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Research-Based Interventions for
Underprepared Algebra Students
48th NCSM Annual Conference
April 2016
Kathi Cook, Manager, Online Course Programs
Anne Joyoprayitno, Course Program Specialist, Secondary Mathematics
The Charles A. Dana Center at The University of Texas at Austin
Agenda •  What problem are we trying to solve? •  One possible approach: Intensifica*on –  Research-­‐based elements –  Sample strategies •  Promising results 1
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1
Failure in Algebra I now exceeds 50% of students
nationally, and many students now enter the course one or
more grade levels behind in math.
2
Many struggling students are hindered by a lack of
motivation and commitment to learning.
3
Three years of mathematics beyond Algebra I are now
essential for college and work readiness.
What do we mean by Intensifica*on? Intensifica*on is a systemic effort to address the contextual needs of students in learning on-­‐level content. IntensificaDon may mean: •  Increasing the amount of time with content
•  Using a variety of pedagogical supports
•  Developing
students’
sense
ofI are
socioMany students
now taking
Algebra
one or more grade
1
levels
behind
in
math,
and
Algebra
I
the most failed
motivational well-being around remains
the content
course nationally.
Manyd
struggling
students
are
hindered byrich a lack of
IntensificaDon oes not mean delaying 2
engagement and commitment to learning.
mathemaDcal experiences unDl students acquire “the Three years of mathematics beyond Algebra I are now
basics.” 3
essential for college and work readiness
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An Architecture for IntensificaDon Struggling students need: Many students now taking Algebra I are one or more grade
levels behind in math, and Algebra I remains the most failed
More course nationally.Challenging
Targeted
1
Time
Curriculum
Interventions
2
Many struggling students are hindered by a lack of
engagement and commitment to learning.
3
Three years of mathematics beyond Algebra I are now
essential for college and work readiness
Architecture for Intensifica7on 3
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What research tells us •  Providing rou7nes and structures that help struggling learners organize criDcal mathemaDcs content increases their learning (Deshler & Lenz). •  Accessing prior knowledge and addressing students’ misconcep7ons increases learning (Swan & Bell, Burkhardt, Shell Centre). •  Engaging students with challenging tasks that involve ac7ve meaning-­‐
making increases learning (Horizon Research, Hiebert & Grouws). •  On-­‐going cumulaDve distributed prac7ce improves learning and retenDon (Rohrer, Mayfield). •  Forma7ve assessment is a key intervenDon for improving student achievement (Black & Wiliam, Hiebert & SDgler). •  PromoDng learners’ beliefs about their own intelligence can increase their moDvaDon and effort to learn mathemaDcs (Dweck, Goode, Midgely, Aronson). Use of high cogni7ve-­‐demand tasks “Not all tasks are created equal, and different tasks will provoke different levels and kinds of student thinking.” Stein, M .K., Smith, M .S., Henningsen, M. A., & Silver, E. A. (2000). ImplemenDng standards-­‐based mathemaDcs instrucDon: A casebook for professional development, Teachers College Press, Columbia University, New York. “The level and kind of thinking in which students engage determines what they will learn.” Hiebert, J., Carpenter, T., Fennema, E., Fuson, K., Wearne, D., Murray, H., Oliver, A., and Human, P. (1997) Making sense—teaching and learning mathemaDcs with understanding, Portsmouth, NH: Heinemann. 4
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Consider this task The formula to find the number of diagonals, d, that can be drawn from one vertex in a polygon with n sides is d = n -­‐ 3 . Use the formula to find d when n is 6. Now, consider this task Find an algebraic rule to describe the relaDonship between the number of sides of a polygon, n, and the number of diagonals that can be drawn from one vertex, d. Use n as the independent variable, and express your rule using funcDon notaDon. Explain how you found the rule. 5
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Compare the tasks The formula to find the number of diagonals, d, that can be drawn from one vertex in a polygon with n sides is d = n -­‐ 3 . Use the formula to find d when n is 6. Find an algebraic rule to describe the relaDonship between the number of sides of a polygon, n, and the number of diagonals that can be drawn from one vertex, d. Use n as the independent variable, and express your rule using funcDon notaDon. Explain how you found the rule. Task implementa7on and cogni7ve demand THE MATHEMATICAL TASKS FRAMEWORK TASKS TASKS TASKS as they appear in curricular/ instruc7onal materials as set up by the teachers as implemented by students Student Learning Smith, M .S., Henningsen, M. A., & Silver, E. A. (2000). Implementing standards-based
mathematics instruction: A casebook for professional development, Teachers College Press,
Columbia University, New York.
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Task implementa7on and student achievement Task Set-­‐Up Task ImplementaDon Student Learning A.
High High High B.
Low Low Low C.
High Low Moderate Intensifica7on strategy: Inquiry-­‐based instruc7on Maintain cogniDve demand through all three parts of the model. 7
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Intensifica7on strategy: Literacy in content [T]he lack of reading-­‐to-­‐learn skills is behind much of poor student performance in the content areas. Many students have not developed specific techniques to appreciate the nuances of the big ideas in the domains of knowledge. In short, for many learners the big ideas are invisible. Gomez, L. M., & Gomez, K. (2007). Reading for learning: Literacy supports
for 21st century work. Phi Delta Kappan, 89(3), 224–228.
Math journal example Based on your invesDgaDon, what conjectures can you make about the rela7onship between algebraic and geometric solu7ons to systems of linear equa7ons? Complete the Math Journal to describe your conjectures. Algebraic result
What does the graph look like?
What might this tell you about the number of solu7ons for the system?
Answer includes one value for x and one value for y.
EquaDons simplify to a false equaDon containing only numbers (for example, 0 = 12).
EquaDons simplify to a true equaDon containing only numbers (for example, 18 = 18).
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Intensifica7on strategy: Learning rou7nes “Some students in school today don’t see a connecDon between their efforts and school success, don’t know what it is they need to pracDce, can’t imagine themselves ever being ‘academic,’ and have never seen ‘academics played.’ . . . A first step in helping students become full parDcipants in the classroom is to ensure that all students value and understand the importance of learning and learning rituals.” Lenz, B. K., Deshler, D. (2004). Teaching Content to All: Evidence-­‐Based Prac*ces in Middle and Secondary Schools. Boston: Pearson EducaDon, Inc. Explicit teaching of rou7nes 9
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Empowering students in the learning process A rouDne for processing homework Intensifica7on strategy: Forma7ve assessment Use evidence about learning to adapt instruction to meet student needs.
KEY FORMATIVE ASSESSMENT MOVES
•
•
•
•
•
Clarify learning intentions and criteria for success.
Engineer classroom discussions to elicit evidence of learning
Provide feedback that moves learners forward
Activate students as instructional resources for each other
Empower students as owners of their own learning.
Wiliam, D., & Thompson, M. (2007). Integrating assessment with learning: What
will it take to make it work? In Dwyer, C. A. (Ed.), The Future of Assessment:
Shaping, Teaching and Learning. Mahwah, N. J.: Erlbaum.
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A rou7ne for reviewing assessments Overall improvement aRer two rounds of feedback +50
Change in grades (percent)
+40
+30
+20
+10
0
-10
Grades
Comments
and grades
Comments
-20
-30
-40
-50
Ruth Butler's research was published as “Enhancing and undermining intrinsic motivation: The
effects of task-involving and ego-involving evaluation on interest and performance.”
British Journal of Educational Psychology, 58, 1–14.
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Intensifica7on strategy: Target misconcep7ons A study by Alan Bell and Malcolm Swan found that students
whose teachers addressed and corrected misconceptions,
rather than simply using remedial measures, achieved and
maintained higher long-term learning results.
Bell, A. & Swan, M. (1993 March). Some experiments in diagnostic teaching.
Educational Studies in Mathematics 24(1), 115–137.
See also www.toolkitforchange.org
A strategy for effec7ve review: Distributed prac7ce Strong positive effects of spaced practice have been found in a wide
variety of contexts. Carlous Caple summarized this body of research as
follows:
The spacing effect is an extremely robust and powerful
phenomenon, and it has been repeatedly shown with many
kinds of material. Spacing effects have been demonstrated
in free recall, in cued recall of paired associations, in the
recall of sentences, and in the recall of text material.… Also
the effect of spaced study can be very long-lasting.
Caple, C. (1996). The effects of spaced practice and spaced
review on recall and retention using computer assisted
instruction. Ann Arbor, MI: UMI.
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Intensifica7on strategy: “Non-­‐cog” supports Social, emoDonal, moDvaDonal supports help students develop: •  Academic iden**es as learners who recognize, value, and seek out high-­‐quality educaDon •  Mo*va*on and commitment to high achievement •  Skills to help create and contribute to a learning community. Intensified Algebra I: Integrated, Cohesive, Design Supports
for teachers
Shaping
attitudes toward
learning
Literacy &
language
supports
Rigorous
algebra
core
Tools to
organize
learning
Assessment
strategies
Ongoing
distributed
practice
Efficient
review and
repair
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Students benefit in the following areas: Want to learn more? Kathi Cook: klcook@ausDn.utexas.edu Anne Joyoprayitno: a.joyoprayitno@ausDn.utexas.edu www.utdanacenter.org/dc-­‐at-­‐ncsm2016 www.agilemind.com/programs/mathemaDcs/intensified-­‐
algebra-­‐I Tweet us at @UTDCKathi, @UTDCAnne, or @utdanacenter using the hashtag #NCSM2016. Please rate this conference presentaDon on the NCSM App by answering four short quesDons. 14