**Annotated Bibliography**

“

**Tailoring Tasks to Meet Students’ Needs**

**,”**McDuffie, Wohlhunter, Breyfogle, Mathematics Teaching in the Middle School, vol 16, no 9, May 2011.

Four strategies to make curriculum/lessons/instruction fit student needs. Eg. ELL & Special Education students.

1. Switch to a familiar context

2. Supplement foundational gaps

3. Incorporate overarching goals

4. Adjust for reading levels

**"Problems That Encourage Proportion Sense,"**Billings, Esther H.M, Mathematics Teaching in the Middle School, vol 7, no 1, Sept 2001.

Students often fail to consider the reasonableness of answers. The use of non-numeric problems can encourage proportion sense in students.

**"Using Assessment for Effective Learning,"**Lee, Clare Mathematics Teaching, June 2001

Formative Assessment can be shown to clearly raise standards. Some specific methods:

1. Ask Questions worth thinking about - questions without easy answers

2. Questions that last a lesson or two - keep students engaged

3. Students write their own questions - quickly identifies strengths and weaknesses

4. Last 5 minutes - students reflect, tell what they know now that they didn't know

5. Give yourself a score out of 5 - do 5 questions from a lesson, have students score themselves (without seeing the answers first) and then review only the questions that students felt they missed

6. What questions do you have about how to complete a task? - student write the "5 burning questions" highlighting what information is still needed to complete a problem

7. Peer homework correcting, using detailed solutions - students grade each others' work, using answer keys with steps given, and must debate about what indicates showing work correctly.

**"Toward an educationally relevant theory of literacy learning: Twenty years of inquiry"**Cambourne, Brain, The Reading Teacher, vol 49, no 3, Nov. 1995

A study that quantified the conditions needed for language growth shows that these same conditions could be applied to all types of learning. The conditions were:

1. Immersion

2. Demonstration

3. Engagement

4. Expectations

5. Responsibility

6. Approximations

7. Employment

8. Response

**"One Teacher's Story,"**Collins, Anne M., Mathematics Teaching in the Middle School, vol 16, no 1, August 2010

Account of a middle school math teacher's attempt to focus on teaching problem solving methods. The teacher encouraged the students to use common problem-solving strategies (model it, make a table, etc...) while solving an involved, multi-step problem. Students were expected to clearly communicate their solutions while justifying their steps, and an alternative (1-4pt) grading scale was utilized.