Organizing Effective Instruction by Sara Bailey https://padlet.com/sara_bailey2/vhz9b8l2weyj Principles to Action https://drive.google.com/file/d/1eiq3yS4CO2_RuxMaz9tnzYTel1ZwtCwD/view en-us 2020-02-25 03:34:54 UTC 2025-05-09 20:43:33 UTC hello@padlet.com Effective teaching of mathematics establishes clear goals for the mathematics that students are learning, situates goals within learning progressions, and uses the goals to guide instructional decisions. sara_bailey2 https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/449907643


]]> 2020-02-25 03:38:26 UTC https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/449907643 Build procedural fluency from conceptual understanding. Effective teaching of mathematics builds fluency with procedures on a foundation of conceptual understanding so that students, over time, become skillful in using procedures l as they solve contextual and mathematical problems. sara_bailey2 https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/449933224 2020-02-25 05:54:13 UTC https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/449933224 Pose purposeful questions. Effective teaching of mathematics uses purposeful questions to assess and advance students’ reasoning and sense making about important mathematical ideas and relationships. sara_bailey2 https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/449933323 2020-02-25 05:55:01 UTC https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/449933323 Facilitate meaningful mathematical discourse. Effective teaching of mathematics facilitates discourse among students to build shared understanding of mathematical ideas by analyzing and comparing student approaches and arguments. sara_bailey2 https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/449933369 2020-02-25 05:55:28 UTC https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/449933369 Use and connect mathematical representations. Effective teaching of mathematics engages students in making connections among mathematical representations to deepen understanding of mathematics concepts and procedures and as tools for problem solving. sara_bailey2 https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/449933447 2020-02-25 05:56:00 UTC https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/449933447 Implement tasks that promote reasoning and problem solving. Effective teaching of mathematics engages students in solving and discussing tasks that promote mathematical reasoning and problem solving and allow multiple entry points and varied solution strategies. sara_bailey2 https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/449933500 2020-02-25 05:56:20 UTC https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/449933500 Support productive struggle in learning mathematics. Effective teaching of mathematics consistently provides students, individually and collectively, with opportunities and supports to engage in productive struggle as they grapple with mathematical ideas and relationships. sara_bailey2 https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/449933769 2020-02-25 05:58:20 UTC https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/449933769 Elicit and use evidence of student thinking. Effective teaching of mathematics uses evidence of student thinking to assess progress toward mathematical understanding and to adjust instruction continually in ways that support and extend learning. sara_bailey2 https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/449933864 2020-02-25 05:58:56 UTC https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/449933864 sara_bailey2 https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/449934001 2020-02-25 06:00:05 UTC https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/449934001 sara_bailey2 https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/449934336 2020-02-25 06:02:31 UTC https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/449934336 sara_bailey2 https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/449934525 2020-02-25 06:03:53 UTC https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/449934525 sara_bailey2 https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/449934757 2020-02-25 06:05:41 UTC https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/449934757 sara_bailey2 https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/449934884 2020-02-25 06:06:31 UTC https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/449934884 sara_bailey2 https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/449934952 2020-02-25 06:07:02 UTC https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/449934952 sara_bailey2 https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/449935079 2020-02-25 06:07:51 UTC https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/449935079 sara_bailey2 https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/449935267 2020-02-25 06:09:26 UTC https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/449935267 ally_titterness https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/450881141 Being fluent means students have flexibility and choice among the methods and strategies used to solve problems. 

Fluency will build upon exploration that students do to solve problems. 

Fluency should not be rushed, and should not only include memorization of facts.]]> 2020-02-26 17:07:45 UTC https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/450881141 ally_titterness https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/450893225 2020-02-26 17:23:34 UTC https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/450893225 ally_titterness https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/450903284 While types of questions are essential, it's the pattern of questions teachers use during discussion are very important. 

The teacher decides the path to take to lead the discussion, which allows the students to engage based on that path, and come to conclusions using higher-level questioning and thinking. ]]> 2020-02-26 17:36:30 UTC https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/450903284 ally_titterness https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/450909099 Some questions teachers can ask to lead discussion:
What do you notice about the graph?
Do you see a pattern in the data?
What are the measures of center for the pennies?]]> 2020-02-26 17:44:18 UTC https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/450909099 ally_titterness https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/451002778 Discourse that focuses on tasks that promote reasoning and problem solving is a primary strategy for developing understanding and meaningful learning in math. 

Five Practices to support student responses: 
1. Anticipating student responses before the lesson begins. 
2. Monitoring students' progress and engagement.
3. Selecting students to present their information in class.
4. Sequencing students' responses in a specific order for discussion.
5.  Connecting students' responses to key ideas. ]]> 2020-02-26 19:41:59 UTC https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/451002778 ally_titterness https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/451014748 2020-02-26 19:58:44 UTC https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/451014748 ally_titterness https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/451016577 It is important to connect teaching and learning with different representations such as, contextual, visual, verbal, physical, and symbolic. 

Students, especially young students and students with learning disabilities, benefit from using physical objects, or acting out processes during problem solving.]]> 2020-02-26 20:01:42 UTC https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/451016577 ally_titterness https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/451019367 2020-02-26 20:05:49 UTC https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/451019367 ally_titterness https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/451020005 Not all tasks provide the same opportunities for student thinking and learning.
Student learning is greatest in classrooms where the tasks consistently encourage higher-level thinking. 
Tasks with high cognitive demands are the most difficult to implement and are most often transformed during instruction. ]]> 2020-02-26 20:06:45 UTC https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/451020005 ally_titterness https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/451021937 Mathematics goals are essential for indication of what is expected of students to learn as a result of instruction. 

"Formulating clear, explicit learning goals  sets the stage for everything else."]]> 2020-02-26 20:09:39 UTC https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/451021937 https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/452469853

]]> 2020-02-29 23:44:39 UTC https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/452469853 Start with Conceptual Understanding and Build Fluency jmccarron09 https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/452470034 "Essentially, conceptual understanding is knowing more than isolated facts, it is also knowing connections between those facts and having those facts well organized."]]> 2020-02-29 23:46:19 UTC https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/452470034 Strategies for Building Procedural Fluency jmccarron09 https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/452470566 This math fluency checklist is a great tool that can be used to encourage students to use different strategies to solve math problems efficiently and accurately.]]> 2020-02-29 23:51:13 UTC https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/452470566 Purposeful Questions jmccarron09 https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/452479048 Effective instruction begins with asking probing, intentional questions. ]]> 2020-03-01 01:03:26 UTC https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/452479048 John Dewey jmccarron09 https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/452480168 Distinction between procedural and conceptual.]]> 2020-03-01 01:12:59 UTC https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/452480168 Socratic Questions jmccarron09 https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/452480471 Asking questions encourages students to think through their answer and apply current knowledge to solve a new problem. Incorporating these six types of Socratic questions will enhance your student's math learning by developing critical thinking skills and math strategies.

]]> 2020-03-01 01:16:07 UTC https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/452480471 How to Use Rubrics to assess evidence of student reasoning. jmccarron09 https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/452480877  A rubric for assessing mathematical reasoning will help teachers be aware of the reasoning actions and formatively assess the reasoning articulated and displayed by students. ]]> 2020-03-01 01:19:52 UTC https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/452480877 jmccarron09 https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/452481518 2020-03-01 01:24:55 UTC https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/452481518 Productive Struggle jmccarron09 https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/452481672 Jo Boaler discussion.]]> 2020-03-01 01:26:21 UTC https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/452481672 Math Goals and Standards jmccarron09 https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/452482842 The Standards for school mathematics describe the mathematical understanding, knowledge, and skills that students should acquire from prekindergarten through grade 12. Each Standard consists of two to four specific goals that apply across all the grades.]]> 2020-03-01 01:35:12 UTC https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/452482842 Tasks that Provide Opportunities to Reason and Relate jmccarron09 https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/452483118 Problem-based tasks (PBTs) are math lessons built around a single, compelling problem.]]> 2020-03-01 01:37:17 UTC https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/452483118 Show Me the Math! jmccarron09 https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/452483807 Mathematical representations are visible or tangible productions – such as diagrams, number lines, graphs, arrangements of concrete objects or manipulatives, physical models, mathematical expressions, formulas and equations, or depictions on the screen of a computer or calculator – that encode, stand for, or embody mathematical ideas or relationships.]]> 2020-03-01 01:42:45 UTC https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/452483807 For example, if you were to ask your six-year-old to help you set the table for dinner, you could ask in a myriad of ways:Request 1: Please set the table with 7 forks, and 7 spoons.Request 2: Please set the table with forks and spoons for 7 people.Request 3: Please set the table with a fork and a spoon for yourself, your sibling, your parents (2 in this example), your grandparent, and your aunt and cousin, who are coming to dinner.Request 4: Please set the table for us and grandma, like you did last night, but your aunt and cousin are also coming for dinner.Request 1 is very explicit and is a simple procedural application of a mathematical skill: counting. Your child is instructed on how many of each item to get and can count 7 forks, and then return to the drawer to count 7 spoons.Request 2 is also a procedural application, though it can be achieved through multiple skills and thereby extends their application beyond simple execution of an explicit task. Your child could count and carry twice as in request 1. Or they could add 7 + 7, counting to 7 as they remove forks from the drawer, and then continuing to count to 14 while removing spoons from the drawer. Or they could pair each fork with a spoon as they take them from the drawer and count 7 sets.Request 3 begins to introduce conceptual thinking. In this request, your child is given the explicit instruction to get forks and spoons plus information about the people their task will serve, rather than an explicit number of people. They must first conceptualize those people around the dinner table, and then equate that to the quantity 7. From there, they could apply any of the procedural skills described above.Request 4 requires more conceptual thinking. It isn’t posed as a calculation or computation at all. Your child will first need to think about how many people were present at dinner the night before. Since their grandparent was present, the table will have 1 more than its usual base of 4. They’ll then have to consider that their aunt and cousin will join the table tonight and add those two additional diners. Then, they’ll have to think about which utensils might be needed. Lastly, they’ll have to go to the drawer and retrieve the appropriate quantity of different utensils. jason_laurence2 https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/453241734 2020-03-02 20:21:14 UTC https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/453241734 The process is important too! jason_laurence2 https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/453245724 Using careful questioning to guide the students toward the solution, or even towards the "right" question.]]> 2020-03-02 20:27:17 UTC https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/453245724 ally_titterness https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/453340260 2020-03-03 00:17:10 UTC https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/453340260 ally_titterness https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/453340466 Clarify, share, and understand learning intentions and success criteria.

 Engineer effective discussions, tasks, and activities,  that elicit evidence of learning.

Provide feedback that moves learning forward. 

Activate students as learning resources for one another. 

Activate students as owners of their own learning. ]]> 2020-03-03 00:17:54 UTC https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/453340466 sara_bailey2 https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/453369951 2020-03-03 01:43:06 UTC https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/453369951 sara_bailey2 https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/453370150 2020-03-03 01:43:36 UTC https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/453370150 sara_bailey2 https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/453370296 2020-03-03 01:44:02 UTC https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/453370296 sara_bailey2 https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/453370419 2020-03-03 01:44:25 UTC https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/453370419 sara_bailey2 https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/453370614 2020-03-03 01:44:56 UTC https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/453370614 sara_bailey2 https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/453370785 2020-03-03 01:45:23 UTC https://padlet.com/sara_bailey2/vhz9b8l2weyj/wish/453370785