Middle School Mathematics Workshop
February 11, 2012
Theme:
Incorporating Authentic, Formative Assessment into
Mathematics Lessons
Duration: Two hours and 30 minutes; Two sessions with a break in
between.
Product: A Lesson Plan (or more) that includes authentic and
formative assessments.
Session I—Formative and Authentic Assessment
1. You can’t learn without feedback.
2. It’s not teaching that causes learning. It’s the attempts by the
learner to perform that cause learning, dependent upon the
quality of the feedback and opportunities to use it.
3. A single test of anything is, therefore, an incomplete
assessment. We need to know whether the student can use
the feedback from the results.
4. We’re wasting our time inventing increasingly arcane
psychometric solutions to the problem of accountability.
Accountability is a function of feedback that’s useful to the
learner, not to a handful of people who design the measures.
The more arcane the measure, the less likely it is that it will
cause any useful progress, despite its validity and reliability Or
to say it the other way around, the more self-evident the
feedback to the performer, the more likely the gains.
─Grant P. Wiggins, from Feedback: How Learning Occurs
Black and Wiliam…define assessment broadly to include all
activities that teachers and students undertake to get
information that can be used diagnostically to alter teaching
and learning. Under this definition, assessment encompasses
teacher observation, classroom discussion, and analysis of
student work, including homework and tests. Assessments
become formative when the information is used to adapt
teaching and learning to meet student needs.
─Carol Boston, from The Concept of Formative Assessment
Assessment is authentic when we directly examine
student performance on worthy intellectual tasks.
Traditional assessment, by contract, relies on indirect or proxy
'items'--efficient, simplistic substitutes from which we think valid
inferences can be made about the student's performance on
more valued challenges.
[Instead, why not] evaluate student problem-posing and
problem-solving in mathematics? Mathematical insight?
Mathematical reasoning?
Effectiveness of solutions?
Accuracy of work? Quality of communication?
─Grant Wiggins from The Case for Authentic
Assessment and “Get Real!” Assessing Quantitative
Literacy
Activity 1: What do we know about formative assessment? (15
min)
Materials: Butcher Paper, Tape, Markers
Procedure
1. Reconsider the definition of Formative Assessment.
Assessments become formative when the information is
used to adapt teaching and learning to meet student
needs.
2. With group members record on butcher paper as many ways
as you can how your group uses Formative Assessment in
your classes.
3. Be ready to discuss these formative assessments near the
end of the activity.
Activity 2: What do we know about authentic assessment? (15
min)
Materials: Butcher Paper, Tape, Markers
Procedure
1. Reconsider the definition of Authentic Assessment:
Assessment is authentic when we directly examine
student performance on worthy intellectual tasks.
2. With group members record on butcher paper as many
a. “worthy” mathematical tasks as you can; and as many
b. unworthy mathematical tasks as you can.
3. Be ready to discuss these tasks near the end of the activity.
Activity 3: Authentic Assessment and the Common Core Standards
(20 min)
Materials: Butcher Paper, Tape, Markers
Stuart Leads the discussion about alignment with the Common
Core Standards. How do their tasks match the Common Core
Standards for Mathematical Practice?
Session II—Creating Authentic Tasks with Formative
Assessments Using the Common Core Standards
Materials: Paper and Pen or Word Processor
Product: A Lesson Plan (or Unit Plan Outline) that includes
authentic and formative assessments, based on the Authentic
Assessment Criteria.
Activity (45-60 min)
1. You may work together in grade levels or plan alone.
2. Integrate the Common Core Standards for Mathematical
Practice into a Lesson Plan (or more, if time permits). You may
instead develop activities that lead to a unit plan. Specifically
develop formative assessments, worthwhile tasks, and
authentic assessments.
3. Be ready to show off your lesson plan.
Lesson Plan Template (or use your own)
Content Standards:
Common Core Standards:
Warm-Up or Anticipatory Set:
Authentic Task(s) (Activities):
Authentic Assessments:
Formative Assessments: