, 1994)

Mastery of mathematics is deeply satisfying, but it is a reward for hard work that is not itself always pleasurable. (Pinker, 2002)

Mathematics is ruthlessly cumulative. Each subassembly of mathematics hangs together by the rivets called chunking and automaticity: with copious practice, concepts adhere into larger concepts, and sequences of steps are compiled into a single large step. (Pinker, 2002)

... recommends the use of six problem-solving strategies that students can monitor on an implementation sheet: read and understand the problem, look for the key questions and recognize important words, select the appropriate operation(s), write the number sentence (equation) and solve it, check the answer, correct any errors. (Mercer, 1992).

One suggested schedule for the class period includes a review of previously covered materials, teacher-directed instruction on the concepts for the day, guided practice with direct teacher interaction. (Palloway and Patton, 1993)

The demonstration step is critical especially if the students are learning a new concept or skill. (Archer and Isaacson, 1989)

Research has pinpointed several concerns regarding the teaching of mathematics... lack of individualized instruction, lack of adequate practice and review, inadequate sequencing of problems, and absence of strategy teaching and step-by-step procedures for teaching problem-solving. (Wilson and Sindelar, 1991)

Guided learning includes the modeling of skills by the teacher and the practicing of skills by students and teachers together. Modeling is a mandatory instructional element when teaching complex skills (Marzano, Pickering, and Pollock, 2001)

Guided practice can lessen the occurrence of failure in students by ensuring that the student knows and is able to perform a particular skill. (Schmidt and Harriman, 1998)

Collecting data regarding student progress will improve both student learning and teacher instruction (Jones, Wilson, and Bhojwani, 1997) ...timely instructional adaptation enhances student progress in mathematics. (L.L. Fuchs, Fuchs, and Hamlett, 1991)

Direct instruction is a systematic approach to teaching where lessons are planned around a carefully specified knowledge base and well-defined objectives. (Becker and Carnine, 19981)

Direct instruction also shows students how to actively apply the skills that they have learned in both basic and complex situations. (Christenson, Ysseldyke, and Thurlos, 1989) ...and benefits both low- and high- achieving students. (American Institute for Research, 1999; also, Gagnon and Maccini, 2001; Hastings et al., 1989; C.L.Wilson and Sindelar, 1991)

Acquisition of mathematics vocabulary—when developed in conjunction with conceptual learning and used in mathematical concepts—is vital to students' understandings of mathematics. (Brown-Kovacic, 2002)

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