Math Standard and Backwards Mapping in Kindergarten

This blog post describes the backwards mapping for a math standard in kindergarten.

Established Goal: (Common Core Standard for Math in kindergarten CCSS.MATH.CONTENT.K.OA.A.1)

Represent addition and subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations.

Understanding(s):

Students will…

• Use addition and subtraction to solve problems in different ways.
• Represent, relate, and operate on whole numbers, initially with sets of objects and eventually with actions and drawings.
• Choose, combine, and apply effective strategies for working with numbers.
• Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Essential Questions:

• How can I find the total when I put two quantities together?
• How can I find what is left over when I take one quantity away from another?
• How can I represent and solve problems using objects, pictures, words and numbers?
• How can I use models to represent addition and subtraction?
• What happens when sets are joined or separated? 

Knowledge:

Students will know...

• Quantities can be joined (put together; composed).
• Quantities can be separated (taken apart; decomposed).
• Composing quantities will give us more than we started with.
• Decomposing quantities will give us less than we started with.
• We can model joining and taking apart sets of objects by drawing pictures, using manipulatives, and acting it out.
• Number models help us solve problems.

Skills:

Students will be able to...

• Use manipulatives, drawings, and numerical expressions to represent addition.
• Use manipulatives, drawings, and numerical expressions to represent subtraction.
• Use numbers to represent quantities and to solve quantitative problems involving joining and separating situations with objects.

Assessments:

Formative: 

1.  During the lesson, the teacher will present addition and subtraction problems for students to resolve in small whiteboards for each student. This formative assessment will help the teacher to check understanding of the students. 
2. During the lesson, the teacher will present addition and subtraction problems for students to resolve in small whiteboards for each student. This formative assessment will help the teacher to check students' understanding. 
3. During the independent work, the teacher will observe the student's work and will ask to some students about their work, for example using questions like “How do you find the result? Show me”. 

Summative:

Each lesson will include a worksheet for independent work of students. These worksheets will be aligned to the objective of each lesson. These will help the teacher to know the level of each student and prepare some modifications or interventions to help lower and higher level students.

At the end of the unit, students will take an assessment which include the following questions:

First part - Addition

1.     If I have two chips, how many chips do I need to complete 5?

2.     3+2= ___

3.     If I have six dots, how many do I need to complete 10?

4.     7+2=___

5.     Juan has 4 apples and Liz give him 3 apples more, how many apples does Juan have in total?

Second part - Subtraction

1.     If I have 4 chips and I take away 3, how many chips do I have left?

2.     4-2= ___

3.     If I have 9 chips and I take away 4, how many chips do I have left?

4.     8-4= ___

5.     Martin had 6 cookies and he ate 2 cookies, how many cookies have Martin now?

Learning Plan:

Activity 1: Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Activity 2: Find the missing number to complete 10 using a ten frame.

Picture by: https://www.teacherspayteachers.com

Activity 3: Using fingers to solve addition problems.  

Picture by: http://www.special-and-determined.com 

Activity 4: Add the dots in two dices and record the equation. 

Picture by: http://www.k12mathworksheets.com

By Jaime Solano 

KIndergarten Teacher 

How to apply rules and procedures in classroom?

When we start the school year, we work with students to build the classroom rules, which will help us to guide the actions in the class. But immediately a question arises on how can we apply these rules and procedures in class? Consequences are the other side of rules and procedures (Marzano, 2007), these are the response when a student or students either follow or break the rules. Consequences can be positive or negative, a combination of both could be more effective rather than focusing in only spectrum. Rules and consequences should be established at the same time and are typically addressed routinely and frequently.

“If you break it, you fix it” is one of the consequence that I use in my classroom. For example, when a student disorganizes the class materials, the consequence is that s/he must organize them back. 

http://www.gliffy.com/go/publish/image/9759479/L.png 

When the students are following rules and procedures it is important to give students a positive consequence that reinforces the action. One kind of reinforcement is the use of a verbal o non-verbal acknowledgement to students who follow the class’ norms or execute successfully a task. The acknowledgement could be provided in by expressing approval or another non-verbal gesture.

For example, students are working in groups and the teacher say “I noticed that X group is working quietly and all of the students are focused in his work”, the teacher’s message recognizes the work of a specific group of students while helping the rest of the students to remember the expected behavior at this moment.

Acknowledging a positive action that is taking place within a specific group in the classroom may help to send a signal to students who need to improve their behavior and are not following the norms, redirecting and motivating students towards accomplishing the expected task or procedure in order to also be noticed by the teacher in a positive manner.

Also, we can complement the verbal or non-verbal recognition with a tangible recognition. This consequence is appropriate when students are consistently following  the rules and it goes beyond a verbal reinforcement; therefore, a student or the students can receive a tangible incentive from the teacher. Some teachers use virtual platforms like www.classdojo.com, where students receive points when they follow the rules, so students who collect a certain number of points receive a material recognition of this accomplishment, for example a letter for the parents.

The “Sun” symbol is a form of tangible recognition that I use in my kindergarten class. When a student constantly follows the rules and procedures, his or her name are posted in a “Sun” in the whiteboard. A name of a student in the “Sun” symbolizes an acknowledgement to a student who follows the rules in the class and sets an example to other peers. If a student completes a week “in sun”, s/he receives a small incentive.

The acknowledgement of a good behavior can be extended to the parents if a student has received verbal and tangible recognition and continues demonstrating an exemplary behavior. Teachers can write a note, send an email or call the parents to inform and congratulate them for the student’s behavior.

As I mentioned before, consequences are both positive and negative. Teachers need to be aware of potential problems and quickly respond to those situations which are at the core of effective classroom management. Robert Marzano defines this type of approach by teachers as withitness. Some of the actions that constitute withitness are: be proactive about potential problems, occupying the entire room physically or visually, noticing potential problems as quickly as possible, and using a series of graduated actions (looking at the suspected students, moving in the direction of students and stopping the class and confronting the behavior.)

Inappropriate behavior requires an explicit and concrete consequence. There are multiple examples of this kind of consequences but I would like to focus in two: Time-out or break and overcorrection. Time-out is a space of time giving to a student to reflect in his or her actions and try to find solutions to improve the behavior. In elementary schools, as it is my case in kindergarten, some students require a break to calm down and reflect. For example, a student is constantly talking and distracting other students in her/his group, the teacher tries to redirect many times but the student continues talking, as a consequence, the teacher request the student to continue his/her work in a different space in the class. The overcorrection is other kind of explicit and concrete consequence that involves engaging students in activities that overcompensate for inappropriate behavior. For example, a student knocks down a box of pencils from another student, so the student that behave negatively must  offer an apology to his classmate and collect the pencils, leaving everything in order.

Another type of consequence for students breaking the rules is the use of group contingency that involves holding the whole class responsible for the behavior of any and all members of the class. I say to my kindergarten students “you are a community and as community you need to be responsible of your behavior and help other friends who need support”. I have a chart to collect points that the whole class receive when they follow the rules as a group, so within the group they need to help each other to follow the rules and change their behavior to avoid losing points as a class. Similarly to the group contingency, a teacher can use home contingency to involve parents. Home contingency involves meeting with parents with the purpose to agree on a specific course of action to improve negative behaviors that are to be stopped in class and the specific positive behaviors that are to be exhibited.

When a situation with the student is out of control, this situation is referred as high-intensity situations. Teachers should be able to contact the principal or assistant principal for help, but teachers need to be prepared to take some actions. The first step is to recognize that the student is so upset that he/she is probably out of control. Then the teacher should step back and calm down. After that, listen to the student and plan the next actions. When the student clams down, the teacher can communicates a simple request intended at diffusing the situation, a good idea is to go outside the classroom to talk.

Finally, the teacher should find an overall plan for improving disciplinary behavior. The information collected from the student about her/his behavior should be used to build the plan. The teacher could determine that the student needs more support and start a RTI (Response to Intervention) to build a collaborative plan of intervention.

Resource: Marzano, Robert J. The art and science of teaching: a comprehensive framework for effective instruction. Association for Supervision and Curriculum Development. Alexandria, Virginia USA. 2007

Examples of High Performance Expectations for Students

A lesson to learn about energy and motion to construct roller coaster by the 5^th grade teacher Donna Migdol. https://www.teachingchannel.org/videos/teaching-stem-strategies

In this video, the teacher sets high performance expectations, so the students respond to this by working with high standards and giving their best effort to achieve quality work.

First, high standards are including in the lesson. Students are learning about energy and motion and they transfer this knowledge to build a model of a roller coaster. The content is challenging them and they are applying this knowledge in a practical experiment.

Students are motivated to be problem solvers. They are giving their best and working hard to find solutions. They work collaboratively to create the roller coaster; they are part of the trial, error and solution. Students are in task individually and in groups, each student has a specific role and responsibility.

Also, students are involved in the whole process of the lesson, but most important is that they are working to produce a quality work. They working in draft of your work, also they use computers to check your ideas and made modifications, they made test to improve their models. Also they work collaboratively and share your opinions.

In this video, we can observe a Math class in Chinese (probably in and bilingual school). The students in this class are participating actively in math problems echoing the song that the teacher is singing. I think that the level of the academic content is challenging the students, it is promoting high expectations for students.

Complementary, the article about math curriculum in China emphasized in the rigor established by parents and teachers to have high expectations from early on. The goal of Math education in China is to develop conceptual and procedural knowledge through rigid practice. They have many time dedicated to math, around 15 hours per week in and out the classroom.

The last video is about Whole Brain Teaching methodology in the classroom. In this video the students are participating in different routines that are clear and involve the whole class. The method used to communicate and guide the students is very interactive and require the participation of the students, also use different forms of communication like body language, songs and visuals. "Whole Brain Teaching" is a great example of how the routines and motivation of students helps to reach high expectations.

Reflections on the videos and how to Implement in kindergarten.

As a Kindergarten teacher, I think that three elements are important to promote high expectations for students. The first element is stablish clear routines, norms and consequence in the classroom. Kindergarten students needs more support to learn the adequate behaviors in the classroom and they are learning to follow procedure like routines and norms. The behavior affects the learning process, for this reason we need an adequate behavior to produce a quality learning environment with high expectations for students. The second element is provide a content that challenge all students. Teachers needs to include the common core standards for the different areas of knowledge and differentiate this for the needs of the students. If each students fells challenging for the content, students are more involve and the learn more. Finally, the last element is promote quality work in the class. Teachers can show examples of how quality work looks like and promote perseverance of students to reach their best. A quality work always is accompanied by an effective system of formative assignments that include rubrics, peer review, teacher feedback, etc. 

Build a Positive Climate in the Classroom

Creating a positive climate in your classroom will allow your students to feel comfortable, safe and engaged. This climate give the students a special environment to learn.

Positive climate is a combination of classroom culture and teacher leadership. The classroom culture include many factors like teacher-student interactions, class room structure, Social and Emotional Safety, positive behavior management techniques and community building. Also, teachers play an important role to build a positive climate. Teachers bring cultural understanding and self-awareness to the classroom and they are a social justice leader. Being a teacher leader in positive climate means embracing the opportunity for ongoing reflection and growth.

As Robert Marzano specified in his book The Art and Science of Teaching “Arguably the quality of the relationships teachers have with students is the keystone of effective management and perhaps even the entirety of teaching.” (Marzano, 2007) the relationship teacher-student is fundamental to create a positive climate in the classroom. Know your students, build a sense of community and use a positive teacher language among others are the keystone in this purpose. To know more about teacher-student interaction, we recommend see the presentation about this topic in the following link: http://prezi.com/_dut7uxolfrn/?utm_campaign=share&utm_medium=copy

In a positive climate of learning the structure of the classroom is student centered. Classrooms reflect the multicultural backgrounds of students and showcase the diversity of our society. For instance, some walls could show pictures of students or short phrases in different languages that students speak. The norms and expectations are clear, just as the students are encourage to participate. Also, in the class student and teachers use gender sing gender-neutral practices. A positive classrooms environment represent the diversity, the positives relationships, promote communication and dialogue between teachers and students.

Social-emotional learning, respect and safety are as important as literacy and critical thinking skills in positive learning environment. Students need to feel both physically and emotionally safe to learn. Teachers should include in the curriculum teaching of social-emotional skills, bullying prevention and community building. In a positive climate in the classroom, students understand and appreciate differences, also they know different forms to solve problems and conflicts with others.

Discipline and behavior management are central to positive classroom culture. Behavior management practices should support safe and build community. The discipline problems could use as an opportunity of growth. A positive behavior management reflect fairness, equity and cultural awareness.

Teachers are the role model to build a positive climate in the classroom. They need to develop skills and attitudes to build bridges between cultures, promoting empathy, flexibility, listening without judgment, appreciation for multiple perspectives and cross-cultural communication. Culturally aware teachers model how we can build a positive climate.   

Teachers can be social justice leaders modeling proactive responses to bias, discrimination, exclusion and bullying. They can sends the message that student safety is a priority and we need to speaking up and responding. For example, teachers can share live experiences that help students to learn their active role to build a positive environment of learning.

Building a positive climate in the classroom requires reflection and steady growth by teachers. Teachers can continue learning strategies participating in professional development activities, joining groups of study or research. Also, evaluate and follow up the strategies implemented in the classroom by teachers is a great opportunity to learn a build more effective responses. Teachers can create alliances that support new strategies, for example with NGO or governmental entities.

In conclusion, build a positive climate in the classroom require an action in the classroom and a commitment of teachers to ensure a comfortable, safe and engaged environment to learn.

By Jaime Solano Cardoso

Special Education Referral

This post includes an interview about the RTI process and a reflection about it.

Interview to School Psychologist of Oyster Adams Bilingual School Primary Campus about the special education referral. http://oysteradamsbilingual.org/ 

• How is a student identified for special education referral (Response to intervention-RTI)?

 All educators in the school and parents can refer a student to start a Response to Intervention-RTI process. Then, the team of educators (problem solving team) looks at the data of the student who has been identified as struggling via the screening process, and finds the gaps between current performance and expected performance. The team discusses why this gap occurring.

• Who takes responsibility for the progress of the child before and after the referral?

RTI is not a “program” or “service” outside of the general education classroom. Rather RTI requires all educators in the school (teachers, special educators, counselors, social workers, administrators, coaches, etc.) to provide students with what they need to make progress.

• What is the school administration's directive for special education?

RTI is an approach to instruction that clearly identifies the specific need of all students and develops different levels of interventions to meet these need. At Oyster Adams, level 2 + 3 of RTI are sometimes referred to the TAG program (Targeted Academic Growth). TAG is managed by me (school psychologist, TAG lead and administrators, who in turn, work closely with TAG and classroom teachers.

Once the cause of the problem has been identified by the problem solving team, the team selects one or two measurable objectives that are likely to close the gap. Base on the objectives, the team need to decide what intervention will be provided, how often, who will provide the intervention, where will be provided, and how will it be determined if the students is responding to the intervention. During the intervention/s TAG and classroom teacher will be careful to monitor student response to intervention.

A student who was flagged by universal screening could continue in Tier 1, with some modifications to differentiate instruction, or move to Tier 2. The goal of Tier 2 intervention is to remediate academic skill deficits with the idea that, in doing so, students will be successful in the Tier 1 program without support. If the students not respond Tier 2 intervention, he may need more intense support and move to Tier 3. Likewise, students who have received Tier 3 intervention respond well and be moved to Tier 2 or Tier 1. The movement across tiers is fluid and should always be made throughout the decision-making process.

• What is the level of parent involvement in referral process and special education?

Parents are involved during the whole process; they always receive the information of the process. Sometimes, the team provide activities for the parents to work in home.

Interviewed by Jaime Solano

Reflection:

After the interview I was able to understand that the process of RTI support the teachers with specific students. A group of specialist in the school help the teacher to find the best way to help the student. Sometimes, we as teachers have limited vision of our students and it is difficult to find new approaches to support students with needs, therefore the groups of persons involved in the RTI process provide a new perspective that present more possibilities.

During the whole process of RTI, the data and follow up is very important. All records of the students play and important role in the decisions because the data shows the needs. Also, the data is needed in the whole process, in the beginning to identify the problem and then to monitor the progress.

The participation of the parents in the whole process is crucial. The parents have to be informed about the child and the interventions planed. The parents can take an active role in the process and support the team to find solutions and implement the plan, parents can continue working with the child at home and support him/her during the process.

Finally, I would like to said that the RTI process might seem difficult and complicated, but it is very useful for students and teachers. This process probably needs a commitment by the teacher, but this will help the students.

How is addressing the national and international organizations the topic of teachers?

Infographic from Global Partnership for Education

Teachers is one of the most important topics in education. The governments, the organizations national and internationals, the NGOs and institutions always include this topic in their agendas. This topic is relevant by the important role that teachers have in the goal of quality education.

I would like to start this post by quoting the challenges that mention the Global Partnership for Education:

• The world will need to recruit 25.8 million school teachers to provide every child with a primary education by 2030. This total includes the creation of 3.2 million new posts and the replacement of 22.6 million teachers expected to leave the profession. (UIS Factsheet 2015)

• In low-income countries, there is an average of 43 students per teacher (EFA GMR 2013/14, Table 10 p. 391). This means that in many schools, teachers have much larger class sizes, making their job much more difficult.

• In one-third of all countries, less than 75% of teachers were trained according to national standards (UIS)

• Countries with more female primary teachers are more likely to have higher enrollment rates for girls in secondary schools. Unfortunately, in some countries, less than 25% of primary teachers are female. (UNESCO eAtlas of Teachers)

• It is difficult to recruit and retain teachers in remote rural areas and in conflict-affected areas, where the majority of out-of-school children are.

• Highlight existing state and district systems that are working to support teacher leadership;

• Share resources to create new opportunities for teacher leadership; and

• Encourage people at all levels to commit to expanding teacher leadership.

Taking in count these challenges, the national and international organization address this topic in different ways. In the next lines I share the perspectives of some organizations.

International:

UNESCO in its Education Strategy 2014 – 2021 explain the three key priorities in this topic. The first priority is to address the challenge of teacher shortages by strengthening national institutional capacities to increase the supply of qualified teachers at country level. The second priority is to contribute to improvement in teaching quality. The third priority will be to inform the global debate about teaching with comparative evidence.

The Organization for Economic Co-operation and Development (OECD) is working to provide valid, timely and comparable information to help countries review and define policies for developing a high-quality teaching profession.

Global Partnership for Education are focus in Improve teacher effectiveness by training, recruiting and retaining teachers and supporting them to provide a good quality education.

Inter-American Development Bank supports the education systems of the Latin American region to attract, develop, motivate, and retain the best professionals into the teaching profession. It also fosters initiatives that strengthen the principals’ roles and instructional support structures.

The World Bank in its Education Sector Strategy 2020: Learning for All has a comprehensive staff learning program will support education staff to strengthen their capacity to implement the new education strategy and develop cutting-edge knowledge and skills in technical and operational topics in order to deliver high quality advice and services to country partners.

National:

U.S. Department of Education has the initiative TEACH TO LEAD to advance student outcomes by expanding opportunities for teacher leadership, particularly those that allow teachers to stay in the classroom.

This initiative seeks to:

The Council of Chief State School Officers  (CCSSO) have an initiative focuses on what are arguably the most important factors in student achievement-effective teachers and leaders. CCSSO is calling for states to change the rules, encourage innovation, learn from other sectors, and apply new principles to transform these professions.

The National Education Association mission is to advocate for education professionals and to unite their members and the nation to fulfill the promise of public education to prepare every student to succeed in a diverse and interdependent world. They believe individuals are strengthened when they work together for the common good. They work in improve the professional status and the quality of public education when they unite and advocate collectively.

By Jaime Solano Cardoso