I’m a Tool1. State your name2. Proudly and boldly proclaim “I’m a tool”3. Describe your purpose as a tool4. Describe methods in which people use you5. Get other people to guess what tool you are
Tools Purpose Method of UsePractice Develops MasteryMastery Produces Growth
PurposeMath is the language by whichwe study and establishrelationships between us andthe universe around us.
Method of UseVerbal Numerical Algebraic Graphical
Verbal If you cant explain it simply, you dont understand it well enough. – Albert Einstein If you don’t understand it well enough any simple explanation won’t be simple.SB
Understanding Statements (Verbal) Major Concepts and Sub-concepts These are the written statements of truth, the core to the meaning(s) of the lesson(s) or unit. These are what connect the parts of a subject to the student’s life and to other subjects. It is through the understanding component of instruction that we teach our students to truly grasp the “point” of the lesson or the experience. Understandings are purposeful. They focus on the key ideas that require students to understand information and make connections while evaluating the relationships that exist within the understandings.
Numerical• Tables• Maps• Can be substituted for variables or unknowns• Can be used to determine patterns• Can be misleading – Patterns may not be established correctly – Placement of numbers is crucial
AlgebraicAll we know is still infinitely less than all that remains unknown. – William Harvey• How many different ways can we use an “x”, or other symbols?• Variable vs unknown.• Do students understand the equals sign?
GraphicalA picture is worth a thousand words. – Unknown• Graphs• Drawings• Any visual representation of data• Calculator
Practice Develops Mastery• He who loves practice without purpose is like the sailor who boards ship without a rudder and compass and never knows where he may cast. – Leonardo da Vinci• In theory there is no difference between theory and practice. In Practice there is. – Yogi Berra• An ounce of practice is worth more than tons of preaching. – Mahatma Gandhi
Verbal NumericalGraphical Algebraic
Name UnitVerbal Numerical Graphical Algebraic
Mastery Produces Growth
Who’s Responsible for Learning?• Teacher or Student• How do teachers know if students are learning?• How do students know if they are learning?
AP Grading5 Proficient work on all objectives and advanced Extremely well qualified work in some objectives4 Proficient work on all course objectives Well qualified3 Proficient work on most important objectives but Qualified not in all objectives2 Proficient work on half the objectives and missing Possibly qualified some important objectives1 No recommendation few objectives if any Proficient work on
5 Point Scale 1 2 3 4 5•No clue. •Feels •Feels •Feels •Masters all•Does few comfortable comfortable comfortable concepts.things right with few with most with all •If there arebut can’t concepts. concepts. concepts. any mistakesexplain them. •More gaps. •Few gaps. •Can explain they are•Hard time why they got minimal.making any the wrongconnections. answers. •Makes more mistakes than would like.
Using the 5 Point Scale• Tests – Corrected but not scored and returned – Students must self assess and score 1-5 • Expectation is for 1-3s to get extra help – Gives students a chance to prove to me what they have learned• In Class Quick Assessment – Hands up 1-5
Goals for 5 Point Scale• More specific to subject, units, and concepts• Used for homework to help students verbalize their strengths and weaknesses