Finding Success in the Math Classroom

Incorporating the process standards into the daily rigor

Students Struggle with Problem Solving

1. The % of students Advanced on the Grade 3 Math SOL in 2011.

2. The % of students Advanced on the Grade 3 Math SOL in 2012.

3. The % of ACPS students Advanced on the Grade 3 Math SOL in 2011.

4. The % of ACPS students Advanced on the Grade 3 Math SOL in 2012.

5. The % of POVERTY students Passing the Grade 3 Math SOL in 2011.

6. The % of POVERTY students Passing the Grade 3 Math SOL in 2012.

7. The % of ACPS POVERTY students Passing the Grade 3 Math SOL in 2011.

8. The % of ACPS POVERTY students Passing the Grade 3 Math SOL in 2012.

55

13

49

12

85

53

In Virginia’s Public Schools:

SOLUTIONS: 12, 13, 35, 48, 49, 53, 55, 82, 85, 88

48

82

A New Trend Line in Student Achievement“Virginia's public schools are beginning a new trend line with the implementation of more challenging standards and assessments. The goal is to build on the progress already made under the Standards of Learning program and ensure that all graduates possess the knowledge and skills needed for success in college and the workplace.”

- Dr. Patricia I. Wright Superintendent of Public Instruction

A New Trend Line in Student Achievement

“…this will be an indication that we are now expecting more of students, not that they are learning less.”

- Dr. Patricia I. Wright Superintendent of Public Instruction

Changes to the Mathematics Standards of Learning Content

• Increased rigor• Moved content to improve the vertical

progression• Removed content from grade levels/subjects• Removed content repeated among grade

levels• Added new content

Process Standards for Students

Students will…• Become mathematical problem solvers that• communicate mathematically;• reason mathematically;• make mathematical connections; and• Use mathematical representations to model

and interpret practice situation

We, as teachers, should be…• Engaging students in the learning, providing

relevant and rigorous activities and tasks• Asking high-leverage questions – make

students work harder than you• Requiring students to communicate their

thinking and listen carefully to them• Making students justify their thinking• Using multiple models

8

Process Goals!

Re-Align Our Instruction

1. Identify content (Analyze SOL and Curriculum Framework – What students should be able to do?)

2. Determine acceptable evidence (assessment).

3. Plan and develop learning experiences & instructional resources/lesson plans.

What do they need to learn?

1. Identify content (Analyze SOL and Curriculum Framework – What students should be able to do?)

2. Determine acceptable evidence (assessment).

3. Plan and develop learning experiences & instructional resources/lesson plans.

SOL 2.8 The student will create and solve one- and two-step addition and subtraction problems, using data from simple tables, picture graphs, and bar graphs. •Identify the appropriate data and the operation needed to solve an addition or subtraction problem where the data are presented in a simple table, picture graph, or bar graph.• Solve addition and subtraction problems requiring a one- or two-step solution, using data from simple tables, picture graphs, bar graphs, and everyday life situations.• Create a one- or two-step addition or subtraction problem using data from simple tables, picture graphs, and bar graphs whose sum is 99 or less.

SOL 2.3 The student will…

a) Identify the parts of a set and/or region that represent fractions for halves, thirds, fourths, sixths, eighths, and tenths (not just unit fractions);

b) Write the fractions; and

c) Compare the unit fractions for halves, thirds, fourths, sixths, eighths, and tenths.

SOL 3.6 The student will represent multiplication and division, using area, set, and number line models, and create and solve problems that involve multiplication of two whole numbers, one factor 99 or less and the second factor 5 or less.

• Model multiplication, using area, set, and number line models.• Model division, using area, set, and number line models. • Solve multiplication problems, using the multiplication algorithm, where one factor is 99 or less and the second factor is 5 or less.• Create and solve word problems involving multiplication, where one factor is 99 or less and the second factor is 5 or less.

SOL 3.3 The student will…

a) Name and write fractions (including mixed numbers) represented by a model;

b) Model fractions (including mixed numbers) and write the fractions’ names; and

c) Compare fractions having like and unlike denominators, using words and symbols (>, <, or =)

How will I know they learned it?

1. Identify content (Analyze SOL and Curriculum Framework – What students should be able to do?)

2. Determine acceptable evidence (assessment).

3. Plan and develop learning experiences & instructional resources/lesson plans.

• Formative– Assessment FOR learning– Diagnostic in nature – informs instruction– Questions (verbal), homework, classwork,

quizzes, benchmark tests– Observations, checklists, interviews, journals,

checklists, reflection activities, self-assessment– Includes a lot of student feedback

Ways to Use an Assessment

Ways to Use an Assessment

• Summative–Assessment OF learning–Provides a numeric evaluation–Tests, projects, simulation tests–Less feedback

Assessment – The Evidence

Performance Task (Grade 2)

CANDY BAR TASK

Joe has 1/3 of a candy bar.Melinda has 1/2 of a different candy bar. Joe says his piece is larger than Melinda’s.

Can this be true? Why or why not?Use pictures, words and numbers to prove your answer makes sense.

19

1

20

Performance Task (Grade 3)

How do I help them learn it?

1. Identify content (Analyze SOL and Curriculum Framework – What students should be able to do?)

2. Determine acceptable evidence (assessment).

3. Plan and develop learning experiences & instructional resources/lesson plans.

There is no decision that teachers make that has a greater impact on students’ opportunities to learn and on their perceptions about what mathematics is than the selection or creation of the tasks with which the teacher engages students in studying mathematics.

Lappan & Briars, 1995

Instruction

• What learning experiences and instructional strategies will promote the desired understanding, knowledge and skills?

• How will you best promote the deepening of insight and interest?

• How will you prepare students for the assessment(s)?

Questioning StrategiesAligned with Math Process Skills

Virginia Math Process Skills

Select a number Between 10 and 50.

Round the sum tothe nearest ten.

Select another number less than 50.

Find the sum.

Create a value for the numerator of a

fraction.

Draw a different modelof the fraction.

Create a value for the denominator of a

fraction.

Draw a modelof the fraction.

Changes to the SOL Assessments

Technology Enhanced Items (TEI)• Fill-in-the-Blank• Creation of bar graphs/histograms• Drag and Drop (Click and drag)• Hot-spots (Click on the box): Select

one of more “zones/spots” to respond (multiple answers)

Technological Enhanced ItemsType 1: Type in your answer (FILL IN THE BLANK)

Technological Enhanced ItemsType 2: Click to create a graph or plot a point. (GRAPHS)

Technological Enhanced ItemsType 3: Click and Drag (DRAG AND DROP)

“TEI-Like” Items in the Classroom

Drag and Drop (Click and drag)• Use of a paper cut out, index card, sticky note,

that can be manipulated to answer a question (sort and categorize, order, label, pull from word bank, etc.)

• Any matching item or activity

Drag and Drop examples:• Complete sentences or phrases with text • Match a figure to a description (ray, line,

line segment, point) • Create change with money • Complete the pattern with a missing figure • Match algebraic properties to examples• Match statement to greater than, less

than, equal to

Technological Enhanced ItemsType 4a: Click on a box (HOT SPOTS)– unspecified amount of solutions

Hot Spot: • “Circle all of these that are ---” • “Circle the two of these that show---” • “Plot the points that---” • “Shade the part of the model that---”

Hot Spot examples: (Select or plot)

• Select all fractions that are equivalent to a given number

• Select all set of coins equal to a certain value• Circle all values or expressions that are equal

to a certain value (greater than or less than)• Select two names that describe a figure • Select the two equivalent values (the decimal

and fraction equivalents)

Hot Spot examples: (Select or plot)

• Shade sections of a whole to represent a fraction or decimal

• Shade a section of a Venn diagram • Shade the figure that represents a rotation of a

figure on a coordinate plane • Select all that are true• Plot values on a number line• Plot the probability of an event

How can you find success?

• Instruction, Assessment, and Backwards Design

• Focus on the Process Standards• Emulate TEI strategies • Create/Find enriched

tasks that have critical thinking opportunities for students