Mathnasium training (Videos)
What are the three components of the Mathnasium Method?
- 10 Rules of Engagement - Curriculum Icons - Mathnasium Vocabulary
What are the fact fluency problems of concern? What do you while they complete them?
- Addition facts with sums over 10 - Subtraction facts with minuends over 10 Ask them: "Are you sure?" Or if they're right "How did you get that?"
What do basic number facts consist of? When does a student have basic number fact fluency? How do you make sure of this?
- Basic operations - When they can effortlessly answer basic number problems; no hesitation in answers AND they can teach their process - Pay attention to how they find the solutions
What does the Number Sense Triangle consist of? Summarize each part.
- Counting - Wholes and parts: whole = part + part...; part = whole - part + part... - Proportional thinking - Quantity and Denomination: How much of what (denomination = name) - The Law of SAMEness (can only combine things with the same denomination
What are desk tools? When do you use them?
- Desk tools are lamented pictures, not literal desk tools -
Name the "Multiplication Fact Fluency" key terms and describe them
- Factor: Two or more numbers in a problem that create a product - Multiplicand: The factor that will be multiplied (like how the first term in a division problem is being divided) - Multiplier: The number that states how many times the multiplicand will be multiplied - Multiplication Fact: A problem that comes directly from the multiplication table b/w 0x0 - 12x12 - Product - Repeated addition: A number added a certain amount of times - Commutative property of Multiplication: states that factors switched will still give the same product
Name and describe the prerequisite skills students need before continuing to Multiplication Fact Fluency
- Half of Multiples of 10: A multiple of 10 is halved and added together to get the product again; for 5s and half of 10s facts - Doubling Numbers Up to 50: Students break apart numbers, separating ones and tens, then double the places and add them together; for 2s, 4s, 8s - Add/subtract 10s; 8s, 9s, 10s, 11,s and 12s - Adding Up to and Over a Multiple of 10: Basically, Up to and Over 10 - Subtracting Through a Multiple of 10: Basically, Add up to and Over 10, but with subtraction
How do you teach the Mathnasium way?
- Help student at the right time - Assist/Teach student based on what they need - Leave student with a goal/task - Read the room; look to see if any students need help
What are the 5 techniques in Multiplication Fact Prescriptive and describe them
- This, that: "This, that many times."; repeated addition - Repeated addition - Count bys: 5, 10, 15, 20; emphasize this, that and repeated addition (4, 5 times; 4+4+4+4+4) - Visual Groups: Draw groups of 10s, 5s, etc. -Turnaround Facts: Communitive property of Multiplication; "Find 7x3 by doing 3x7
What should you look for when you Administer the Multiplication Fact Fluency Checkup?
- Watch for finger counting or other bad techniques - If two of the first 5 questions are missed, students will have to go through Numerical Fluency Addition and Subtraction Facts - Ask students how they got that to make sure addition and subtraction fluency are good
What are the Laws of Wholes and Parts?
- Whole = sum of parts - Part = whole minus so
Learning Center Basics
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Multiplication Fact Fluency Instruction
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What does team teaching consist of?
1) Engage students at strategic moments 2) Interact based on student's needs 3) Disengages, leaving student with appropriate task 4) Walks around observing when not instructing
Name and describe the steps of team teaching
1) Rotate and read the floor: - Watch for student indicators: Asking for help, staring off into space, distracted, talkative, not working, working on a page for a long time - Instruct multiple students, reactive and proactive engagements, 6 interactions per student, 3:1-4:1 ratio Team communication - When student doesn't get explanation, partially or completely corrected work, sensitive needs, when unattended students need help - Center Director should be told about behavioral problems, performance in school, need extra practice 2) Initial Engagement: - Record information for workout plan Ongoing Engagement - Update workout plan: Instructor's initial, homework spot check, tally of pages completed, Responsive engagement (see card below) Proactive engagement (see card below) 3) Interact with students Effectively Any engagement should be within the 10 rules of Engagement Guidelines for Instruction delivery - Sit across from student - Use a nice voice - Concise explanations (short, simple) Types of student interactions (see card below) 4) Disengage and Communicate - Before leaving student, leave them with a task (5 - 10 problems) - For students who don't want to continue work w/o instructor, tell them you'll be near to help if they need it, compliment their efforts thus far, offer extra punches, offer to play a game afterwards Document session progress on workout plan Communicate and Re-enter Rotation - Immediate concerns should be told to center director immediately Notes to Center Director - Summarize student progress - Actions needed for a student's learning plan Final Engagement - Have at leas a page w/ Mastery check - Write down any concepts or misconceptions for review in the future ("Things to work on next session" section)
What are the 10 Mathnasium Rules of Engagement?
1) Use the Mathnasium Teaching Constructs. Use the Teaching Icons as guides 2) Do not repeat inefficient explanations 3) Reteach concepts if a student is struggling. Extend knowledge back to the point at which they were 4) Praise, encourage, and criticize 5) Use Socratic Questioning when it's appropriate. Use Direct Teaching when it's appropriate 6) Use Mathnasium vocabulary because it makes sense. Avoid confusing nomenclature 7) Use manipulatives and Desk Tools when appropriate to clarify and reinforce concepts visually. 8) Enable students to achieve metacognition, an awareness of one's own thinking process. 9) Require students to use mental math to enhance numerical fluency and limit reliance on pencil and paper 10) Master Team Teaching.
What are the techniques used for facts 0s and 1s, 2s, 10s, and 5s?
1s - Common multiplication techniques 2s- Doubling the number 10s - Add one to tens place value, then add a 0 in the ones place 5s - Multiply by 10 then take half
What are the techniques used for the rest of the facts?
3s - Use 2s facts, adding one more of the multiplicand 4s - Multiplicand doubled, then added with itself 11s - Use 10s facts, adding one more of the multiplicand to get 11 as the multiplier. You could also just do it normally 12s - Separate 12 so that you have 10s and other number. Do 10 times multiplier, 2 times multiplier, then add 9s - Find 10 times multiplier, then subtract once by multiplier (9 = 10 - 1) 6s - 5s facts; Find 6 times 5, then one more 6 7s - 5s, 2s; Multiply multiplicand by 5, then 2, then add together 8s- Similar to 9, will use 10s and 2s; doubling technique: double multiplicand by 2s, 4s, 8s
What rule do you carry out when you use desk tools?
7th rule of engagement
Tips on Teaching Number Facts
Addition: Break down a number to two smaller numbers (AMOUNT SHOULD ALWAYS BE LESS THAN 10) - Counting by ones: "What number is [quantity] bigger/smaller than [quantity]? - Numbers that add up to number make what? Combinations of 10: - What number and how much more would make 10? - 10 and how much more would make [sum] - Tell students that teen numbers can be broken down into 10 and a digit Doubles: - How much is quantity + same quantity? (all the way up to 12+12)
How is Socratic Questioning different from Direct Teaching?
Asks questions to guide student v concepts of ideas to students
What are the Three Stages of Learning
Awareness, competency, mastery
What is smart counting?
If given a row of numbers to add, see if you can combine some of them to make multiples of tens
What are the five modes used to deliver the Mathnasium program?
Mental: Doing math in your head Visual: Pictures Verbal: Direct teaching + Socratic questioning + asking students how they got their answer Tactile: Desk tools and manipulatives Written: Solving problem on paper
What are the types of student interactions?
Normal instruction - Responsive or proactive - Determine teaching methods (socratic, direct, or both) use icons for visual cues as to how to teach - General approach to instruction 1) Show the student how to do it on one problem 2) Watch the student work on another exercise, correcting, commenting, or asking them questions when necessary 3) Disengage and give them some problems to work on Correcting student work - Pages should be corrected as soon as possible - Ask students to explain answers, even if it's correct - Spot-check written work while rotating around the floor; intervene if you see an error being made Mastery Checks Transitioning between activities Re-engaging a student
What is "scaffolding"
Progressively moving student away from being dependent on a teacher
List and quickly summarize all key icons:
Quantity, Denomination, and the Law of SAMEness: Tells instructor to teach what is in the name Manipulatives: Instructor should use manipulatives to help student Bypass Page: Proof Bypass Page: Thinking in 10s: Instructor should use thinking in 10s strategy Draw a picture Wholes and Parts: When ascepts of wholes and parts need to be emphasized Complements: Whole minus part should be used to solve the problem Proportional thinking: This should be used while doing the work Direct Teaching Point out a Pattern: Student/Instructor should point out what being repeated in a set of problems Extending Knowledge: Instructor has opportunity to extend knowledge Place Value: Instructor should think of place value when teaching student Doubling: Should be used to solve the problem Mental Math Desk tools Counting Grouping: Grouping strategy can be used for work Use a calculator Socratic Questioning
What is the difference between proactive and responsive engagement?
Responsive engagement: Response to students in time, be genuine in helping the student Proactive engagement: - Seek opportunities - Monitor students - Follow-up on previously assigned tasks - Correct errors before they become habits - Intervene to correct behavior
Are manipulatives like desk tools?
These are physical objects
Name the three types of students. How would you encourage them to continue working?
Unruly, distracted, unwilling: Talk to the student and ask them to go back to their work. Make sure they begin their work. If they are interacting with other students, move them Overloaded, fatigued: Take a break and play a game, or go do a topic that's more visual or interactive Quiet, shy: Check on them often, as they are usually too scared to ask for help
Addition and Subtraction fact techniques are...? What prerequisite knowledge is needed?
Up to and Over 10: 8+5 -> 8+2+3 -Know what can create 10 (complements of 10) -How to break apart and put numbers back - Find 10 + single digit number Doubles +/- one (7+7 = 14, therefore, 7+8=15) - Students need to know doubles facts (1+1, 12+12, etc.) How far apart? - Up to and Over 10 (17-9 -> to get to 9 to 10 is one jump, the rest is 7, 1+7=8) - Sums under 10 - Complements of 10 - 10 + single-digit number
What is Multiplication Fact Fluency
When students can effortlessly recall multiplication facts 0x0 - 12x12
When does a student have Numerical Fluency?
When they can effortlessly recall basic operation problems
DeskTools and Manipulatives
note: - pt. 1 + 1/2 of pt. 2 -> example teaching of drawings - rest of pt. 2 + pt. 3 example teachings of manipulatives