Algebra+for+All+August+20

=Algebra For All - August 20 Session=

Welcome visitors!

Below you'll find our brainstorming thoughts from our 8/20/08 PD session on helping ALL students have access to and understand algebra concepts and skills. It's written mostly as a train of thought (as the day went along), so it won't be letter perfect, and you certainly may find some things with which you don't totally agree.

=Part 1: Why do students do well in Algebra? What makes them successful?=

They understand the vocabulary. They do their homework. Thye have an entertaining teacher. They have prior knowledge. They're not afraid to ask questions. They're not afraid to ask for help. They know their basic skills and facts. They have a good memory. They are procedurally oriented. They know how to use a calculator, but are not dependent on it. They have self-confidence. They are natural problem solvers. They are comfortable with numbers and think in a logical way. They are mentally mature enough to handle abstract thoughts. They are perfectionists, sometimes to the point of OCD. They share information. They care about their performance and have a positive attitude about class. They take notes and review and study from them. -typed by Shannon

=Part 2: Our Experiences and Mental Models are not our Students'=

See the [|Beloit College Mindset List] for 2008 Other things from our experience that students now many not necessarily share...

-playing cards -playing board games -rolling dice -records vs. CDs vs. mp3s -cooking from scratch and measuring -sewing and using the measuring tools and units -making projects which require measuring (measuring tape, ruler, etc.) -using hand tools (wrenches, socket wrenches, etc., that come in multiple sizes) -the general "Cultural Literacy" teachers bring (books we've read, TV shows we've seen, movies we've seen, songs we've heard, etc.) vs. those which students bring -even for travel, we may have gone on more "road trips" growing up, while students often have flown those long distances instead (missing those map-reading skills, directional skills, estimating distances, estimating times, etc.)

=PART 3: "Nine Powerful Practices" article, by Ruby Payne, from Educational Leadership (ASCD), April 2008=

1. Build relationships of respect need to show caring attitude pay attention to nonverbal signals how much should students know about you? family pics, "getting to know you", tell stories, bulletin board very important to call students by name, say "hi" - builds collaboration

2. Making Beginning Learning Relational -kids can teach each other; collaborate -work in cooperative groups -the "we are in it together" attitude -students may work alone, but must occasionally be involved in "group work"

3. Teach Students to Speak in Formal Register. -all students do not speak and write as we do -different rules of behavior and language apply to different situations/environments -students need to be able to switch back and forth depending on environments -MEAP will be in formal register

4. Assess Each Student's Resources -it is not very likely that all students will come with the same resources -students have varying personal resources (perserverance, patience, focus, flexible thinking, logical thinking, interpersonal skills, etc.) -students have varying external resources (computer/calculator access, even basic materials access - paper, ruler, posterboard, etc.) -play on students' strengths -create lessons, assignments, assessments which play to students' strengths and don't penalize students for the resources they don't have -some students have knowledgable adults (or older teens) who can help them with work (may or may not know the math) -other students are on their own once they leave the school building -How does your school provide support for students? Tutoring, before and after school? Access to materials? Access to computers, to calculators, rulers, protractors, templates, etc.?

5. Teach the Hidden Rules of School -life at school is often very different from life at home -some things are not allowed at school that may be allowed or even encouraged at home -so that all students can be successful, we need to overtly teach these rules These include things like... -taking care of your own materials, and keeping track of them; keeping them in good condition for the next person -not getting into other people's materials or "stuff" - some things at school are community property (the ream of notebook paper in the corner, or the can of pencils to borrow); other things are not (students' bookbags, things on shelves or in cupboards or closets, etc.) -how to disagree while being agreeable -how to respond to criticism or correction -how to show others you appreciate them or to show that they did a good job -dealing with personal space -how to show respect at school

6. Monitor Progress ...allows continuity for students as they move teacher to teacher and building to building ...provides understanding of student strengths and weaknesses ...allows for better decision making from all levels from individual student through district ...some content areas may warrant more time in the school day than others - not every subject needs a single, full class period every day; some need more at times, some need less ...technology can help with progress monitoring; Benchmark & Inform ...frequent, timely, and detailed feedback to all - students, parents, teachers, administrators; need to be able to adapt quickly

7. Translate the Concrete to the Abstract -use mental models (stories, analogies, songs, visual representations) -help students make that connection between concrete things and abstract ideas -be aware as a teacher when you are using your own mental models and model this to the kids

8. Teach Students How to Ask Questions -help students understand how to pinpoint what they don't really understand and ask about it -have students work in pairs to question each other -as a teacher, use better questioning strategies to better pinpoint what students do and don't know -help students find strategies to do something productive when they don't really know what to do next

9. Forge Relationships with Parents -understand that many parents really do care, but have terribly busy work and home schedules -offer parents real-life suggestions to help them help their kids -be reasonable with your expectations of parents -especially with the new GLCE, HSCE, many parents are way out of their comfort zone with mathematics. -are initial parent contacts welcoming? -does the school facility come across as welcoming to visitors, especially parents? -do non-teaching staff deal with parents in warm, courteous ways? -be careful when meeting with parents, especially if a whole team meets with one parent - it's easy for the parent to feel way outnumbered -do we use language with parents that is free from jargon, that they will understand? -do we make recommendations to parents that they really probably can't fulfill (get a tutor, buy a supplemental book, go to websites)? -do parents see evidence that the school staff really cares about their child?

=Strategies for helping struggling students=

Teach the students the rules of the school vs. rules for outside of school; there really can be two or more sets. And, the sets can both be valuable (and valued) as they work in their environments. After giving a test, go through as a class and go over the ones most students got wrong (feedback and pushing the need to learn); provide parallel problems for all students to do afterwards. These could be used to improve their grade. Mental models/aids to help connect content - doing analogies, visuals, color coding, charts, ties to music, CONNECTIONS within and among content. Helping them make connections to what's familiar to them - their background, interests, etc. Remember the Golden Rule when interacting; especially watch your nonverbal communication - does your body language and tone of voice match what's coming out of your mouth? Dealing w/parents - get to parents early with something good to say, then if you need to call later they tend to be more supportive. Send positive postcards to parents or to students - it's nice to get good mail. Make sure students have the resources they need (all 8 kinds, if possible) to be successful - this may mean the school provides some of those. Ensure students can be comfortable about asking questions, and know how to ask questions. Idea of flexing with your team to create more time for a subject from time to time. Setting up a positive relationship with the kids, and letting them know that anyone can do math. Cooperative learning and collaborative learning, ensuring studnets work with different students over the course of time. This also enables students to learn to work with all people, not just the ones they really like or already get along with. Not being afraid of technology - use tech tools with kids, and help them learn to use the technology resources; tech is not a threat but a tool. Ensure that parents feel welcome, not intimidated. Be respectful, avoid educational jargon, don't gang up on them unawares. Making sure your students fully understand your expectations - if you really expect completed work, don't accept incomplete work, for example.

=WRITING IN MATHEMATICS=

Vocabulary: not just do they know the vocabulary, but do the students understand the meaning? Can they use the terms correctly in original settings? Writing & Vocabulary - after a new concept is taught: do they understand the concept? Can they make connections? Describe..., explain..., compare... Create a cartoon dealing with the vocabulary at hand Use "interactive notes" with the students (may or may not be electronic). Scaffold the notes and have students fill in key terms, key ideas, create original examples, etc.

POWER STRATEGY: Compare & Contrast Research has shown that having students compare and contrast concepts is very powerful and results in better learning. Students can do this via writing, graphic organizers, annotated diagrams, etc.

Students can be expected to write not just sentences but paragraphs.

HANDWRITING HINTS: Some students miss points just because of their handwriting, 1's and 7's (use a crossbar on the 7's); 2's and z's (use a crossbar on the z's); s's and 5's (use hooks on the ends of the s's).

Have students write out the process they use to solve a problem. In algebra, doing this with solving an equation is like doing a paragraph proof (see the QL expectations).

POWER STRATEGY: Error Analysis As a class, the teacher can have them analyze common errors made while solving the problems at hand (such as incorrectly cancelling terms from numerator to denominator). These problems might also come from a recent test or quiz. ALSO, having students FIX and EXPLAIN WHY THEY MISSED their own test or homework problems is GREAT. This is a form of rapid feedback.

WHEN TO WRITE??

-START of class ...as a review from prior material ...as a preview of today's/future material ...to ask questions about last night's homework or about concepts ...to respond to a prompt ("My favorite thing about the distributive property is...")

-END of class ...Exit slips. Students respond to a prompt,answer a question, or solve a problem. This is also formative assessment. Gives students a chance to SUMMARIZE (another POWER STRATEGY)

-IN THE MIDDLE of class ...trouble slips. Students note a question or idea they're having trouble with, and share it with their group, or pass to the teacher. Can be formative assessment if teacher provides help/modifies lesson right away. ...provide a chance to SUMMARIZE ...provide a chance to COMPARE & CONTRAST ...provide a chance for ERROR ANALYSIS