https://padlet.com/jesscropsey/2vva3ly9iode TE 857 Synthesis en-us 2018-04-22 21:54:04 UTC 2025-10-16 23:15:06 UTC hello@padlet.com jesscropsey https://padlet.com/jesscropsey/2vva3ly9iode/wish/254191300 1)  Encourages communication and reflection (Caulfield et al 2003)
2) Has high cognitive demand - requires complex & non algorithmic thinking; justifications and explanations for answers and/or methods; an understanding of mathematical concept, processes, & relationships (Smith & Stein 1998)
3)  Is open-ended with more than one solution pathway 
4)  Is accessible to all - the problem has multiple entry points and allows for the use of a variety of intelligences
5)  Draws from multiple mathematical knowledge bases (MMKB) which includes their mathematical thinking and home/community-based knowledge about mathematics (Drake 2015)
6)  "Matters" - engaging & interesting to students, links home (or work) and school (relatable to their lives), may include real-world application, and may be a problem that students pose themselves]]> 2018-04-22 22:00:21 UTC https://padlet.com/jesscropsey/2vva3ly9iode/wish/254191300 jesscropsey https://padlet.com/jesscropsey/2vva3ly9iode/wish/254192302 * Create readily modified tasks -- simply change the numbers involved (to increase difficulty) or slightly alter the question (moving from "closed" question to an "open-ended" one
* "Open spaces" by encouraging students to develop their own solution strategies and then share and explain those strategies; by encouraging multiple representations or asking students to solve it different ways; by asking students to find connections in their homes or communities (Drake et al 2015)]]> 2018-04-22 22:12:14 UTC https://padlet.com/jesscropsey/2vva3ly9iode/wish/254192302 jesscropsey https://padlet.com/jesscropsey/2vva3ly9iode/wish/254192503 1)  Anticipate student responses ahead of time
2)  Monitor student work and engagement with the task
3)  Select particular students to present their mathematical work
4)  Sequence the student responses that will be displayed in a specific order
5)  Connect different student responses to each other and to key mathematical ideas
(Smith et al 2009)]]> 2018-04-22 22:14:16 UTC https://padlet.com/jesscropsey/2vva3ly9iode/wish/254192503 jesscropsey https://padlet.com/jesscropsey/2vva3ly9iode/wish/254192691 "Giving students too much or too little support, or too much direction, can result in a decline in the cognitive demand of the ask."  (Orchestrating Discussions, Pg. 550, Mathematics Teaching in the Middle School)]]> 2018-04-22 22:16:35 UTC https://padlet.com/jesscropsey/2vva3ly9iode/wish/254192691 jesscropsey https://padlet.com/jesscropsey/2vva3ly9iode/wish/254194195 While a "good" task doesn't necessarily require collaborative learning, often this approach will enhance the learning experience for all as they problem-solve, communicate, and reflect together.  ]]> 2018-04-22 22:34:10 UTC https://padlet.com/jesscropsey/2vva3ly9iode/wish/254194195 jesscropsey https://padlet.com/jesscropsey/2vva3ly9iode/wish/254213786 "Teaching and learning are social processes, and learning is enhanced in a collaborative environment." (summary of Vygosky found in Simic-Muller et al 2009)]]> 2018-04-23 01:30:08 UTC https://padlet.com/jesscropsey/2vva3ly9iode/wish/254213786 jesscropsey https://padlet.com/jesscropsey/2vva3ly9iode/wish/254215985 * Requires a group-worthy task (no one student could solve it on their own)
* Fosters conceptual thinking and demands conversation, thus deepening students' understanding
* Has high cognitive demand
* Often involves group roles that can assist with cooperative learning]]> 2018-04-23 01:45:11 UTC https://padlet.com/jesscropsey/2vva3ly9iode/wish/254215985