Norms Silence your technology Limit sidebar conversations
Objectives Understand the different types of knowledge Understand the definition of fluency Create a common understanding of a number talk Familiarize ourselves with the new scope and sequence, pacing guide, and assessments
Four Assessment Questions Directions: Solve each of the following problems. Under each problem write a brief description of 1) the type of knowledge used; 2) the length of time and amount of challenge faced; 3) how you solved it. Think of how each question varied in each of these areas. Keep these four problems in mind during our discussion about the four Types of Knowledge. We will revisit them at the end and identify how they relate.
Major Shifts in Mathematics 1.Focus Students have sufficient time to think about, practice, and integrate new ideas 2.Coherence Across grade levels and link to major topics within grade levels 3.Rigor In major topics, pursue with equal intensity: a. deep conceptual understanding b. procedural skill and fluency c. application and modeling
Skills (Procedure) Description Procedures Usually Doing Something Verbs Characteristics of Assessment Questions Routine Little or No Context Focus on Procedure and/or Answer One Short Answer Length Varies How this Knowledge is Learned & Retained Modeling Repeated Practice of the Same Steps Repeated Exposure
Facts Description Descriptions Vocabulary Formula Recollection Characteristics of Assessment Questions Routine No Context Focus on Recall One Short Answer Closed Length Varies How this Knowledge is Learned & Retained Repeated Exposure Memorization Techniques (songs) Drill
Concepts Description Ideas Understanding Things Nouns Characteristics of Assessment Questions Non-Routine In Context Focus on Explanation Extended Answer Open Middled or Open Ended Medium Minutes How this Knowledge is Learned & Retained Exploration Inquiry/Discovery Experimentation Hands- On/Manipulative s Sufficient Time for In-Depth Study Experienced in New Contexts
Relational Knowledge Description Application of Multiple Types of Knowledge Synthesis Analysis or Evaluation Characteristics of Assessment Questions Non-Routine In Context Focus on Applying Knowledge Extended Answer Open Middled or Open Ended Longer Minutes How this Knowledge is Learned & Retained Exposure to Open-Ended Questions Class/Group Discussions Collaboration Authentic Experiences
Revisit assessment questions At your table try to identify which Type of Knowledge corresponds to each of the four questions.
Defining Fluency Number off 1 -2 at your table Read the corresponding text 1.Simple, Fast, and Accurate? I Think Not! 2.CCSS California Framework Engage in a table discussion around the major points of the readings
One Liner Defining “Fluency” As a group, come to consensus on what fluency is and define it using a “one liner” on a piece of 8.5 x 11 paper.
Our classrooms are filled with students and adults who think of mathematics as rules and procedures to memorize without understanding the numerical relationships that provide the foundation for these rules. Number Talks, page 4
Quick Write Think about mental math. How do we use mental math in our everyday life?
What is a number talk? A number talk is a quick (5-15 minutes) classroom routine used to develop computational fluency that promotes students to: – Clarify thinking. – Investigate and apply mathematical relationships. – Build a repertoire of efficient computational strategies. – Make decisions about choosing efficient strategies for specific problems. – Consider and test other strategies to see if they are mathematically logical. – Build connections between key conceptual ideas.
5 Key Components 1.Classroom Environment and Community 2.Classroom Discussions 3.The Teacher’s Role 4.Role of Mental Math 5.Purposeful Computational Problems
1. Classroom Environment and Community Students should feel comfortable – Offering responses for discussions – Questioning themselves and their peers – Investigating new strategies Accept all ideas and answers 5 Key Components
2. Classroom Discussions Transfers the ownership of learning to the students Mistakes are an opportunity for learning 5 Key Components
3. The Teacher’s Role Facilitator Questioner Listener Learner 5 Key Components
4. The Role of Mental Math Encourages students to build on number relationships Encourages students to utilize the value of the entire number 199 + 199 = 5 Key Components
5. Purposeful Computation Problems Careful planning before number talks is necessary to design “just right” problems for the students. 5 Key Components
How Do I Prepare for Number Talks? Designated location allowing proximity Appropriate wait time Accept, respect, and consider all answers Encourage student communication
Student Communication Flexibility in mathematical thinking develops as we push ourselves and our students to reason through different approaches Model appropriate ways to respond to other students’ strategies Children should clearly hear the message that they are to think about other strategies continually
Recording Student Thinking Anticipate how students will respond Think through possible strategies beforehand Consider which mathematical ideas you want to highlight Make sure your notation is mathematically correct 30 + 30 = 60 – 3 = 57 should not be written
Having the opportunity to ponder other approaches strengthens our own mathematical foundation and understanding.
Accountability with Students Finger Signals for Efficient Strategy Keep records of Problems. Small-Group Number Talks Class Strategy Charts Exit Ticket Weekly Computation Assessment
Starting with Small Steps 1.Start with smaller problems to elicit thinking from multiple perspectives. 2.Be prepared to offer a strategy from a previous student. 3.It is all right to put a student’s strategy on the back burner. 4.Limit your number talks to 5-15 minutes. 5.Be patient with yourself and your students as you incorporate number talks into your regular math time.
“To achieve mathematical understanding, instruction and learning must balance mathematical procedures and conceptual understanding…Student understanding is further developed through ongoing reflection about cognitively demanding and worthwhile tasks.” - Introduction to the Common Core p. 6
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