onMoveEx.jsx

// ... imports and stylesheet

export default class Events extends React.Component {
  constructor() {
    super()

    this.state = { count: 0 }
  }

  render() {
    return (
      <View 
        onMove={() => this.setState({ count: this.state.count + 1 })}
        style={styles.view}
      >
        <Text>
          {this.state.count}
        </Text>
      </View>
    );
  }
};

AppRegistry.registerComponent('Events', () => Events);