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All teachers make mistakes, after all, and Khan should not, the reasoning goes, be called out for making the same mistakes we all make.

There certainly are broken models in education, but there is absolutely no evidence that competent knowledge of student learning and thinking is one that teachers can afford to jettison.

researchers are finding evidence that particular kinds of PCK are associated with greater gains in student learning in elementary mathematics.

revolutionize

The equal sign (=) i

content knowledge alone is inadequate

The standard American curricular treatment, in which students are instructed to append zeroes to the shorter decimal to equalize the number of digits helps students to perform this task correctly, but fosters its own misconceptions.

he exercises offer no intellectual rigor and do not address our central concern.

PCK knows from both educational research and professional experience

If Khan’s videos occasionally popped up in a Google search, we would be content to have him carry on. There is lots of worse information available on the web. But Khan is hailed as “unbelievable” ( Bill Gates) and his work as “sparking a revolution in education

discuss the meaning of the equal sign frequently and explicitly, and (2) model correct use of the equal sign.

Khan will put the video out there and see how people react to it.

Newsweek

here are a few other online tools helping to reshape education.

“Math is the killer,” Gates told me recently. His foundation had researched unemployment and found math to be a significant stumbling block. “If you ask people, ‘Hey, there are these open nursing jobs, why don’t you go and get one?’ math is often the reason they give for not applying,” Gates says. “‘Why didn’t you pass the police exam?’ Math.”

ligious Knowledge and Deep Understanding The Creeds of the apostolic and ancient Churches, including the Apostles Creed and Nicene Creed, expressed the Christian understanding of God. Through the Creeds, Christians are linked with the faith of believers throughout history.

Religious Knowledge and Deep Understanding The Catholic Church in Australia comprises a number of geographical dioceses and archdioceses. There are a variety of roles and responsibilities within the leadership structure of the Catholic Church in Australia (i.e. deacon, priest, bishop, archbishop, cardinal). The Church in Australia is a member of a larger communion of churches in the Oceania region. Within the Australian Catholic Church, as well as across Oceania, local and regional churches are influenced by their different cultures and histories.

Religious Knowledge and Deep Understanding The writings and key messages of significant reformers (c.650CE-c.1750CE), such as Catherine of Siena, Clare of Assisi and Thomas Aquinas, challenged the Church to question its nature and role in the world.

Religious Knowledge and Deep Understanding Concern for the good of the community is a basic principle of Christian morality. According to Church teaching, personal gifts are meant to be at the service of others and of the common good. The good of the community can be protected and promoted in a variety of ways.

Religious Knowledge and Deep Understanding Prayer in the Christian tradition, including formal prayers such as Sign of the Cross, Our Father and Hail Mary, nurtures the spiritual life of believers.

eligious Knowledge and Deep Understanding Meditative prayer uses silence and stillness to assist believers to listen and talk to God. Believers use a range of practices (including silence and stillness, and praying with icons and images) for preparing the body and the mind for meditative prayer, and engaging in the ‘work of meditation’. Christian iconography expresses in images the same Gospel message that Scripture communicates by words. Praying with scripture is a form of meditative prayer in the Christian tradition. There are a variety of ways to pray with scripture, including Lectio Divina (Benedictine tradition) and Ignatian Meditation.

Religious Knowledge and Deep Understanding The beliefs, values and practices of early Church communities (c.6 BCE - c. 650 CE) were influenced by ancient Mediterranean societies such as Greece, Rome and Egypt. Recurring broad patterns of historical change (namely Construction: Searching for Unity, Order and Authenticity; Deconstruction: Challenges to Unity, Order and Authenticity; Reconstruction: Restoring unity, order and authenticity) are evident in the story of the early Church as it came to understand its nature and role in the world.

ayer in the Christian tradition, including the ancient monastic prayer of The Liturgy of the Hours, nurtures the spiritual life of believers. The Liturgy of the Hours follows a prescribed pattern of Psalms, Scripture and intercessions, and is prayed at set times throughout the day. Believers pray on behalf of others and with others.

Religious Knowledge and Deep Understanding All Christians are united through their baptism (Galatians 3.27-29) in the name of Jesus Christ and receive the gift of the Holy Spirit (Acts 2:38). The term ‘ecumenism’ (from the Greek Oikoumene meaning ‘of the whole inhabited earth’) refers to the movement which seeks to bring about the unity of all Christians. All Christians are called to give witness to the ecumenical spirit through pray

eligious Knowledge and Deep Understanding In a time of great challenge and change (c.650 CE-c.1750CE), the Church had to respond to many internal and external threats to its physical existence, cultural influence, political control, social structure, roles and relationships and economic power. Recurring broad patterns of historical change (namely Construction: Searching for Unity, Order and Authenticity; Deconstruction: Challenges to Unity, Order and Authenticity; Reconstruction: Restoring unity, order and authenticity) are evident in the story of the Church in a time of challenge and change (c.650CE-c.1750CE) as it was forced to question its nature and role in the world.

Religious Knowledge and Deep Understanding Grace is the gift of God that enables people to overcome sin; to love, believe and hope in God and grow in goodness. The Church names this work of grace ‘justification’. Virtues are attitudes and dispositions that guide people to ‘do good and avoid evil’. In Christian teaching, the cardinal (pivotal) virtues are prudence, justice, fortitude and temperance. Living a virtuous life - ‘doing good’ - requires knowledge and understanding, practice and perseverance.

sisted by the Holy Spirit, the Church draws on the teaching of Jesus and its living Tradition to respond to emerging moral questions. Catholic social teaching proposes principles for reflection, provides criteria for judgment and gives guidelines for action. A consistent theme in Catholic social teaching is that the good of people be the criterion in making moral judgments about social and economic structures.

isten and talk to God. Believers use a range of practices (including centred breathing and attending to posture) for preparing the body and the mind for meditative prayer and for engaging in the ‘work of meditation’. Praying with scripture is a form of meditative prayer in the Christian tradition. There are a variety of ways to pray with scripture, including Augustinian Prayer and Franciscan Contemplative prayer. All forms of vocal and meditative prayer are intended to lead believers to contemplation. Contemplative prayer is the simple awareness of the presence of God. It is pray

eligious Knowledge and Deep Understanding Christians believe that the nature of God is revealed in the Old Testament. The divine name, “I Am Who Am”, is understood in the sense that God is the fullness of being, every perfection, without origin and without end. Christian tradition expresses the riches of the divine name in a variety of terms such as goodness, abounding i

r sources combined to form the Pentateuch. They are: the Priestly source (P), Deuteronomist (D), the Elohist (E), and the Jahwist (J). Key themes of the Pentateuch include: creation, sin, covenant, law and promise, worship, and Chosen Peopl

eligious Knowledge and Deep Understanding The inspired writings of various religious and lay leaders (e.g. Catherine McAuley, Nano Nagle, Edmund Rice, Don Bosco, Elizabeth Seton and Mary MacKillop) responded in new ways to the needs of the faithful, especially through education, works of charity, and health care (c.1750CE-c.1918CE).

In a time of great challenge and change (c.1750 CE - c.1918 CE), the Church had to respond to many internal and external threats to its physical existence, cultural influence, political influence, social structure, roles and relationships and economic power. Recurring broad patterns of historical change (namely Construction: Searching for Unity, Order and Authenticity; Deconstruction: Challenges to Unity, Order and Authenticity; Reconstruction: Restoring unity, order and authenticity) are evident in the story of the Church in a time of challenge and change (c.1750 CE - c.1918 CE) as it was forced to question its nature and role in the world.

Respect for each person, as created in the image of God and as a reflection of God, is expressed through moral behaviour towards oneself and others. Two key principles of Catholic social teaching, namely respect for the dignity of the human person and human rights and responsibilities, provide guidelines for developing a healthy understanding of one’s personal identity and of human relationships.

Assisted by the Holy Spirit, the Church draws on the teaching of Jesus and its living tradition to respond to emerging moral questions about scientific and technological advances. Catholic social teaching proposes principles for reflection, provides criteria for judgment and gives guidelines for action. The principles of Catholic social teaching, especially promotion of peace, stewardship, and common good, provide guidelines for scientific and technological advancement.

personal journals, poetry, books, pastoral statements, conciliar documents), search for the mystery of God in the midst of world events and the course of human history (c.1918CE to the present), such as war and peace, genocide and reconciliation, globalisation and community, consumerism and sufficiency, relativism and morality, development and ecology.

hristians believe God’s unending love and mercy for humanity were revealed to the people of Israel and expressed fully through the person of Jesus.

he Eucharist draws on historical and scriptural foundations, including Last Supper (1 Corinthians 11:23-28) and sacrifice. The Eucharist recalls Jesus’ example of service and love (John 13:1-20), and those who share the Eucharist are sent out to carry on Jesus’ mission in the world. The Eucharist is a means of reconciliation and forgiveness of sins as expressed through prayers and actions in the Mass (e.g. penitential rite, eucharistic prayer and prayers before communion, sign of peace). Eucharist is the primary and indispensable source of nourishment for the spiritual life of believers.

In a time of great challenge and change (c.1918 CE to the present), the Church had to respond philosophically and theologically to unprecedented threats to both human ecology and environmental ecology from science, technology, materialism, consumerism and political ideologies. The Church’s philosophical and theological responses involved rethinking and reforming its cultural influence, political influence, social structure, roles and relationships, economic power and evangelising mission. Recurring broad patterns of historical change (namely: Construction: Searching for Unity, Order and Authenticity; Deconstruction: Challenges to Unity, Order and Authenticity; Reconstruction: Restoring unity, order and authenticity) are evident in the story of the Church in a time of challenge and change (c. 1918 CE to the present) as it was forced to question its nature and role in the world.

is obliged to follow their conscience which requires careful and lifelong formation. Conscience formation for Christians entails not only consideration of facts, but is guided by prayer and reflection on the Word of God, the life and teaching of Christ, the witness and advice of others, and the authoritative teaching of the Church.

bout economic structures and development. Catholic social teaching proposes principles for reflection, provides criteria for judgment and gives guidelines for action. The principles of Catholic social teaching, especially participation, economic justice, global solidarity and development, preferential option for the poor, stewardship, and subsidiarity, provide guidelines for just economic order and development. Christians believe that human work shares in God’s creative activity. Work enables each person to use

The Prayer of St Francis, The Canticle of Creation and The Magnificat. The Prayer of St Francis is a prayer for peace. In a world often troubled by war and violence, it calls us to be instruments of Christ’s peace and love. The Magnificat (Luke 1:46-55) is Mary’s song of hope in God’s salvation and justice for all. The Canticle of Creation is a prayer of praise for the creator God.

ive prayer uses silence and stillness to assist believers to listen and talk to God. Believers use a range of practices (including praying with the help of nature) for preparing the body and the mind for meditative prayer, and for engaging in the ‘work of meditation’. Lectio of Nature is a form of meditative prayer in the Christian tradition. All forms of vocal and meditative prayer are intended to lead believers to contemplation. Contemplative Prayer is the simple awareness of the presence of God. It is prayer without words or images. Centering Prayer provides a way of enriching and nurturing the spiritual life of believers.

emporary Christian spiritual writings reflect the signs of the times in the light of the Gospel, and use a variety of mediums and modes of communication to reveal the mystery of God and of life.

eligious Knowledge and Deep Understanding Christians believe that the mission of Jesus is continued in the world and in the Church through the activity of the Holy Spirit.

major Christian traditions, some rituals are prepared according to formal principles and rubrics. These rituals are referred to as liturgy. Liturgical adaptation is provided for in

istian moral teaching provides guidelines and limits regarding ethical and moral responses to global issues and challenges, such as justice, tolerance, reconciliation, peace, ecology, nonviolence, respect and appreciation for others.

eligious Knowledge and Deep Understanding Prayer in the Christian tradition nurtures the spiritual life of believers. Vocal prayer, meditative prayer and contemplative prayer are ancient examples of thi

Select and use appropriate equipment, including digital technologies, to systematically and accurately collect and record data (ACSIS200)