Language Demands of the Mathematics Classroom: A Discussion of the M-Zone Project

1. Language Demands of the Mathematics Classroom: A Discussion of the M-Zone Project Christopher S. Hlas, Joe Morin, Lori Loomis, Joelle Astrup, Mary Rettke, Jill Thompson Wisconsin Mathematics Council – 39th Annual Green Lake Conference

2. Overview • M-Zone Project • Example with reform curriculum • Example with traditional curriculum • Collaboration • Outcomes • Questions & Contact information Wisconsin Mathematics Council – 39th Annual Green Lake Conference

3. The Problem Students with core language processing difficulties General Education Math Instruction Students with LD Math Instruction Curricula with high language demands Wisconsin Mathematics Council – 39th Annual Green Lake Conference

4. The Solution ? Math Teachers Language-based accommodations Special Ed Teachers Wisconsin Mathematics Council – 39th Annual Green Lake Conference

5. What does the LLD learner experience? When you do pillar deductions you need to remove the subordinatenumeral from the superior numeral. If the subordinate numeral is too big, you must loan a deka from the deka pillar and combine it to the units pillar number. Then you can deduct. When you do _________ you need to _________the _________away from the _________number. If the bottom number is too big, you must borrow a _________from the tens column and __________it to the _________column number. Then you can _________. Wisconsin Mathematics Council – 39th Annual Green Lake Conference

6. So what does this mean when I’m teaching a student who has LLD? It means I have to think about the language modality I depend on to convey the content. Wisconsin Mathematics Council – 39th Annual Green Lake Conference

7. What are language-based processing demands in math? Teacher to student oral discourse Peer to peer oral discourse Text-based Wisconsin Mathematics Council – 39th Annual Green Lake Conference

8. _____ discourse storage of new words retrieval of previously learned words efficiencies in making connections coherent mental models Auditory sequential memory Semantic memory Compartment-ilized knowledge Impaired meaning-making Wisconsin Mathematics Council – 39th Annual Green Lake Conference

9. _____ narrative Labored decoding Inaccurate pronunciation Adapting to narrative structure Maintaining cohesion Frequent miscues and lack of fluency Leading to misinterpret-tion Trouble with expository syntax Self-monitoring for inconsistencies Wisconsin Mathematics Council – 39th Annual Green Lake Conference

10. Mathematics language demands • Vocabulary (words) • Symbols • Diagrams • Grammar & syntax Framework adapted from D.L. Ball – How does mathematical language figure in the Work of Teaching? Wisconsin Mathematics Council – 39th Annual Green Lake Conference

11. ______ demands • Vocabulary, definitions, names:hypotenuse, square, Pythagoras… • English vs. math prime, table, obtuse, right, period … In a right triangle, the sum of squares of the legs equal the square of the hypotenuse. Wisconsin Mathematics Council – 39th Annual Green Lake Conference

12. ______ demands • Variables, constants, formulas, etc. • Inconsistent & different meanings () <> • English vs. Math: - . ! A2 + B2 = C2 Wisconsin Mathematics Council – 39th Annual Green Lake Conference

13. ______ demands • Cartesian coordinates • Geometric shapes • Tables • Charts Wisconsin Mathematics Council – 39th Annual Green Lake Conference

14. _________ demands Vocabulary: Hypotenuse of a _____ triangle Symbol: 2+3/4 vs. (2+3)/4 3+4 = 4+3 vs. 4-3 = 3-4 5+4 = 9+3 = 12+1 =13 sin(x) vs. sin*x Wisconsin Mathematics Council – 39th Annual Green Lake Conference

15. Language demands: Recap • _______ • _______ • _______ • _______ Wisconsin Mathematics Council – 39th Annual Green Lake Conference

16. _______ Planning ToolPrinciples of effective instruction E – Explicit Instruction D – Distributed practice F – Feedback I – Big Ideas R – Purposeful Redundancy S – Mediated Scaffolding T – Task relevance Wisconsin Mathematics Council – 39th Annual Green Lake Conference

17. Planning Template Wisconsin Mathematics Council – 39th Annual Green Lake Conference

18. Structure of ED FIRST Oral Discourse: 4) Vocabulary density & Familiarity Language Demand Instructional Components d) Use positive & negative examples & place word in recognizable context Listing of ED FIRST Adjustments Resource for Oral 4 (d) Barton & Heidema pg. 69 Resources that expand on the procedures for implementing each ED FIRST Adjustment Wisconsin Mathematics Council – 39th Annual Green Lake Conference

19. M-zone Resource Referencing System From Teaching Reading in Mathematics, Barton & Heidema, pg. 69 Wisconsin Mathematics Council – 39th Annual Green Lake Conference

20. General accommodations • Reform curriculum, no SPED collaboration • General accommodation examples • Inverse variation patterns • Pythagoras vocab • Accentuating the negative (vocab, wkst, reflections) Wisconsin Mathematics Council – 39th Annual Green Lake Conference

21. Targeted accommodations • Traditional curriculum • Guided notes (guided journals) • Adding & subtracting decimals • Measuring in metric units Wisconsin Mathematics Council – 39th Annual Green Lake Conference

22. Collaboration • Flexibility of types depending on the situation/content • Consulting • Parallel Teaching • Supportive Teaching • Team Teaching Wisconsin Mathematics Council – 39th Annual Green Lake Conference

23. Outcomes • Pilot project • Flexibility • Teacher perspectives • Student perspectives • Pull-out vs. inclusion • Applicable to all students • Flexibility Wisconsin Mathematics Council – 39th Annual Green Lake Conference

24. Questions? Project information http://www.uwec.edu/SPED/MZone Joe Morin (morinje@uwec.edu) Slides/handouts http://people.uwec.edu/hlascs/research/wmc07.htm Chris Hlas (hlascs@uwec.edu) Wisconsin Mathematics Council – 39th Annual Green Lake Conference