Transcript Step 1: DMR and Number Sense PowerPoint Presentation

How can teachers build mathematically powerful
students who can solve real-life problems, communicate
their understanding to others, and perform well on local
and state assessments?
5 Steps to A Balanced Mathematics Program
Step 1: Math Review and Mental Math
Step 2: Problem Solving
Step 3: Conceptual Understanding
Step 4: Mastery of Math Facts
Step 5: Common Formative Assessments
Build computational and procedural skills
Develop mathematical reasoning and problem-solving
abilities
Deepen conceptual understanding
Demonstrate understanding in a variety of assessment
formats
https://www.youtube.com/watch?v=KdxEAt91D7k
How can we help students
develop number sense?
•Model different method for computing
•Ask students regularly to calculate mentally
•Have class discussions about strategies for computing
•Make estimation an integral part of computing
•Question students about how they reason numerically both
when they make mistakes AND when they arrive at the correct
answer
•Pose numerical problems that have more than one possible
answer
-Marylin Burns
Number Sense Activity
Dot Plates
What patterns did you notice?
Students with number sense naturally decompose
numbers, use particular numbers as referents, solve
problems using the relationships among operations and
knowledge about the base-ten system, estimate a
reasonable result for a problem, and have a disposition to
make sense of numbers, problems, and results.
•Knowledge of the number system
•Patterns in the number system
•Sense of quantity
•Reasonable answer
As students build their number sense,
mathematics takes on greater meaning.
Mathematics becomes more about
reaching understandings than following a
rigid set of rules. With strong number
sense, children become more apt to
attempt problems and make sense of
mathematics. It is the key to understanding
all math.
Jessica Shumway
Number Sense Routines
Reasoning with Fractions
https://www.mathreasoninginventory.com/Home/ReasoningFractions
Reasoning with Whole Numbers
https://www.mathreasoninginventory.com/Home/ReasoningWholeNumbers
Snapshot of Students
Misunderstanding
(Math Solutions by Marilyn Burns)
Jonathan
http://mathsolutions.wistia.com/medias/m7fb9l118b
Cena
http://mathsolutions.wistia.com/medias/57gylipbbg
Jo Boaler Professor Stanford University
http://www.youtube.com/watch?v=Jeel4Qjow4s
Reasoning About Division – Teaching Channel
https://www.teachingchannel.org/videos/common-core-teaching-division
Ten –Frame and Dot Card Images
https://mathsolutions.wistia.com/medias/09jhvdzx89
Build Ten Frame on Floor
https://mathsolutions.wistia.com/medias/a47aut7kzw
Leprechaun Traps: Addition within 100 (1st Grade Class)
https://www.teachingchannel.org/videos/grade-1-math
Reasoning About Division – Teaching Channel
https://www.teachingchannel.org/videos/common-core-teaching-division
A systematic method to deal with student
misconceptions using error analysis, specific feedback,
and reflection. This step creates immediate gains in
student learning.
Mental math promotes number sense development and
enhances math fact development.
Repeated Reasoning
• multiple opportunities to practice the same skill
• 24 attempts to reach 80% (Marzano)
Effective Feedback
• Specific and timely feedback is the single most powerful
modification that enhances student achievement. (Hattie)
Relational Thinking
• math interconnected concepts and ideas
• emphasizing reasonable answers, number sense, students
making sense of the math
Category Development
•Skills and concepts students should know but
typically don’t
•Concepts and skills that are vital to success in their
grade level
•Reinforce grade-level or course Priority Standards
•Front Load Upcoming Unit
2-5 problems from different categories
10-15 minutes at the beginning of math period
Student Collaboration
• Classroom environment that values students’ explanation of
their understanding
Key Statement Ideas
• Essential Understanding that we wants students to have
Error Analysis
• Timely and Specific Feedback
• Focus based on students misconceptions
Student Reflection
• Specific to error
• Stating what they know mathematically
Daily Math Review
1st Grade
Set Up:
•Students sit on the rug close to the teacher.
•Students have a designated partner.
•Categories and problems based on number sense.
•Students have necessary manipulatives for categories.
•Students have a paper template to record work.
Categories are completed one at a time using the
following sequence:
Teacher reads problems problem and then the student
and teacher read the problem together.
Students try the problem independently using available
manipulatives and paper and pencil.
Students turn to face their partners and discuss what
they tried and what they think the answer is and record
on their paper what they tried.
Class solves the problem together
The students star work that is correct on their paper
and circle and fix work that is incorrect or incomplete.
Students turn back to their partner and participate in
reflection by sharing how they did on the problem.
The class says they key statement for the problem
together 2 times.
• Teacher-directed
• Student-directed
• Group answer
• “Pass the Pen” method
• Speedy (end of cycle when most students
have mastered)
Advanced Student:
• Give the option of helping others
• Provide individualized bonus problem
• Solve problems multiple ways
Struggling Student:
• Peer collaboration
• Oral response in reflection
• Pictorial reflection work
• Small group/individual help teacher
• Survival Box
Ten problems (max.)
• 2 to 4 per category
Correct quiz with students
• increases student engagement &responsibility
Collect data to inform decisions
• 90% students get 100% on category to take it off DMR
Mental Math
Mini-Math Workout for the Brain
Students need regular
opportunities to develop effective
computation strategies that are
base on number sense. Helping
student use number strategies is
an effective way to develop
number sense. Students need
daily practice to develop and
retain strong number sense and
effective computational skills.
Mental Math Steps
•
•
•
•
•
•
•
Teacher says a string of numbers and operations (5 + 10 – 3 x 2)
Students think, then write the answer
Teacher repeats the string of operations
Students check their work mentally
The whole class tells the answer chorally
Teacher asks 3 students to tell how they thought of the answer
Do 2-3 problems
Mental math problems should be related to the same
theme. Stay with theme 2 weeks
Mental Math Themes
•
•
•
•
•
•
one more/less than given number
counting by 2, 5, 10
Anchors of 5 and 10
Doubles, fact families, number facts
math vocabulary
measurement (time, money, calendar,
inches, feet, etc.
Start with one more than 5 (6); double
that number (12) think what is one less
than that number (11)
Start with a dozen; subtract half....
•
•
•
•
•
•
number operations
fractional operations and concepts
math vocabulary
exponents
square roots
percent-decimal-fraction
Start with square root of 144 (12); add
square root of 81 (21); divide by 7 (3) cube
the result (27)....
Mental Math
Table Assignment
1. Choose 3 different mental math themes and
write problems for each.
2. Share with group
3. Nominate 1 to share
with larger group
Daily Math Review and
Mental Math
•Reinforce prior learning of math skills
•Provide daily practice for mathematical
computation problems
•Promote mathematical reasoning and develop
number sense
•Includes specific feedback, error analysis, and
student reflection
Start with concepts students should know but don’t
Critical areas for students success
Daily Math Review Complete Cycle
Category: Fractions on a Number Line
(3.NF.2a)
Category: Subtracting with regrouping with a
zero (3.NBT.2)
Category: Subtracting with two regroupings
(3.NBT.2)
Misconception: Students do not understand
where a fraction is represented on a 0-1
number line; knowing equal parts on a number
line
Misconception: Students do not always know
how and when to regroup multi-digit numbers.
(1 regrouping with a zero)
Misconception: Students do not always know
how and when to regroup multi-digit numbers.
(2 regroupings)
9 Questions:
9 Questions:
9 Questions:
1.
Which shape on the
number line
represents ½?
2. Which shape on
the number line
represents ¼?
3.
Which shape on the
number line
represents 3/4?
4. Which shape on
the number line
represents 2/4?
5. Which shape on
the number line
represents 4/4?
6.
7.
1.
680-547
2.
350-229
1.
425-286
2.
617-459
3.
950-443
4.
508-246
3.
934-678
4.
361-185
5.
704-682
6.
5.
500-236
6.
7.
8.
7.
8.
9.
9.
8.
9.
Key Statement: Fractions on a number line
have equal parts.
5 Reflection Starters:
1. Next time I will
Key Statement: Sometimes you need to
regroup when solving a subtraction problem.
2. I didn’t understand #
because
3. To help me solve this, I
knew
Key Statement: Sometimes you need to
regroup more than once when solving a
subtraction problem.
4. I need to remember__
because_
5. I learned that
Daily Math Review Assessment
90% of the students need to get 100% on a category to “retire” the category.
2 – 4 questions per category.
Category:
Fractions on a Number Line
(3.NF.2a)
Questions:
Which shape on the number line
represents ½?
Category:
Which shape on the number line
represents 3/8?
Which shape on the number line
represents 5/8?
Subtracting with regrouping with
a zero (3.NBT.2)
Questions:
740-318
Category:
570-245
603-461
Subtracting with two regroupings
(3,NBT.2)
Questions:
743-356
460-179
852-584
Daily Math Review Assessment
Name:
Date
Fractions on a Number Line
1
0
1. Which shape on the number
line represents ½?
2. Which shape on the number
line represents 3/8?
3. Which shape on the number
line represents 5/8?
2. 570-245 =
3. 603-461 =
2. 460-179 =
3. 852-584 =
Subtraction: 1 Regrouping and a Zero
1. 740-318 =
Subtraction: 2 Regroupings
1. 743-356 =
New Albany, Indiana
2009
2012
68.5 % proficient
89% proficient
(increase of over 800 students passing)
Special Education Students
2009
39.1% proficient
2012
80.5 % proficient
Example of cohort of students over 4 years:
4th grade 2009 66% proficient
5th grade 2010 82% proficient
6th grade 2011 86% proficient
7th grade 2012 88.1% proficient