Iden%fying  and  Implemen%ng  Lesson  Goals  to  Measure  Learning  

in  Mathema%cs  

 August  16,  2016  

 Mark  Alcorn,  Mathema%cs  Coordinator,  SDCOE  

mark.alcorn@sdcoe.net  @mark4math  

   

Standards  or  Lesson  Goals?          

Learning  Inten%ons    • Understand  the  quality  of  the  task  determines  what  students  learn  about  mathema%cs    

   • Understand  the  differences  between  measuring  learning  at  the  lesson  level  vs.  the  chapter/unit  level  

   • Understand  how  using  mathema%cs  goals  can  allow  teachers  and  students  to  measure  learning  throughout  the  lesson  

 

Success  Criteria    •  I  can  iden%fy  characteris%cs  of  high-­‐quality  tasks      •  I  can  explain  how  lesson  goals  can  guide  and  assess  learning  at  the  lesson  level    •  I  can  iden%fy  a  next  step  for  implemen%ng  lesson  goals  in  my  classroom/school/district  

Write  a  lesson  goal  for  this  task  

• What  types  of  tasks  should  students  engage  in  to  meet  the  demands  of  the  California  Mathema%cs  Standards?  

 • What  language  could  we  use  to  define  these  tasks?  

Doing  Mathema%cs?  

“Memorization” Tasks

What are the decimal and percent equivalents for the fractions and ?

Expected Student Response:

= .5 = 50%

= .25 = 25%

“Procedures With Connections” Tasks

Using a 10 x 10 grid, identify the decimal and percent equivalents of .

Expected Student Response:

Pictorial Fraction Decimal Percent

Lower-Level Demand

Cognitive Demands of Mathematical Instructional TasksHigher-Level Demand

a) On column will be 10% since there are 10 columns. So four squares is 10%. Then 2 squares is half a column and half of 10% which is 5%. So the 6 shaded blocks equal 10% plus 5% or 15%.

b) One column will be .10 since there are 10 columns. The second column has only 2 squares shaded so that would be one half of .10 which is .05. so the 6 shaded blocks equal .1 plus .05 which equals .15.

c) Six shaded squares out of 40 squares is which is equivalent to

Stein, M. & Smith, M. (1998) Mathematics Teaching in the Middle School. National Council of Teachers of Mathematics

“Procedures Without Connections” Tasks

Convert the fraction to a decimal and a percent.

Expected Student Response:

Fraction Decimal Percent

“Doing Mathematics” Tasks

Shade 6 small squares in a 4 x 10 rectangle. Using the rectangle, explain how to determine each of the following: a) the percent of area that is shaded, b) the decimal part of the area that is shaded, and c) the fractional part of area that is shaded.

One Possible Student Response:

Memoriza%on  

Procedures  without  Connec%ons  

Procedures  with  Connec%ons  

Doing  Mathema%cs  

Some  characteris%cs  of  a  high-­‐quality  task  

• Reflects high cognitive demand (Stein et. al., 1996)

• Allows multiple ways to enter the task and to show competence (Lotan, 2003)

• Provides access to a wide range of learners (Piggott, 2012)

• Encourages creativity and imaginative application of knowledge (Piggott, 2012)

• Exposes what students know and provides information for next steps (Hiebert, et. al., 1997)

• Encourages reflection and communication (Hiebert, et. al., 1997)

• Promotes connections between two or more representations (Lesh, Post & Behr, 1988)

• Leaves behind something of mathematical value (Hiebert, et. al., 1997)

  Kevin is preparing for the Rock and Roll Marathon. In his training run, Kevin drinks 2/3 cup of water for every mile he runs. His water bottle holds 4 cups of water. How many miles can he run before his water runs out?  Draw  a  picture  or  model  first  to  represent  the  situa%on.  

Rock  and  Roll  Run  

High-­‐Level  Task…now  what?    What will students understand about mathematics by the end of the lesson that they did not know at the start? Which students should I select to share their thinking?

Which  students  should  share  their  strategy?  

Grain  size  of  mathema%cs  Why is it harder to express mathematical understandings at the lesson level vs. chapter/unit level?  http://math.serpmedia.org/5x8card/phil-daro-on-the-5x8-card.html

Implica%ons  • Shift to chapter/unit collaborative planning regarding

mathematics content

• After this shift, what happens at the lesson level?

  Kevin is preparing for the Rock and Roll Marathon. In his training run, Kevin drinks 2/3 cup of water for every mile he runs. His water bottle holds 4 cups of water. How many miles can he run before his water runs out?  Draw  a  picture  or  model  first  to  represent  the  situa%on.  

Rock  and  Roll  Run  

Pre-­‐Plan  ques%ons  that  address  the    Standards  for  Mathema%cal  Prac%ce  

SMP #1 – Does your answer make sense? How do you know? SMP #2 – Could we have used another operation? SMP #3 – What would happen to the answer if we used a larger water bottle that holds 8 cups? How do you know? SMP #4 – How did you represent the quantities in the situation? SMP #5 – Which tools help represent the situation? SMP #6 – Does your solution make sense in this context? SMP #8 – What patterns did you notice in your picture? Note: Students will engage in additional SMPs beyond these identified as the focus of the lesson.

Lesson # ___ of ___Common Core Standards:1.

2.

3.

Lesson Goals (Learning Intentions):

Task:

Strategy Who and What Order

Standards for Mathematical Practice1 2 3 4 5 6 7 8

Question:

Question:

Question:Evidence of Learning (Success Criteria):

x x

Kevin drinks 2/3 cup of water for every mile he runs. His water bottle holds 4 cups of water. How many miles can he run before his water runs out?

Students will examine patterns in their drawing or model to determine the operation

How did you represent the quantities in the situation? What patterns did you notice in your picture?

BEFORE DURING BEFORE/DURING

Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

5.NF.7

Coach Isabella bought 8 pizzas for the hungry soccer team. Each member of the soccer team ate ½ pizza. How many people ate pizza? Explain how your sketch/model connects to your equation.

Shared  student  work  is  based  on  the  goal    

A  lesson  goal…why?   • What rationale would you provide to encourage a colleague to consider setting a lesson goal in mathematics?

Lesson  Goals  in  Primary  Grades    4 children are sharing 3 candy bars so that everyone gets the same amount. How much candy bar can each child have?

Ideas  for  Implementa%on  • Use  a  criteria  to  analyze  the  quality  of  mathema%cs  tasks      •  Introduce  the  tool,  “Ques%ons  to  support  Engagement  in  the  Standards  for  Mathema%cal  Prac%ce”  as  a  method  to  support  student  engagement  with  high-­‐quality  mathema%cs  tasks  

   • Form  lesson  goals  in  mathema%cs  based  on  1-­‐3  ques%ons  from  the  above  tool  

   • Encourage  students  to  track  their  learning  based  on  the  lesson  goal  

Resources  •  Leinwand,  Steven,  Daniel  J.  Brahier,  DeAnn  Huinker,  et.  al.  Principles  to  Ac.ons:  Ensuring  Mathema.cal  Success  for  All.  Reston,  VA:  NCTM  2014.  

 •  Smith,  Margaret  S.  and  Mary  Kay  Stein.  5  Prac.ces  for  Orchestra.ng  Produc.ve  Mathema.cs  Discussions.  Reston,  VA:  NCTM,  2011.  

Next  Steps  •  Iden%fy  1-­‐2  next  steps  for  implemen%ng  lesson  goals  in  your  classroom/school/district  

Be  prepared  to  share  an  idea  with  your  colleagues  

Upcoming  Professional  Learning  Ge#ng  Smarter  about  Tasks  and  Talk  (2-­‐day):    October  4  &  25,  January  24  &  27,  February  23  &  March  9    Advanced  Tasks  and  Talk  (1-­‐day):    October  6,  October  13,  December  13,  or  April  18    Teaching  FracAons  for  Meaning  and  ApplicaAon  (1-­‐day):    October  12  or  February  14      Mark  Alcorn  -­‐  mark.alcorn@sdcoe.net  Twiker:  @mark4math  Web:  www.sdcoe.net