Bellevue Community Math Night Report to the Curriculum Selection Committee

1. Bellevue Community Math NightReport to the CurriculumSelection Committee David A. Orbits 2/25/2010

13. Learning Productivity • “Adams and Englemann’s principal objective of direct instruction is to provide instruction to accelerate the performance of the students, • teach more in less clock time, • aim at teaching generalizations beyond rote learning, • sequence learning and constantly monitor the performance of students as they move to achieve their challenging goals.” [Hattie] • Important for all students to combat boredom • Even more important for Low-Income students, many of whom arrive at school with a lower stock of knowledge. Often they start school already behind their peers in reading and math. • More efficient classroom learning means more material can be covered in the school year with better long-term memory retention. • Increased rigor of the revised math standards argues for improved classroom learning efficiency.

14. Teacher Productivity • Teachers need well structured text, with examples, plenty of practice problems, and with review problems for memory reinforcement spaced out during the school year. • A text with a weak structure forces teachers to cobble together material from other sources which is both labor intensive and exacerbates quality variation from classroom to classroom. • Students who can learn some of the material directly from a good text or with the help of a parent at home are a direct benefit to teacher productivity, leaving more teacher time for students not having these advantages. • Weak (or new) teachers won’t know what parts of a weak text should be skipped or backfilled. • A good text helps the new / weak teachers because of (1) the reduced prep time, (2) it lets them become productive more quickly, and (3) they can use the text to refresh their own math skills. • While math standards specify the curriculum content, many teachers tend to teach directly from the text depending on their knowledge and skill. Factors that vary in any large workforce. • In schools serving a Low Income population, class time is where all the math learning must take place because there is generally no one at home who can help teach math. This makes both learning and teaching efficiency and productivity very important.

15. Why Minimal Guidance During Instruction Does Not Work “After a half-century of advocacy associated with instruction using minimal guidance, it appears that there is no body of research supporting the technique. In so far as there is any evidence from controlled studies, it almost uniformly supports direct, strong instructional guidance rather than constructivist-based minimal guidance during the instruction of novice to intermediate learners. Even for students with considerable prior knowledge, strong guidance while learning is most often found to be equally effective as unguided approaches. Not only is unguided instruction normally less effective; there is also evidence that it may have negative results when students acquire misconceptions or incomplete or disorganized knowledge.” (p. 83) [my emphasis] Kirschner P, Sweller J, Clark R, “Why Minimal Guidance During Instruction Does Not Work: An Analysis of the Failure of Constructivist, Discovery, Problem-Based, Experiential, and Inquiry-Based Teaching”, Educational Psychologist, 41(2), 75–86, 2006, Lawrence Erlbaum.

16. Teaching Method Effect Sizes Source: Hattie J., “Visible Learning: A synthesis of over 800 meta-analyses relating to achievement”, Routledge, Dec., 2008, ISBN: 0415476186.

17. Direct Instruction Direct Instruction Teaching is not simply a teacher lecturing for the period. Direct Instruction involves seven major steps (paraphrasing from Hattie): 1. The teacher needs to have a “clear idea of the lesson’s learning intentions. What, specifically, should the student be able to do, understand, care about as a result of the teaching?” 2. “What success criteria of performance are expected? Students need to know about the standards of performance and when and what they will be held accountable for from the lesson/activity.” 3. “ … use a "hook" to grab student attention. The aim is to put students into a receptive frame of mind; to focus attention on the lesson; to share the learning intentions.”

18. Direct Instruction 4. “There are guides to how the teacher should present the lesson.” Provide students “information needed to gain the knowledge or skill using lecture, video, audio, pictures, etc.” Model “examples of what is expected from students as an end product of their work.” … “Check for understanding by monitoring student work before proceeding. It is essential that students practice doing it right.” 5. Have each student “demonstrate their grasp of the new learning by having them work through an activity or exercise under the teacher’s direct supervision. During guided practice teacher moves about the room determining level of mastery, providing feedback, and individual remediation as needed.” This step needs to happen in the classroom with both a sufficient number of problems and various problem contexts so the teacher and aides can help correct student misunderstanding and mistakes. This may require several class periods but is critical for those students where help is unlikely to be available at home.

19. Direct Instruction 6. Lesson closure helps students “make sense of what they have just been taught. ““Any questions? No. OK, let’s move on” is not closure. Closure is used to cue students that they have reached an important point in the lesson or the end of the lesson, to help organize student learning, to help form a coherent picture, to consolidate, eliminate confusion and frustration, and to reinforce the major points to be learned.” 7. Reinforcement Practice “Once students have mastered the content or skill, it is time to provide for reinforcement practice. It is provided on a repeating schedule so that learning is not forgotten.” This practice should provide “enough different contexts so the skill or concept may be applied to any relevant situation and not only in the context in which it was originally learned.”

20. Student – Teacher Feedback Hattie describes feedback (d=0.72) as not only teacher to student but more importantly, student to teacher, “When teachers seek, or are at least open to feedback from students as to what students know, what they understand, where they make errors, when they have misconceptions, when they are not engaged—then teaching and learning can be synchronized and powerful. Feedback to teachers helps make learning visible.” (p. 173)

21. The Effects of Overlearning and Distributed Practise on the Retention of Mathematics Knowledge In two experiments, 216 college students learned to solve one kind of mathematics problem before completing one of various practise schedules. In Experiment 1, students either massed 10 problems in a single session or distributed these 10 problems across two sessions separated by 1 week. The benefit of distributed practise was nil among students who were tested 1 week later but extremely large among students tested 4 weeks later. In Experiment 2, students completed three or nine practice problems in one session. The additional six problems constituted a strategy known as overlearning, but this extra effort had no effect on test scores 1 or 4 weeks later. Thus, long-term retention was boosted by distributed practise and unaffected by overlearning. Unfortunately, most mathematics textbooks rely on a format that emphasises overlearning and minimises distributed practise. An easily adopted alternative format is advocated. Rohrer, D. and Taylor, K., “The Effects of Overlearning and Distributed Practise on the Retention of Mathematics Knowledge”, Applied Cognitive Psychology, 20: 1209–1224 (2006)

22. Professor Kirschner letter to Dr. Rasmussen of Issaquah School District (13 Feb 2010) “Let me begin by saying that I myself am not acquainted with the method that the district has chosen, though I have taken the time to peruse the website of the publisher and read what the publisher says about the method. In my opinion, which is based upon years of research on learning materials, learning material development, and learning & cognition the choice that your school district is about to make will impact your students in a very negative way.”

24. Reference Material Adams G., & Engelmann S., “Research on Direct Instruction: 25 Years beyond DISTAR”, Seattle, WA: Educational Achievement Systems, 1996. Colvin G., “Talent Is Overrated: What Really Separates World-Class Performers from Everybody Else”, 2008, ISBN: 1591842247 Dehaene, S., "Reading and the Brain", Viking, 2009, ISBN-0670021105 Good T. L., “Teaching Mathematics in Grades 3-5 Classrooms”, Teachers College Record, Date Published: April 07, 2008, http://www.tcrecord.org ID Number: 15196 Hattie J., “Visible Learning: A synthesis of over 800 meta-analyses relating to achievement”, Routledge, Dec., 2008, ISBN: 0415476186. Kandel E., “In Search of Memory: The Emergence of a New Science of Mind”, Nobel Laureate, 2007, ISBN: 0393329372 Kirschner P, Sweller J, Clark R, “Why Minimal Guidance During Instruction Does Not Work: An Analysis of the Failure of Constructivist, Discovery, Problem-Based, Experiential, and Inquiry-Based Teaching”, Educational Psychologist, 41(2), 75–86, 2006, Lawrence Erlbaum. Klahrl D. and Nigam M., “The equivalence of learning paths in early science instruction: effects of direct instruction and discovery learning”, American Psychological Society, Volume 15—Number 10, pgs 661-667, 2004. http://www.psy.cmu.edu/faculty/klahr/personal/pdf/KlahrNigam.PsychSci.pdf

25. Reference Material Mayer, R, “Should there be a three-strikes rule against pure discovery learning? The case for guided methods of instruction.”, American Psychologist, 59, 14–19, 2004. NMAP Panel on Standards of Evidence, http://www.ed.gov/about/bdscomm/list/mathpanel/report/standards-of-evidence.pdf Nuthall G., “The Cultural Myths and Realities of Classroom Teaching and Learning: A Personal Journey”, Teachers College Record, 107 (5), 2005, 895-934. http://www.tcrecord.org/Content.asp?ContentId=11844 Rohrer, D. and Taylor, K., “The Effects of Overlearning and Distributed Practise on the Retention of Mathematics Knowledge”, Appl. Cognit. Psychol. 20: 1209–1224 (2006) Stanovich P. J. and Stanovich, K. E. “Using Research And Reason in Education - How Teachers Can Use scientifically based Research to Make Curricular & Instructional Decisions”, May 2003, http://www.nifl.gov/partnershipforreading/publications/html/stanovich/ Sweller J., “Instructional design in technical areas”, Camberwell, Australia: ACER Press, 1999. Sweller, J., “Instructional Implications of David C. Geary's Evolutionary Educational Psychology”, Educational Psychologist, v43 n4, p214-216, Oct 2008, ERIC: EJ815161. Willingham, D. T., “Why Don't Students Like School: A Cognitive Scientist Answers Questions About How the Mind Works and What It Means for the Classroom”, 2009, ISBN: 0470279303

26. Other Q&A Discussion Topics • How the problems of HS start in Elementary and why the Direct Instruction model is needed there for Low-Income students. • The achievement data by scoring level and school in Bellevue, LWSD and Seattle • The problems with Inquiry based learning as described by NMAP, Hattie and Kirschner • The Direct Instruction model for classroom instruction and how it helps all students but especially Low-Income students and the data in Hattie • Learning and Teaching productivity • The problems with research conducted by the education community • The cost of a HS dropout