Teach Knowledge, According to the NMP Re

Teacher Knowledge According to the NMP Report : 

Teacher Knowledge According to the NMP Report H. Wu Long Beach December 10, 2008

Need of effective teachers to bring the NMP Report to the classroom : 

Need of effective teachers to bring the NMP Report to the classroom If the NMP Report is a musical composition, then teachers are the performing artists who will bring the composition to life. Producing effective teachers is therefore the central concern for the implementation of the findings of the NMP.

A principal recommendation (ES, #7) : 

A principal recommendation (ES, #7) All elementary teachers, including special education teachers, should know the topics in Critical Foundations of Algebra, and the use of symbols, and linear and quadratic equations. All middle school teachers, including special education teachers, should know the topics in Critical Foundations of Algebra and all of the Major Topics of School Algebra.

A second principal recommendation (ES, #19) : 

A second principal recommendation (ES, #19) Need better teachers education to improve teachers’ effectiveness in the classroom. A critical component of this recommendation is that teachers must know, in detail as well as from a more advanced perspective, the mathematics they need for teaching, both prior to and beyond the level they are assigned to teach.

Effective teachers are identified by consistent achievement gains of their students : 

Effective teachers are identified by consistent achievement gains of their students This is a crude statement about effectiveness, for four reasons. Achievement gain is usually measured by multiple-choice items; such items capture only a small part of mathematical proficiency, e.g., not the process of multi-step, sequential thinking, and often cannot address essential mathematical content. Too often standardized tests are mathematically flawed.

Effective teachers (cont.) : 

Effective teachers (cont.) Example. Percentage of flawed items in NAEP (NMP Report on Assessment, page 8-3): 4th grade: 5% are seriously flawed, and 28% are marginally flawed. 8th grade: 4% are seriously flawed, and 23% are marginally flawed. State standardized test are generally worse than NAEP.

Effective teachers (cont.) : 

Effective teachers (cont.) Crude measure of effectiveness (cont.) While there is a positive correlation between teachers’ effectiveness and their content knowledge in terms of certification status, courses completed, or test scores, there is as yet no research evidence of the kind of content knowledge that is needed for effective teaching. Nor is there any research evidence of the kind of pedagogical content knowledge that is needed for effective teaching.

Effective teachers (cont.) : 

Effective teachers (cont.) Much more research is needed before we can pinpoint what “effectiveness” is. (The point of absolute certainty may never be reached.) Consequently, research does not show what effective professional development (PD) is. However, while waiting for research to catch up with reality, we have to get on with the business of improving teacher quality by exercising professional judgment.

A partial recommendation : 

A partial recommendation There is ample evidence that many teachers do not have the requisite content knowledge of the existing school mathematics curriculum. A general recommendation, consistent with Recommendation #17 (ES), is to provide PD that addresses this baseline level of content knowledge so that teachers at least know the mathematics in the curriculum.

What stands in the way? : 

What stands in the way? Teachers need to learn not just facts, but also how the facts fit together (Recommendation #1 in ES). They must see the need for precise definition of each concept (e.g., fraction, decimal), and know how to explain every fact by the use of definitions and logical reasoning. This is not what one finds in most textbooks or PD materials (CKS Report, Appendix B; also Report on Instructional Materials).

What stands in the way? (cont.) : 

What stands in the way? (cont.) Acquiring this kind of knowledge requires intensive immersion, but traditional PD, consisting of one or two days of activities and not focusing on content, would not get it done. Initiating a new tradition in PD requires good judgment, the help of knowledgeable mathematicians, and considerable financial investment.

Math PD for elementary teachers : 

Math PD for elementary teachers It is NOT realistic: There is a huge scale problem. Teachers are already asked to do too much. NMP does suggest the use of mathematics teachers who teach only math, while noting insufficient research evidence to justify a recommendation (ES Recommendation #29). Realistic starting point: grade 4. Too much is riding on it for states NOT to try.