Raising Math Achievement by Teaching for Mastery

Susan E. Neece, NBCT, Ph.D.

Author of Mastering Math – Every Student in All Schools

Copyright 2007

Professor Walden University – 6-8th Grade Math Master’s Program

  1. Introductions
  2. Background on Edison
  3. Over 70% low-income, over 50% minority, and 20% IEP students
  4. 80% passed 2007 ISAT
  5. 91% White students passed, 71% Black students passed, 73% low-income students passed, 24% IEP students passed
  6. Mastery
  7. Teacher Directed Spiraling
  8. Routine – Teacher Directed Spiral Curriculum
  9. Bell-to-bell engagement with the students
  10. 5-10 minutes – review problems (Scantron – item analysis). This is essential. You are spiraling problems they have not mastered. Also throw in concepts they do know so they do not forget. If the lesson will be short, then I spend more time on this review. The key is to engage the students. Keep the class flowing.
  11. 20-30 minutes – Lesson (direct instruction – lots of modeling, guided practice, and checking for understanding). Choral response. One small objective is covered.
  12. 13 minutes – assignment – Assignment is short (about 12 problems – Versa Tile Books). The assignment is completed in class. The goal is mastery (mission statement). I walk around and grade it as they are doing it. They have to redo all problems until they are correct (forcing mastery). When they start finishing with 100% of the problems correct, then I ask them to walk around and help me grade papers. When several students start finishing then I pair up students to help each other. The goal at the end of the period is 100% of the students have 100% on their math assignment. This is the 100-100-100 (100% of the students have 100% of their assignments turned in with 100% accuracy) system for achieving mastery. Grading – make all students successful (failure does not motivate anyone).
  13. Participation grade. 20 points a week for participation. Do math the entire period. I do not have to say anything to them. They know the class routine. Making the Grade weekly printout sheets helps them monitor their progress.
  14. Forcing Mastery
  15. Unit Tests
  16. Goal Setting
  17. Positive Attitude
  18. Communication between math teachers at different grade levels
  19. Communication between math teachers of the same grade level
  20. Communication between all teachers in the building
  21. Remedial Math Classes
  22. Math Specialist
  23. Math Elective Class
  24. Advanced Classes and the Standards
  25. Special Education Students and the Standards
  26. Monitoring Subgroups
  27. Administering the Standardized Test
  28. The Expectation is College
  29. Administration

Susan Neece, Ph.D. is a professor at Walden University and a math specialist at Edison Junior High in Rock Island, IL. She is a National Board Certified Teacher for Early Adolescence Mathematics and recruits/mentors teachers through the National Board process. Her book, Mastering Math – Every Student in All Schools can be purchased at

She may be reached at or

Math Mastery Testimonial: "Susan, I just got done reading your book. I am implementing your Math Mastery Techniques. I just wanted to write and let you know what a fantastic day I had today teaching. I used your program and although I don’t have it down perfectly . . . it was an outstanding experience. I have one period where it is all I can do to keep their attention. Today, they paid attention and participated. They were so excited about getting immediate feedback and could not wait to check along with me. Thank you, Thank you! The kids took ownership right away. I have one student who never, and I mean never did homework. He did his work. I think he felt very empowered by the process. I think this is going to make all the difference. Again, thank you so much!!" Alice Strickler – High School Pre-Algebra – Luray, Virginia

Period ____

DATE

/

TEST

/

EXCEED

(100%–90%) / MEET (89%–70%) /

BELOW

(69%–40%) / WARNING
(39%–0%)

Goal: Exceed or Meet

Example of a documentation sheet for the wall in the classroom. Each period should have its own sheet.

(P. 27 from Mastering Math – Every Student in All Schools. Copyright 2007 Susan Neece

Math Mastery Techniques Checklist - (P. 45 from Mastering Math – Every Student in All Schools. Copyright 2007 Susan Neece

Posted mission statement
Goal sheets are posted in the classroom – all tests are documented on the goal sheets – individual students also have a goal sheet
Supply pencils and paper
Lesson:
Teacher Directed Spiraling
Engaged with students bell to bell – never sit or stand in one place
Keeps the class flowing – activity not exceeding 20 minutes in length – at least three changes throughout the class (Teacher Directed Spiral Review, Lesson, Assignment)
Students participate – choral responses, whiteboard responses, individual responses – all students are focused
Direct Instruction – model many problems – guided practice
Explain how concept is used in real life
Explain why concept is needed for higher mathematics – show them an example, if possible
Curriculum must be challenging
Align lesson with state standards
Lesson focus is on one small objective with one set of directions
Assignment is short (10–12 problems) and completed in class
Students work with a partner (family atmosphere – students pushing each other to meet the goals of the class)
Teacher walks around the room and corrects the assignment as the students are completing it – students redo the problems they miss until all problems are correct
As students finish their assignment earning 100%, they walk around and help the teacher correct papers – they also help students who are struggling
100/100/100 System of Achieving Mastery – 100% of the students handing in 100% of their assignments with 100% accuracy
Students must feel successful – goal is not to fail the students – failure is not motivation
Expectation that students will study math definitions at home, review notes, and do logic problems if they have time
Forcing Mastery of certain topics by forcing 100% on quizzes – retake daily until 100% is achieved
Be flexible, not anal, when it comes to the work students show
Use Scantron© sheets for tests – run an item analysis
Tests should be multiple choice to mirror the standardized test – students must learn strategies for taking multiple choice tests
Make the tests about 70% review and 30% new material
Give the students a review that is exactly like the test only with different numbers in the problems so they can study for the test and do not have any surprises
The students should make test corrections
The students should receive their test back the day after they took it
Every day is an instructional day
Keep positive and demand mastery
Monitor the subgroups
Repeatedly tell your students that you expect them all to attend college
Make your students believe they have the potential to graduate from college with at least a Bachelor’s degree
Only positive “I can” attitudes are tolerated in the classroom
Be friendly and care about their education–let the students know you care about them
Use TI-12 Math Explorer™ calculators almost daily in class (if your standardized test allows calculators to be used)
Distribute updated grade sheets weekly for communication with parents and so the students can keep track of their grade – post grades online – can use Making the Grade™ Program

Problem Solving

** First they must understand the problem. They must know the vocabulary, which numbers are important and how to underline key information. Model this for them.

Use the following layout:

  1. My strategy is ______. (Choose from the three choices: make a chart, draw a picture, and guess & check. If you guess and check then you organize it into a chart.)
  1. Show strategy:
  1. The answer is ______
  2. My strategy is a chart because I need to organize my information. I organized my chart into items and cost. (Continue with explanation.)

Or

My strategy is a picture because I needed to visualize what was happening in the problem. (Continue explaining)

Or

My strategy is guessing and checking because I knew clues so I needed to guess to see what worked. (Continue explaining).

EXPLAIN WHAT YOU DID AND WHY YOU DID IT.

** They can only write on two sides of paper. One of the sides has the problem written on it.

** Rubric scoring – any 1's or 0's and they fail – all 2's is failing – can only get a 0 if there is no effort – if they try in any one area then the lowest score they can receive is a 1

11 or 12 points is exceeds

10 – 7 is a meets (as long as no 1's or 0's)

** Kids have a difficult time understanding that you can get a 1 in one category and a 4 in the other. If the answer is totally off but they explain what they did and why then they can still get a 4 for explanation.

** Stress they cannot have an "I can't do it attitude" – only positive attitudes – as soon as they say they don't get it then their brain shuts down.